WEBVTT 00:00:00.050 --> 00:00:02.500 The following content is provided under a Creative 00:00:02.500 --> 00:00:04.019 Commons license. 00:00:04.019 --> 00:00:06.360 Your support will help MIT OpenCourseWare 00:00:06.360 --> 00:00:10.730 continue to offer high quality educational resources for free. 00:00:10.730 --> 00:00:13.340 To make a donation or view additional materials 00:00:13.340 --> 00:00:17.225 from hundreds of MIT courses, visit MIT OpenCourseWare 00:00:17.225 --> 00:00:17.850 at ocw.mit.edu. 00:00:21.790 --> 00:00:23.350 MARK SEIFTER: Hi, everyone. 00:00:23.350 --> 00:00:26.510 A few of you may know me from my tutorial, 00:00:26.510 --> 00:00:30.250 but if you don't I'm Mark Seifter I'm the senior TA here 00:00:30.250 --> 00:00:34.370 at 6034 and these Friday omega recitations are going 00:00:34.370 --> 00:00:36.606 to be a little bit different than any 00:00:36.606 --> 00:00:37.980 of the other things in the class. 00:00:37.980 --> 00:00:41.990 All right, so, what is omega recitation. 00:00:41.990 --> 00:00:45.630 Omega recitation is in this lecture style room, 00:00:45.630 --> 00:00:48.230 but I hope to make it more like a recitation or a tutorial 00:00:48.230 --> 00:00:50.310 by, unfortunately for some of you, 00:00:50.310 --> 00:00:54.740 perhaps, calling on you guys to participate during the omega 00:00:54.740 --> 00:00:58.110 recitation, as we attempt to work with some of the material 00:00:58.110 --> 00:01:00.930 that Patrick has given us the big picture 00:01:00.930 --> 00:01:01.970 for in the lectures. 00:01:01.970 --> 00:01:03.700 And if you've gone to recitation so far 00:01:03.700 --> 00:01:06.400 you may received a little bit of enrichment 00:01:06.400 --> 00:01:08.230 into how the algorithms work. 00:01:08.230 --> 00:01:10.130 Well, here in omega recitation we're 00:01:10.130 --> 00:01:13.810 going to figure out how you can work the algorithms. 00:01:13.810 --> 00:01:18.070 And that's very important, because in this class being 00:01:18.070 --> 00:01:23.120 able to work the algorithms by hand in some of these examples 00:01:23.120 --> 00:01:25.430 I put up here, or like Patrick sometimes 00:01:25.430 --> 00:01:27.950 does in lectures to teach you the algorithms, 00:01:27.950 --> 00:01:29.500 is a crucial way of demonstrating 00:01:29.500 --> 00:01:33.590 that you understand how the algorithms work, and we use it 00:01:33.590 --> 00:01:34.880 on a quiz. 00:01:34.880 --> 00:01:37.690 The way we use it on the quiz is we-- well 00:01:37.690 --> 00:01:39.110 this is an old quiz problem. 00:01:39.110 --> 00:01:40.040 It's from last year. 00:01:40.040 --> 00:01:41.480 It tripped up a lot of people. 00:01:41.480 --> 00:01:43.490 So we're going to go over it today. 00:01:43.490 --> 00:01:47.120 I'm going to tell you all the tricks that tripped up 00:01:47.120 --> 00:01:49.820 a lot of people, in addition to emphasizing tricks 00:01:49.820 --> 00:01:53.720 that I've picked up over of the three years of TA-ing 00:01:53.720 --> 00:01:56.650 this course before, so that you will not fall prey 00:01:56.650 --> 00:01:58.600 to any of these tricks. 00:01:58.600 --> 00:01:59.520 Hopefully. 00:01:59.520 --> 00:02:01.900 I say hopefully, because some of these tricks 00:02:01.900 --> 00:02:05.029 I talked about omega recitation last year 00:02:05.029 --> 00:02:06.570 and people still got tricked by them. 00:02:06.570 --> 00:02:09.100 I guess maybe some people didn't come to omega recitation 00:02:09.100 --> 00:02:11.820 or they were just very tricky tricks. 00:02:11.820 --> 00:02:14.040 So be sure to come to omega recitation. 00:02:16.944 --> 00:02:18.110 Pay attention to the tricks. 00:02:18.110 --> 00:02:20.130 Pay attention to how these things are solved. 00:02:20.130 --> 00:02:23.220 Ask questions if you're not sure. 00:02:23.220 --> 00:02:25.010 And when we get done with the hour 00:02:25.010 --> 00:02:27.350 together I'm hoping that everyone's 00:02:27.350 --> 00:02:31.820 going to do really well on the rules part of the first quiz. 00:02:31.820 --> 00:02:35.510 So without further ado, if there are 00:02:35.510 --> 00:02:38.730 no questions on that, which I don't think there probably 00:02:38.730 --> 00:02:42.260 will be, let's move on to the problem at hand. 00:02:42.260 --> 00:02:43.980 As some of you may have noticed, it 00:02:43.980 --> 00:02:45.520 is a Harry Potter based problem. 00:02:45.520 --> 00:02:49.430 One of our TAs last year was a big Harry Potter fan. 00:02:49.430 --> 00:02:53.290 So what we have here a series of rules 00:02:53.290 --> 00:02:55.740 and a series of assertions. 00:02:55.740 --> 00:02:59.850 Now if you happen to be real go getter and have already looked 00:02:59.850 --> 00:03:01.610 at all the past quizzes online, you 00:03:01.610 --> 00:03:03.640 may have already seen this problem. 00:03:03.640 --> 00:03:06.310 And if you really, really have attention to detail 00:03:06.310 --> 00:03:08.740 you may notice something a little bit different in the way 00:03:08.740 --> 00:03:11.700 I wrote it as compared to the way it was written online. 00:03:11.700 --> 00:03:15.140 In fact, you may, if you have a lot of times a detail, 00:03:15.140 --> 00:03:17.710 but you're not really in on Scheme or LISP, 00:03:17.710 --> 00:03:21.680 you may think the way I wrote it is much easier to understand. 00:03:21.680 --> 00:03:24.260 And in case you can't understand the other way, 00:03:24.260 --> 00:03:26.440 and in case one of the TAs decides 00:03:26.440 --> 00:03:29.900 to write it in a LISP-like way again, let me explain. 00:03:29.900 --> 00:03:34.270 If you look at one of my rules, say if x is ambitious, 00:03:34.270 --> 00:03:36.880 and x is a squib, then x has a bad term. 00:03:36.880 --> 00:03:40.530 That's rule 0 up at the top. 00:03:40.530 --> 00:03:44.270 That's written in sort of what we call in fixed notation. 00:03:44.270 --> 00:03:45.610 It's easy, it's simple. 00:03:45.610 --> 00:03:48.160 All operators are in the order you would expect. 00:03:48.160 --> 00:03:50.950 2 plus 3 equals 5. 00:03:50.950 --> 00:03:53.220 There's another kind of notation that is sometimes 00:03:53.220 --> 00:03:54.630 used on previous quizzes. 00:03:54.630 --> 00:03:57.720 And by sometimes, good number of times, actually. 00:03:57.720 --> 00:04:00.420 I'm not sure why we still use it that way, because of the fact 00:04:00.420 --> 00:04:03.810 that the class has move on to Python, but we do, sometimes. 00:04:03.810 --> 00:04:05.480 And that's called prefix notation. 00:04:05.480 --> 00:04:08.510 In prefix notation, the operator comes first. 00:04:08.510 --> 00:04:13.580 So for instance, plus 2 3 equals 5. 00:04:13.580 --> 00:04:14.547 The plus comes first. 00:04:14.547 --> 00:04:15.880 The function, then, comes first. 00:04:15.880 --> 00:04:18.050 In this case, the function is plus. 00:04:18.050 --> 00:04:20.680 So if we were writing this in prefix notation, in fact, 00:04:20.680 --> 00:04:26.150 the way I received it, when it said, "if and x is ambitious, 00:04:26.150 --> 00:04:28.760 x is a squib, then x has a bad term. 00:04:28.760 --> 00:04:31.620 The and went first and there's a parentheses 00:04:31.620 --> 00:04:35.144 which included everything that was scoped under the and. 00:04:35.144 --> 00:04:37.310 Does anyone have any questions about prefix notation 00:04:37.310 --> 00:04:39.640 in case it comes up? 00:04:39.640 --> 00:04:43.160 Just remember, if things start being written 00:04:43.160 --> 00:04:45.270 in a really weird way with lots and lots 00:04:45.270 --> 00:04:47.740 and lots of parentheses, whatever's 00:04:47.740 --> 00:04:50.705 outside the parentheses, whether it be "plus" or "and" 00:04:50.705 --> 00:04:55.192 or "or" is an operator that acts on the things that are inside. 00:04:55.192 --> 00:04:57.150 However, we're not going to deal with that now, 00:04:57.150 --> 00:05:00.050 because I think the most important thing is 00:05:00.050 --> 00:05:02.930 to understand is the rules, and the less important thing 00:05:02.930 --> 00:05:05.030 is to understand prefix notation. 00:05:05.030 --> 00:05:07.100 And you can do a problem at home that's 00:05:07.100 --> 00:05:10.570 written in prefix notation to test yourself on that. 00:05:10.570 --> 00:05:13.270 So what rules do we have here. 00:05:13.270 --> 00:05:15.510 We've got equals 0 through 5. 00:05:15.510 --> 00:05:18.720 For some reason they are labeled with P's. 00:05:18.720 --> 00:05:21.420 They are often labeled with either P's or R's. 00:05:21.420 --> 00:05:24.930 The secret on why they are labelled with P's is that one 00:05:24.930 --> 00:05:28.062 year somebody labeled them with P's for like "proposition" 00:05:28.062 --> 00:05:29.020 or something like that. 00:05:29.020 --> 00:05:32.410 And then other TAs looked at that test and sometimes also 00:05:32.410 --> 00:05:36.320 labeled it with P's and it sort of down the line continued 00:05:36.320 --> 00:05:40.050 to be labeled with P's, and sometimes with R's. 00:05:40.050 --> 00:05:42.500 So these P's are these six rules. 00:05:42.500 --> 00:05:46.820 The first rule is if x is ambitious, and x is a squib, 00:05:46.820 --> 00:05:49.090 then x has a bad term. 00:05:49.090 --> 00:05:51.860 So what's the deal with these question mark x's? 00:05:51.860 --> 00:05:55.800 The question mark before an x, or perhaps a y down here, 00:05:55.800 --> 00:05:59.340 indicate that there's a variable waiting to be bound. 00:05:59.340 --> 00:06:01.920 We're not assuming there's a Harry Potter character named 00:06:01.920 --> 00:06:05.130 x, and only if that question mark x, the mystery character, 00:06:05.130 --> 00:06:09.220 only if mystery x character is ambitious can that person 00:06:09.220 --> 00:06:10.710 possibly have a bad term. 00:06:10.710 --> 00:06:13.470 What we're seeing is any character in the Harry Potter 00:06:13.470 --> 00:06:15.240 universe, or not the Harry Potter 00:06:15.240 --> 00:06:20.520 universe, maybe a rhinoceros, can fit into that x. 00:06:20.520 --> 00:06:22.850 So for instance, if a rhinoceros is ambitious, 00:06:22.850 --> 00:06:26.920 and a rhinoceros is a squib, then a rhinoceros has bad term. 00:06:26.920 --> 00:06:31.250 That rule saying, for any x this is true. 00:06:31.250 --> 00:06:33.950 And it's very important how we treat the question mark 00:06:33.950 --> 00:06:37.620 x, and how we bind question mark x, 00:06:37.620 --> 00:06:40.540 when we do both back chaining and forward chaining. 00:06:40.540 --> 00:06:44.820 I'll get back to that, because some people made some very, 00:06:44.820 --> 00:06:48.720 very small mistakes that really messed up 00:06:48.720 --> 00:06:51.130 a lot of their forward and backward chaining last year. 00:06:51.130 --> 00:06:52.296 It was actually very tricky. 00:06:52.296 --> 00:06:56.240 Jeremy, the TA who wrote this was very clever, 00:06:56.240 --> 00:06:59.500 and it makes it really great case study for you guys. 00:06:59.500 --> 00:07:03.125 All right, so Rule 1, if x lives in Gryffindor tower 00:07:03.125 --> 00:07:05.140 then x is a protagonist. 00:07:05.140 --> 00:07:06.750 By the way, for conciseness I'm going 00:07:06.750 --> 00:07:09.390 to be using GT for Gryffindor tower 00:07:09.390 --> 00:07:11.530 when I write these in later on, and I'll 00:07:11.530 --> 00:07:13.920 use SD for Slytherin dungeon. 00:07:13.920 --> 00:07:17.460 Speaking of which, Rule 2, if x lives in Slytherin dungeon, 00:07:17.460 --> 00:07:21.960 then x is a villain, x is ambitious. 00:07:21.960 --> 00:07:24.040 Why there are two things here? 00:07:24.040 --> 00:07:27.570 Well, after the "if" we have what we call antecedent, 00:07:27.570 --> 00:07:30.580 that's something that needs to be true in order for this rule 00:07:30.580 --> 00:07:32.030 to match. 00:07:32.030 --> 00:07:35.600 After the "then" we have what is called the consequent, 00:07:35.600 --> 00:07:37.509 and in this case there are two consequents. 00:07:37.509 --> 00:07:39.050 Anyone who lives in Slytherin dungeon 00:07:39.050 --> 00:07:42.440 is automatically a villain and also ambitious. 00:07:42.440 --> 00:07:45.330 So you can think of there being sort of an "and 00:07:45.330 --> 00:07:49.730 therefore" for the purposes of both of those assertions 00:07:49.730 --> 00:07:52.520 would be added to the knowledge base. 00:07:52.520 --> 00:07:56.320 Rule 3, if x is the protagonist or x is a villain, 00:07:56.320 --> 00:08:02.730 and x is ambitious, then x studies a lot. 00:08:02.730 --> 00:08:09.440 By the way, the scope for this, just to be sure 00:08:09.440 --> 00:08:14.610 that we're clear, is this. 00:08:14.610 --> 00:08:18.470 So we need them to be a protagonist 00:08:18.470 --> 00:08:22.930 or villain and no matter what they have to be ambitious. 00:08:22.930 --> 00:08:26.460 Rule 4, if x studies a lot, and x is a protagonist, 00:08:26.460 --> 00:08:28.540 x becomes Hermione's friend. 00:08:28.540 --> 00:08:33.950 And Rule 5, if x snogs y, and x lives in Gryffindor tower and y 00:08:33.950 --> 00:08:38.130 lives in Slytherin dungeon, then x has a bad term. 00:08:38.130 --> 00:08:39.760 So those are our six rules that we 00:08:39.760 --> 00:08:42.330 can use to understand Jeremy's world of the Harry Potter 00:08:42.330 --> 00:08:43.730 universe. 00:08:43.730 --> 00:08:47.060 And we also start off with four assertions. 00:08:47.060 --> 00:08:50.210 Let me not underestimate the value of always looking 00:08:50.210 --> 00:08:50.960 to the assertions. 00:08:50.960 --> 00:08:55.180 It's one of my white star ideas that are up here on the board. 00:08:55.180 --> 00:08:56.740 Let me see. 00:08:56.740 --> 00:08:57.240 This. 00:08:57.240 --> 00:08:59.270 Perfect. 00:08:59.270 --> 00:09:02.640 Always check the assertions before using a rule. 00:09:02.640 --> 00:09:05.260 This really tripped people up last year, and you'll see why, 00:09:05.260 --> 00:09:08.734 because we're doing last year's problem. 00:09:08.734 --> 00:09:10.150 Our four assertions that we start. 00:09:10.150 --> 00:09:14.200 With assertion 0, Millicent lives in Slytherin dungeon. 00:09:14.200 --> 00:09:16.980 Assertion 1, Millicent is ambitious. 00:09:16.980 --> 00:09:18.580 Assertion 1 is what tripped people up, 00:09:18.580 --> 00:09:20.820 so remember that Millicent is ambitious. 00:09:20.820 --> 00:09:23.690 Assertion 2 Seamus lives in Gryffindor tower. 00:09:23.690 --> 00:09:27.380 And assertion 3, Seamus snogs Millicent. 00:09:27.380 --> 00:09:30.010 So those those are our four assertions 00:09:30.010 --> 00:09:32.820 that we've already started with. 00:09:32.820 --> 00:09:35.020 Now the two things we're going to have to do 00:09:35.020 --> 00:09:38.400 are backward chaining and forward chaining. 00:09:38.400 --> 00:09:41.657 Now when you guys learned these two backward chaining 00:09:41.657 --> 00:09:43.840 and forward chaining, raise your hand 00:09:43.840 --> 00:09:46.500 if thought forward chaining was harder than backward chaining. 00:09:50.470 --> 00:09:51.032 I knew it! 00:09:51.032 --> 00:09:52.990 I can prove whatever point I want because noone 00:09:52.990 --> 00:09:54.320 wants the raise their hand. 00:09:54.320 --> 00:09:56.710 I also think backward chaining is higher than forward 00:09:56.710 --> 00:09:57.210 chaining. 00:09:57.210 --> 00:09:59.251 Raise your hand if you think backward chaining is 00:09:59.251 --> 00:10:00.680 higher than forward chaining? 00:10:00.680 --> 00:10:02.190 First of all, we have a good number of people. 00:10:02.190 --> 00:10:04.580 Second of all, since no one wants to raise their hand, 00:10:04.580 --> 00:10:06.050 I could just ask it the other way. 00:10:06.050 --> 00:10:09.510 That's a pro tip if you're ever with a large group of people. 00:10:09.510 --> 00:10:12.680 You can prove any point you want by asking the other direction. 00:10:12.680 --> 00:10:14.100 No one will raise their hand. 00:10:14.100 --> 00:10:18.370 So I agree that backward chaining is higher than forward 00:10:18.370 --> 00:10:18.970 chaining. 00:10:18.970 --> 00:10:22.680 And I disagree with Patrick that we're going to get out early, 00:10:22.680 --> 00:10:25.169 so let's start with backward chaining first. 00:10:25.169 --> 00:10:27.460 So that we make sure that we spend the bulk of our time 00:10:27.460 --> 00:10:27.959 with it. 00:10:27.959 --> 00:10:31.580 The forward chaining, well, you just 00:10:31.580 --> 00:10:33.710 go through pretty methodically and add new rules. 00:10:33.710 --> 00:10:36.660 Backward chaining, you have to draw this crazy tree. 00:10:36.660 --> 00:10:39.880 There's a lot of places to get lost in the middle of the road. 00:10:39.880 --> 00:10:42.220 So let's do some backward chaining. 00:10:42.220 --> 00:10:45.540 And to do that, I'll do it over here on the left side. 00:10:45.540 --> 00:10:47.880 So when we're doing backward chaining, 00:10:47.880 --> 00:10:50.470 we have to remember a few things that are written directly 00:10:50.470 --> 00:10:51.140 on the quiz. 00:10:51.140 --> 00:10:53.140 So you're not going to have to worry about that. 00:10:53.140 --> 00:10:55.290 But they're still pretty important. 00:10:55.290 --> 00:10:59.460 So-- actually, I'll write it on here first. 00:10:59.460 --> 00:11:01.470 I'm going to read them off. 00:11:01.470 --> 00:11:03.850 So when working on a hypothesis, the backward chainer 00:11:03.850 --> 00:11:05.510 tries to find a matching assertion 00:11:05.510 --> 00:11:08.050 in the list of assertions first. 00:11:08.050 --> 00:11:10.850 If no matching assertion is found, 00:11:10.850 --> 00:11:13.880 the backward chainer will try to find a rule 00:11:13.880 --> 00:11:15.250 with a matching consequence. 00:11:15.250 --> 00:11:17.460 A rule that has something in the then that 00:11:17.460 --> 00:11:20.220 can prove the assertion is trying to figure out. 00:11:20.220 --> 00:11:21.920 So for instance, if I was doing backward 00:11:21.920 --> 00:11:27.140 chaining on Seamus [? Snaus ?] Millicent, what happens? 00:11:27.140 --> 00:11:28.960 I'm immediately done because there's 00:11:28.960 --> 00:11:31.680 an assertion that's assertion three that says 00:11:31.680 --> 00:11:33.280 Seamus [? Snaus ?] Millicent. 00:11:33.280 --> 00:11:34.180 I proved it. 00:11:34.180 --> 00:11:34.920 I'm done. 00:11:34.920 --> 00:11:35.530 I'm happy. 00:11:35.530 --> 00:11:37.240 We can leave, we can go home. 00:11:37.240 --> 00:11:40.380 Unfortunately, that's not what the quiz asks us to do. 00:11:40.380 --> 00:11:44.080 Now, let's say that instead, we were supposed to say, 00:11:44.080 --> 00:11:46.850 I don't know, Seamus is a protagonist. 00:11:46.850 --> 00:11:49.890 Well then, we'd wind up looking through here 00:11:49.890 --> 00:11:54.170 and we would look at the fact that rule one can prove 00:11:54.170 --> 00:11:56.150 that someone is a protagonist. 00:11:56.150 --> 00:11:58.490 And we'd curse and try to prove whatever 00:11:58.490 --> 00:12:01.650 is in the antecedent of rule one, which is, OK, well, 00:12:01.650 --> 00:12:04.360 does he live in Gryffinder Tower? 00:12:04.360 --> 00:12:06.420 Assertion two, he does. 00:12:06.420 --> 00:12:07.621 So that's some really quick. 00:12:07.967 --> 00:12:09.550 And if that was too, fast don't worry. 00:12:09.550 --> 00:12:12.360 We're going to go step by step with the actual problem. 00:12:12.360 --> 00:12:15.826 But I just wanted to give two really easy problems, really 00:12:15.826 --> 00:12:17.200 quickly, how it's going to do it. 00:12:17.200 --> 00:12:19.730 Let's go step by step with the real problem. 00:12:19.730 --> 00:12:21.230 Let's keep in mind, backward chainer 00:12:21.230 --> 00:12:24.360 never adds new assertions to the list of assertions. 00:12:24.360 --> 00:12:29.470 And if you have a tiebreak, you always 00:12:29.470 --> 00:12:34.080 order based on rule order first, P0 through P5. 00:12:34.080 --> 00:12:39.130 And if the same rule matches with more than one thing 00:12:39.130 --> 00:12:41.030 in your list assertions, then you 00:12:41.030 --> 00:12:44.860 tiebreak based on the order of the assertions. 00:12:44.860 --> 00:12:46.200 Very important. 00:12:46.200 --> 00:12:49.560 Disambiguation and tie-breaking are a big place 00:12:49.560 --> 00:12:51.970 to get messed up. 00:12:51.970 --> 00:12:56.330 So we're going to try to prove that Millicent 00:12:56.330 --> 00:12:59.490 becomes Hermione's friend. 00:12:59.490 --> 00:13:04.110 And so I'm going to abbreviate some of the things, 00:13:04.110 --> 00:13:06.750 but not for the very first line. 00:13:06.750 --> 00:13:13.360 So Millicent becomes Hermione's friend. 00:13:13.360 --> 00:13:15.990 We start drawing a goal tree. 00:13:15.990 --> 00:13:21.580 Now you guys are going to learn exactly what these mean very 00:13:21.580 --> 00:13:25.370 soon, in fact, next lecture. 00:13:25.370 --> 00:13:29.620 But for now, trust me when I say these goal trees are depth 00:13:29.620 --> 00:13:31.120 first. 00:13:31.120 --> 00:13:34.150 And I'll explain what that means because some people have 00:13:34.150 --> 00:13:37.070 messed themselves up and spent more time than they needed to 00:13:37.070 --> 00:13:41.190 by treating the goal tree in a different way. 00:13:41.190 --> 00:13:43.950 Now, Millicent becomes Hermione's friend. 00:13:43.950 --> 00:13:46.110 Let's pretend that we are the backward chainer. 00:13:46.110 --> 00:13:48.640 We're trying to prove that this is true or disprove 00:13:48.640 --> 00:13:51.470 and say, well, it's definitely not true with what we have. 00:13:51.470 --> 00:13:54.290 So let's see. 00:13:54.290 --> 00:13:56.260 I'm now going to make you guys help. 00:13:56.260 --> 00:13:58.560 And people in the back think they won't be called on. 00:13:58.560 --> 00:14:00.160 So I often like to call on people in the back. 00:14:00.160 --> 00:14:02.380 What do you think is the first thing we should do? 00:14:02.380 --> 00:14:04.070 Very first thing? 00:14:04.070 --> 00:14:05.820 Yes, look for a matching assertion. 00:14:05.820 --> 00:14:07.020 Excellent. 00:14:07.020 --> 00:14:10.030 Do we have a matching assertion, everyone? 00:14:10.030 --> 00:14:10.860 No, we don't. 00:14:10.860 --> 00:14:13.220 That would be the world's easiest quiz problem. 00:14:13.220 --> 00:14:14.790 We do not have a matching assertion. 00:14:14.790 --> 00:14:15.600 Great. 00:14:15.600 --> 00:14:20.470 So, since we don't have a matching assertion, what now? 00:14:20.470 --> 00:14:23.565 AUDIENCE: We start to look at the rules. 00:14:23.565 --> 00:14:24.690 MARK SEIFTER: That's right. 00:14:24.690 --> 00:14:29.060 And do you see any rule that could prove that Millicent 00:14:29.060 --> 00:14:30.220 becomes Hermione's friend? 00:14:30.220 --> 00:14:31.245 AUDIENCE: P4. 00:14:31.245 --> 00:14:32.370 MARK SEIFTER: That's right. 00:14:32.370 --> 00:14:35.520 You can see in P4, x, which can be anybody. 00:14:35.520 --> 00:14:38.620 Anyone is capable of being Hermione's friend. 00:14:38.620 --> 00:14:39.310 Great. 00:14:39.310 --> 00:14:44.210 So P4 is our rule of the hour. 00:14:44.210 --> 00:14:47.300 So we're going to use P4. 00:14:47.300 --> 00:14:52.760 And when we use P4 to prove that Millicent becomes Hermione's 00:14:52.760 --> 00:14:55.330 friend, we're going to have to add something 00:14:55.330 --> 00:14:56.720 or another to the goal tree. 00:14:56.720 --> 00:14:57.824 So let's see. 00:14:57.824 --> 00:14:59.490 What do we have to add to the goal tree? 00:15:01.760 --> 00:15:03.301 AUDIENCE: We have to see if Millicent 00:15:03.301 --> 00:15:04.385 studies a lot [INAUDIBLE]. 00:15:04.385 --> 00:15:05.509 MARK SEIFTER: That's right. 00:15:05.509 --> 00:15:06.470 Does everyone see that? 00:15:06.470 --> 00:15:08.350 In order for her to become Hermione's friend, 00:15:08.350 --> 00:15:10.676 by rule four, we have to see if she studies a lot 00:15:10.676 --> 00:15:11.550 and is a protagonist. 00:15:11.550 --> 00:15:12.373 Question? 00:15:12.373 --> 00:15:13.248 AUDIENCE: [INAUDIBLE] 00:15:18.400 --> 00:15:20.830 MARK SEIFTER: OK, that's a very good question. 00:15:20.830 --> 00:15:23.330 You're going to get screwed up if you look at the antecedent 00:15:23.330 --> 00:15:25.190 in backward chaining first. 00:15:25.190 --> 00:15:27.170 It's backwards partially for a reason. 00:15:27.170 --> 00:15:28.950 You need to look at the consequent. 00:15:28.950 --> 00:15:30.040 Now why is that? 00:15:30.040 --> 00:15:32.550 Well, let's say there is a rule six that 00:15:32.550 --> 00:15:37.310 said if x becomes Hermione's friend, 00:15:37.310 --> 00:15:43.090 then Hermione feeds x Polyjuice Potion, or something like that. 00:15:43.090 --> 00:15:45.150 Will that rule help us in back chaining 00:15:45.150 --> 00:15:49.072 to figure out if Millicent becomes Hermione's friend? 00:15:49.072 --> 00:15:51.229 AUDIENCE: [INAUDIBLE] 00:15:51.229 --> 00:15:53.270 MARK SEIFTER: Some people are shaking their head. 00:15:53.270 --> 00:15:55.760 But think about it, will that rule be able to prove it? 00:15:55.760 --> 00:15:56.280 No. 00:15:56.280 --> 00:15:58.120 Now, if they do become Hermione's friend 00:15:58.120 --> 00:15:59.300 and we want to do some forward chaining, 00:15:59.300 --> 00:16:00.758 we'll figure out that they're going 00:16:00.758 --> 00:16:03.240 to transmute into some kind of other thing because 00:16:03.240 --> 00:16:04.240 of the Polyjuice Potion. 00:16:04.240 --> 00:16:06.040 But it's not going to help us do the one 00:16:06.040 --> 00:16:07.581 thing we want to back chain, which is 00:16:07.581 --> 00:16:08.912 to prove that thing on the top. 00:16:08.912 --> 00:16:10.620 So we actually need to look for something 00:16:10.620 --> 00:16:13.110 that has our current goal in its consequent. 00:16:13.110 --> 00:16:14.640 Then we add on the antecedents. 00:16:14.640 --> 00:16:17.430 As people I've asked so far-- sorry, I 00:16:17.430 --> 00:16:19.110 don't know your names-- like Patrick, 00:16:19.110 --> 00:16:22.700 have correctly given me every time, which is excellent. 00:16:22.700 --> 00:16:26.400 So notice also that she didn't say 00:16:26.400 --> 00:16:28.955 x studies a lot needs to be added to the goal tree. 00:16:28.955 --> 00:16:31.195 She said Millicent studies a lot. 00:16:31.195 --> 00:16:32.290 Oh, another question. 00:16:32.290 --> 00:16:34.410 Great. 00:16:34.410 --> 00:16:38.200 AUDIENCE: So obviously after putting rule 4 there, 00:16:38.200 --> 00:16:41.837 shouldn't we first check the assertions-- check 00:16:41.837 --> 00:16:44.405 on the assertions instead of our conditions [INAUDIBLE] 00:16:47.000 --> 00:16:48.540 MARK SEIFTER: So the question is, 00:16:48.540 --> 00:16:50.700 once we put rule four in there, should 00:16:50.700 --> 00:16:52.885 we check to see if those antecedents of rule four 00:16:52.885 --> 00:16:57.110 are already in the assertions before checking other rules? 00:16:57.110 --> 00:16:58.100 The answer? 00:16:58.100 --> 00:17:01.110 You're not only correct, sir, you're exactly one step ahead. 00:17:01.110 --> 00:17:04.010 So I'm going to assume I called on you for the very next thing. 00:17:04.010 --> 00:17:07.770 That's exactly what we do once we draw it onto the tree. 00:17:07.770 --> 00:17:10.000 You're exactly on the way. 00:17:10.000 --> 00:17:12.099 Further question? 00:17:12.099 --> 00:17:14.130 Perfect. 00:17:14.130 --> 00:17:16.760 All right, great. 00:17:16.760 --> 00:17:19.994 So again, we're putting up Millicent studies a lot. 00:17:19.994 --> 00:17:21.119 Millicent is a protagonist. 00:17:21.119 --> 00:17:23.530 We're not putting up x. 00:17:23.530 --> 00:17:25.190 Some people did that. 00:17:25.190 --> 00:17:28.200 And of course it's an n node as we heard. 00:17:28.200 --> 00:17:30.970 We need them both to be true or we're not going 00:17:30.970 --> 00:17:32.300 to be able to continue onward. 00:17:32.300 --> 00:17:35.860 So we have-- I'm going to use m for Millicent. 00:17:35.860 --> 00:17:39.580 Millicent studies a lot. 00:17:39.580 --> 00:17:44.680 Also over here, Millicent is a protagonist. 00:17:49.361 --> 00:17:51.860 And we've already heard that we need 00:17:51.860 --> 00:17:54.430 to search in the assertions before we 00:17:54.430 --> 00:17:58.315 go into any rules for what we're looking for next. 00:17:58.315 --> 00:18:00.690 The question is, what are we looking for next and in what 00:18:00.690 --> 00:18:01.290 order? 00:18:01.290 --> 00:18:03.540 This is where that thing I told you about depth search 00:18:03.540 --> 00:18:04.860 is crucial. 00:18:04.860 --> 00:18:06.944 We are going to look here on the left node. 00:18:06.944 --> 00:18:09.360 And if it has any children, if we have to keep going down, 00:18:09.360 --> 00:18:13.470 we are not going to look here yet. 00:18:13.470 --> 00:18:14.810 There's a few reasons for that. 00:18:14.810 --> 00:18:16.200 One of which is that we're lazy. 00:18:16.200 --> 00:18:18.290 The evaluation, if you learned about it, 00:18:18.290 --> 00:18:21.350 is also-- if you learn about lazy evaluation, is also lazy. 00:18:21.350 --> 00:18:23.845 And if we can disprove this study's a lot branch, 00:18:23.845 --> 00:18:26.220 we don't have to do any work with the protagonist branch. 00:18:26.220 --> 00:18:26.720 We're done. 00:18:26.720 --> 00:18:28.110 We're out of here. 00:18:28.110 --> 00:18:31.270 And it's a loss. 00:18:31.270 --> 00:18:34.460 So we're going to move down the study's a lot branch. 00:18:34.460 --> 00:18:36.360 And we already heard from the audience, 00:18:36.360 --> 00:18:39.250 we need to look to see if it's in the assertions. 00:18:39.250 --> 00:18:43.020 Everyone, is Millicent studies a lot in the assertions? 00:18:43.020 --> 00:18:45.430 No, it's not. 00:18:45.430 --> 00:18:48.560 Well then, now we're going to get to that question 00:18:48.560 --> 00:18:52.000 that I had before about the antecedent or the consequent. 00:18:52.000 --> 00:18:55.192 Because study lies here in the antecedent of rule four, 00:18:55.192 --> 00:18:57.400 but we're not going to be able to use rule four here. 00:18:57.400 --> 00:18:59.920 In fact, that's how we got here in the first place. 00:18:59.920 --> 00:19:05.950 So the question is-- let's see, the question 00:19:05.950 --> 00:19:12.360 is, do we have a rule in the consequent that matches 00:19:12.360 --> 00:19:14.952 Millicent studies a lot. 00:19:14.952 --> 00:19:15.910 Yeah, that's right, P3. 00:19:19.030 --> 00:19:19.730 That's right. 00:19:19.730 --> 00:19:23.280 So P3 would give us Millicent studies a lot. 00:19:23.280 --> 00:19:28.180 And so therefore what will we add to the goal tree? 00:19:28.180 --> 00:19:31.655 AUDIENCE: We add both that is Millicent either a protagonist 00:19:31.655 --> 00:19:33.150 or a villain and [INAUDIBLE]. 00:19:33.150 --> 00:19:34.920 MARK SEIFTER: Yeah, she. 00:19:34.920 --> 00:19:37.950 Turns out to be a girl. 00:19:37.950 --> 00:19:39.900 So that's exactly right. 00:19:39.900 --> 00:19:42.920 We heard that we need to add-- we 00:19:42.920 --> 00:19:46.845 need to add an AND node, which also has an OR 00:19:46.845 --> 00:19:48.480 node at the bottom of it, because this 00:19:48.480 --> 00:19:50.650 is a little bit of a complicated rule. 00:19:50.650 --> 00:19:54.380 So we have an AND node. 00:19:54.380 --> 00:19:55.980 So we have an AND node. 00:19:55.980 --> 00:19:57.630 And the first thing on the AND node 00:19:57.630 --> 00:20:08.230 is Millicent is a protagonist or Millicent is a villain. 00:20:12.240 --> 00:20:16.105 And the second thing on the AND node is Millicent is ambitious. 00:20:19.525 --> 00:20:21.650 Actually, that is the second thing on the AND node. 00:20:21.650 --> 00:20:23.390 I hope that's what I said. 00:20:23.390 --> 00:20:24.525 All right, the second thing on the AND node 00:20:24.525 --> 00:20:25.608 is Millicent is ambitious. 00:20:29.160 --> 00:20:37.657 So here's our handy little tree. 00:20:37.657 --> 00:20:39.490 Now this is where it's important, as I said, 00:20:39.490 --> 00:20:41.850 we're doing a depth first search. 00:20:41.850 --> 00:20:44.490 We're going down along the left branch. 00:20:44.490 --> 00:20:50.885 So where do you think we're going to go next on this tree? 00:20:50.885 --> 00:20:53.350 AUDIENCE: [INAUDIBLE] 00:20:53.350 --> 00:20:55.467 MARK SEIFTER: Not quite. 00:20:55.467 --> 00:20:56.300 That's a good guess. 00:20:56.300 --> 00:20:57.760 You didn't say we're trying to prove 00:20:57.760 --> 00:20:59.220 m is a protagonist on the right branch, which 00:20:59.220 --> 00:21:00.261 is a very common mistake. 00:21:00.261 --> 00:21:01.376 What do you do? 00:21:01.376 --> 00:21:02.834 AUDIENCE: You should go down to see 00:21:02.834 --> 00:21:05.410 if there's a consequence for m is-- 00:21:05.410 --> 00:21:06.870 Millicent is a protagonist. 00:21:06.870 --> 00:21:08.210 MARK SEIFTER: Which one of the two Millicent 00:21:08.210 --> 00:21:09.835 is a protagonist do we want to look at? 00:21:12.232 --> 00:21:13.440 Yeah, the farthest down left. 00:21:13.440 --> 00:21:14.800 That's right. 00:21:14.800 --> 00:21:16.624 So you guys will learn depth for search 00:21:16.624 --> 00:21:18.290 on Monday, at which point it will become 00:21:18.290 --> 00:21:19.498 much clearer what I'm saying. 00:21:19.498 --> 00:21:22.530 But yeah, you always follow the left branch as far down 00:21:22.530 --> 00:21:23.947 as you can. 00:21:23.947 --> 00:21:26.030 Then you take the right branch of that same branch 00:21:26.030 --> 00:21:27.585 that you followed. 00:21:27.585 --> 00:21:29.710 Great, so we're going to try to find that Millicent 00:21:29.710 --> 00:21:30.980 is a protagonist. 00:21:30.980 --> 00:21:32.800 What do we do first? 00:21:32.800 --> 00:21:34.332 Everyone? 00:21:34.332 --> 00:21:36.016 Check assertion, yes. 00:21:36.016 --> 00:21:36.640 Is it in there? 00:21:36.640 --> 00:21:37.970 No, it's not. 00:21:37.970 --> 00:21:38.990 OK. 00:21:38.990 --> 00:21:42.150 So, therefore we're going to try to find 00:21:42.150 --> 00:21:47.270 a rule as we heard about whether Millicent is a protagonist. 00:21:47.270 --> 00:21:51.740 So, all the way in the back? 00:21:51.740 --> 00:21:54.938 All the way in the back, is there a rule that matches? 00:21:54.938 --> 00:21:56.157 AUDIENCE: [INAUDIBLE] 00:21:56.157 --> 00:21:57.990 MARK SEIFTER: That matches in its consequent 00:21:57.990 --> 00:22:00.810 that Millicent is a protagonist. 00:22:00.810 --> 00:22:05.712 AUDIENCE: Um, there is a rule. 00:22:05.712 --> 00:22:06.420 MARK SEIFTER: OK. 00:22:06.420 --> 00:22:07.590 Well, let's give it a try. 00:22:07.590 --> 00:22:08.637 Which one? 00:22:08.637 --> 00:22:09.220 AUDIENCE: One. 00:22:09.220 --> 00:22:10.761 MARK SEIFTER: Rule one, that's right. 00:22:10.761 --> 00:22:15.380 So therefore, we would have to add what to our goal tree? 00:22:15.380 --> 00:22:18.419 AUDIENCE: Another [INAUDIBLE]. 00:22:18.419 --> 00:22:19.252 MARK SEIFTER: Right. 00:22:19.252 --> 00:22:21.188 And what's on that please? 00:22:24.092 --> 00:22:25.060 AUDIENCE: [INAUDIBLE] 00:22:25.060 --> 00:22:27.238 MARK SEIFTER: Yeah, Millicent lives in Gryffindor Tower, 00:22:27.238 --> 00:22:27.738 perfect. 00:22:27.738 --> 00:22:31.550 So, our new thing that we're searching for 00:22:31.550 --> 00:22:35.350 is-- pretend this connects. 00:22:35.350 --> 00:22:37.170 Actually, I guess it does connect. 00:22:37.170 --> 00:22:41.860 We're looking for m lives in Gryffindor Tower. 00:22:41.860 --> 00:22:43.484 Great. 00:22:43.484 --> 00:22:45.650 And since it's depth first, that's where we go next. 00:22:45.650 --> 00:22:47.270 Great, we're on a roll. 00:22:47.270 --> 00:22:50.792 So what do we do first? 00:22:50.792 --> 00:22:53.440 Do we have that in assertions? 00:22:53.440 --> 00:22:55.750 Some people say yes, but the answer is no. 00:22:55.750 --> 00:22:58.910 We have, in fact, Seamus living in Gryffindor Tower. 00:22:58.910 --> 00:23:00.390 Most of you said "no." 00:23:00.390 --> 00:23:01.000 You're right. 00:23:01.000 --> 00:23:02.650 The majority rules. 00:23:02.650 --> 00:23:04.310 We don't have any assertions. 00:23:04.310 --> 00:23:08.180 However, do we have a rule with that in the consequent? 00:23:08.180 --> 00:23:08.920 No. 00:23:08.920 --> 00:23:09.690 So what do we do? 00:23:13.647 --> 00:23:15.980 People are saying different things that are all correct. 00:23:15.980 --> 00:23:16.790 Backtrack, you say. 00:23:16.790 --> 00:23:17.420 Go to the next. 00:23:17.420 --> 00:23:18.170 We can't prove it. 00:23:18.170 --> 00:23:20.520 All correct. 00:23:20.520 --> 00:23:22.960 Put a big x. 00:23:22.960 --> 00:23:24.282 This isn't true. 00:23:24.282 --> 00:23:24.990 Now we'd look up. 00:23:24.990 --> 00:23:26.100 We're on an OR node. 00:23:26.100 --> 00:23:32.490 So we're not done yet because either of those can be true. 00:23:32.490 --> 00:23:36.120 So now we go back up, backtrack, Millicent is a villain. 00:23:38.850 --> 00:23:40.778 What do we do first? 00:23:40.778 --> 00:23:42.152 Check assertions. 00:23:42.152 --> 00:23:43.070 Is it in there? 00:23:43.070 --> 00:23:44.330 No, it's not. 00:23:44.330 --> 00:23:46.880 Don't worry, we're getting to one where it will be, 00:23:46.880 --> 00:23:50.460 where about 40%-- or 30% to 40% of the class lost 00:23:50.460 --> 00:23:54.160 points, very, very soon. 00:23:54.160 --> 00:23:58.770 So, we see that Millicent is a villain. 00:23:58.770 --> 00:24:00.430 And it's not in the assertions. 00:24:00.430 --> 00:24:03.930 So therefore, is there any rule that 00:24:03.930 --> 00:24:06.230 has that in its consequent? 00:24:09.684 --> 00:24:10.559 AUDIENCE: [INAUDIBLE] 00:24:12.749 --> 00:24:15.040 MARK SEIFTER: We're looking for Millicent is a villain. 00:24:17.658 --> 00:24:18.533 AUDIENCE: [INAUDIBLE] 00:24:22.902 --> 00:24:24.360 MARK SEIFTER: Oh, you can't see it. 00:24:24.360 --> 00:24:26.200 All right, I will move it down slightly. 00:24:26.200 --> 00:24:29.422 It got a little bit off kilter when I put in the parentheses 00:24:29.422 --> 00:24:30.130 around the "and." 00:24:30.130 --> 00:24:32.350 Hold on. 00:24:32.350 --> 00:24:32.900 There you go. 00:24:36.830 --> 00:24:41.150 AUDIENCE: If [INAUDIBLE] is a protagonist or is a villain. 00:24:41.150 --> 00:24:43.422 [INAUDIBLE] 00:24:43.422 --> 00:24:44.880 MARK SEIFTER: We're trying to prove 00:24:44.880 --> 00:24:46.088 that she's a villain, though. 00:24:46.088 --> 00:24:49.255 So do we have any with that in the consequent? 00:24:49.255 --> 00:24:50.755 [INAUDIBLE] anything that will prove 00:24:50.755 --> 00:24:53.070 that she's a villain if we fire off that rule. 00:24:56.150 --> 00:24:58.162 Want to give here a little bit of help? 00:24:58.162 --> 00:24:58.703 AUDIENCE: P2. 00:24:58.703 --> 00:25:01.569 If she lives in Slytherin, then she's a villain [INAUDIBLE]. 00:25:01.569 --> 00:25:02.860 MARK SEIFTER: Ah, see that now? 00:25:02.860 --> 00:25:05.200 It had two, so it was a little bit harder. 00:25:05.200 --> 00:25:07.510 Now some people ask, what about that ambitious thing? 00:25:07.510 --> 00:25:09.426 Can we like add that to the tree or something? 00:25:09.426 --> 00:25:10.190 No. 00:25:10.190 --> 00:25:12.800 The backward chainer is single-minded, focused, 00:25:12.800 --> 00:25:14.097 and stupid. 00:25:14.097 --> 00:25:16.430 Even though it's later going to need to prove that she's 00:25:16.430 --> 00:25:18.239 ambitious, it doesn't care. 00:25:18.239 --> 00:25:19.530 It just sees the villain there. 00:25:19.530 --> 00:25:21.200 Villain, oh, that's great. 00:25:21.200 --> 00:25:23.370 As long as we've got the antecedent 00:25:23.370 --> 00:25:27.690 we are going to be happy. 00:25:27.690 --> 00:25:29.290 This is actually an important point, 00:25:29.290 --> 00:25:32.200 not in this particular problem, but in some other problems. 00:25:32.200 --> 00:25:36.280 So by using P2, we're obviously going 00:25:36.280 --> 00:25:40.151 to have the antecedent x lives in Slytherin dungeon. 00:25:40.151 --> 00:25:41.150 And x here is Millicent. 00:25:41.150 --> 00:25:42.816 So Millicent lives in Slytherin dungeon. 00:25:47.720 --> 00:25:49.600 All right, so what's the first thing 00:25:49.600 --> 00:25:51.380 we do when we see this new assertion? 00:25:54.430 --> 00:25:55.430 We check the assertions. 00:25:55.430 --> 00:25:56.910 Is it in there? 00:25:56.910 --> 00:25:57.600 Yes. 00:25:57.600 --> 00:25:59.183 That's not where everyone lost points, 00:25:59.183 --> 00:26:01.314 but yes, it is in there. 00:26:01.314 --> 00:26:02.290 Check. 00:26:02.290 --> 00:26:05.260 This OR node is happy. 00:26:05.260 --> 00:26:08.680 Now we move up to the AND node with Millicent is ambitious. 00:26:08.680 --> 00:26:11.080 So Millicent is ambitious. 00:26:11.080 --> 00:26:11.830 What do we do now? 00:26:14.830 --> 00:26:18.770 AUDIENCE: So isn't the consequent of P2 00:26:18.770 --> 00:26:21.210 that x is a villain and x is ambitious. 00:26:21.210 --> 00:26:25.114 I don't know if it's [INAUDIBLE] or whatever, 00:26:25.114 --> 00:26:28.042 but in our assertions we have that Millicent is ambitious. 00:26:28.042 --> 00:26:29.994 Is that necessary to let us-- 00:26:29.994 --> 00:26:31.954 MARK SEIFTER: To let us use rule two. 00:26:31.954 --> 00:26:33.940 Actually, no. 00:26:33.940 --> 00:26:40.660 The question is, do we need the x is 00:26:40.660 --> 00:26:45.520 ambitious to be in our list of assertions in order to use P2. 00:26:45.520 --> 00:26:48.280 For instance, if we didn't have the assertion that Millicent 00:26:48.280 --> 00:26:51.167 is ambitious, would P2 have a problem firing? 00:26:54.030 --> 00:26:56.315 So, it's a very interesting question. 00:26:56.315 --> 00:26:57.940 It's sort of what actually I was trying 00:26:57.940 --> 00:27:02.140 to mention earlier when I said it's single-minded, 00:27:02.140 --> 00:27:04.550 it's focused, it doesn't care about the other one. 00:27:04.550 --> 00:27:06.341 Because you might say, well, wait a minute, 00:27:06.341 --> 00:27:08.300 P2 could never have actually fired 00:27:08.300 --> 00:27:10.520 if it didn't have both of its consequents. 00:27:10.520 --> 00:27:14.130 But in fact, the backward chainer doesn't care. 00:27:14.130 --> 00:27:16.560 All that the backward chainer is looking to do 00:27:16.560 --> 00:27:19.760 is to prove whether or not there's 00:27:19.760 --> 00:27:23.880 a possibility that Millicent might be a villain. 00:27:23.880 --> 00:27:26.530 It's not trying to say, oh, all the results 00:27:26.530 --> 00:27:30.455 of some certain rules are making Millicent a villain 00:27:30.455 --> 00:27:33.390 and all the other things that are there, like ambitious, are 00:27:33.390 --> 00:27:34.522 in the database. 00:27:34.522 --> 00:27:35.730 It's not the forward chainer. 00:27:35.730 --> 00:27:37.130 It actually doesn't care. 00:27:37.130 --> 00:27:39.560 This sometimes leads to unnecessary computation. 00:27:39.560 --> 00:27:42.110 But it's very simple, and it's very simple to code. 00:27:42.110 --> 00:27:45.160 So it often will probably speed you up in the long run. 00:27:45.160 --> 00:27:48.150 Like if there's, for instance, 100 thing in the then 00:27:48.150 --> 00:27:50.226 and you only care about one of them, 00:27:50.226 --> 00:27:52.100 it would be a waste, almost, to add those 99. 00:27:52.100 --> 00:27:57.030 There's a follow up over here somewhere? 00:27:57.030 --> 00:27:57.530 [INAUDIBLE] 00:28:00.946 --> 00:28:03.386 AUDIENCE: Order m of 99. 00:28:03.386 --> 00:28:04.362 And so [INAUDIBLE] 00:28:10.230 --> 00:28:11.740 MARK SEIFTER: You can try. 00:28:11.740 --> 00:28:13.600 However, then at that point, every time 00:28:13.600 --> 00:28:15.520 you check the assertions, you'd be 00:28:15.520 --> 00:28:17.250 attempting to check those 99. 00:28:17.250 --> 00:28:19.270 Also, you might not have used those rules. 00:28:19.270 --> 00:28:22.660 The question is, could you make a hash table 00:28:22.660 --> 00:28:26.190 with all of the 100 things that were in the consequent? 00:28:26.190 --> 00:28:28.840 And then, after having made that hash table 00:28:28.840 --> 00:28:31.320 since you were already walking through those anyway 00:28:31.320 --> 00:28:33.300 when you were checking it, you could add those 00:28:33.300 --> 00:28:34.049 to the assertions. 00:28:34.049 --> 00:28:36.830 The problem is that you might not necessarily 00:28:36.830 --> 00:28:40.200 want-- with the backward chainer-- you might not 00:28:40.200 --> 00:28:42.340 necessarily want to think that all 00:28:42.340 --> 00:28:46.860 those things in the consequent are necessarily true. 00:28:46.860 --> 00:28:49.620 However, you might not care about them. 00:28:49.620 --> 00:28:51.590 And then you have to make an order 00:28:51.590 --> 00:28:54.090 and computation every time you check that list of assertions 00:28:54.090 --> 00:28:55.271 in the upper left. 00:28:55.271 --> 00:28:56.146 AUDIENCE: [INAUDIBLE] 00:28:59.819 --> 00:29:02.110 MARK SEIFTER: You don't know what assertions there are. 00:29:02.110 --> 00:29:04.200 You have to check the entire list of assertions 00:29:04.200 --> 00:29:06.240 in the upper left every time you get 00:29:06.240 --> 00:29:07.760 to a new node in the goal tree. 00:29:07.760 --> 00:29:09.550 So each one is order 1. 00:29:09.550 --> 00:29:13.060 But I'm not saying to find a specific assertion is order n. 00:29:13.060 --> 00:29:15.530 I'm saying every time you get a new node in the goal tree, 00:29:15.530 --> 00:29:17.999 you have to check all the assertions you've added. 00:29:17.999 --> 00:29:20.540 AUDIENCE: You have to do that anyway. [INAUDIBLE] assertions. 00:29:20.540 --> 00:29:22.748 MARK SEIFTER: Yeah, you'd have to check for the four. 00:29:22.748 --> 00:29:26.710 But let's say that there were 10,000 consequents of P2. 00:29:26.710 --> 00:29:28.930 You would have to check 10,000 instead of four 00:29:28.930 --> 00:29:31.750 if you added them all after proving 00:29:31.750 --> 00:29:33.990 P2 was true on the goal tree. 00:29:33.990 --> 00:29:37.820 Also, another important note is that you might not 00:29:37.820 --> 00:29:39.420 use every branch of the goal tree, 00:29:39.420 --> 00:29:41.160 if there's like an OR that's up higher 00:29:41.160 --> 00:29:43.110 and you wind up using a different branch, in which case 00:29:43.110 --> 00:29:44.901 you'd probably have to make a separate hash 00:29:44.901 --> 00:29:47.910 table for every sub-branch that you have 00:29:47.910 --> 00:29:50.060 and then remember which hash tables were updated 00:29:50.060 --> 00:29:51.850 based on which sub-branch. 00:29:51.850 --> 00:29:53.430 And then sub-branches die. 00:29:53.430 --> 00:29:56.906 It's probably more effort than it's worth. 00:29:56.906 --> 00:29:58.530 It's certainly an interesting question. 00:29:58.530 --> 00:30:01.890 It's a great question for a debate in recitation. 00:30:01.890 --> 00:30:03.980 Also, I'm happy to talk about it later. 00:30:03.980 --> 00:30:07.750 I think that someone who very intelligently made hash tables 00:30:07.750 --> 00:30:10.180 and thought the problem through, as Patrick said, 00:30:10.180 --> 00:30:12.342 more knowledge can mean a better-- well, 00:30:12.342 --> 00:30:14.550 actually maybe he hasn't said more knowledge can mean 00:30:14.550 --> 00:30:16.924 a better search because we haven't done that lecture yet, 00:30:16.924 --> 00:30:18.020 but-- 00:30:18.020 --> 00:30:20.270 AUDIENCE: You're talking about implementation decision 00:30:20.270 --> 00:30:23.975 and using hash table might well be a good way to do this. 00:30:23.975 --> 00:30:27.056 The problem is that we're presuming some things about how 00:30:27.056 --> 00:30:30.444 the rules are firing and what [INAUDIBLE] they're 00:30:30.444 --> 00:30:33.832 firing that depend on the order of assertions in the table. 00:30:33.832 --> 00:30:36.736 So if we used the hash table, we'd lose the order. 00:30:36.736 --> 00:30:38.597 [INAUDIBLE] 00:30:38.597 --> 00:30:39.680 MARK SEIFTER: That's true. 00:30:39.680 --> 00:30:40.195 That's true. 00:30:40.195 --> 00:30:41.820 But I'm thinking like if someone wanted 00:30:41.820 --> 00:30:44.790 to make that implementation as like do some research in rules 00:30:44.790 --> 00:30:48.890 based systems, it's possible you can increase the running speed. 00:30:48.890 --> 00:30:53.260 In this class, we are not completely as focused 00:30:53.260 --> 00:30:54.940 on the fastest algorithms. 00:30:54.940 --> 00:30:57.440 But I still think that a cool thing to try. 00:30:57.440 --> 00:30:59.860 Questions from people in the crowd? 00:30:59.860 --> 00:31:00.800 We'll start with you. 00:31:00.800 --> 00:31:02.420 AUDIENCE: So ignoring the hash table? 00:31:02.420 --> 00:31:03.920 MARK SEIFTER: Ignore the hash table. 00:31:03.920 --> 00:31:06.296 That's a good idea because it's a little extra enrichment 00:31:06.296 --> 00:31:06.795 thing. 00:31:06.795 --> 00:31:08.500 It's not anything you would possibly 00:31:08.500 --> 00:31:10.646 need to know for the quiz. 00:31:10.646 --> 00:31:14.630 AUDIENCE: [INAUDIBLE] So if it became 00:31:14.630 --> 00:31:17.618 an [INAUDIBLE] are you using this "then" statement 00:31:17.618 --> 00:31:19.610 because you want the villain. 00:31:19.610 --> 00:31:23.096 So along with using this you get x is ambitious. 00:31:23.096 --> 00:31:26.582 [INAUDIBLE] used after that, another "then" statement 00:31:26.582 --> 00:31:29.072 that we also use that says x is not ambitious. 00:31:29.072 --> 00:31:31.845 So how would you resolve that? 00:31:31.845 --> 00:31:33.220 MARK SEIFTER: So the question is, 00:31:33.220 --> 00:31:36.370 let's say you used rule two somewhere in the tree 00:31:36.370 --> 00:31:38.480 to get that x is a villain, which 00:31:38.480 --> 00:31:40.480 then says that x is ambitious. 00:31:40.480 --> 00:31:44.900 Then later, you have x is not ambitious 00:31:44.900 --> 00:31:50.192 somewhere in one of the other rules that you then later need. 00:31:50.192 --> 00:31:51.900 The question is, how do you resolve that? 00:31:51.900 --> 00:31:52.750 What does it do? 00:31:52.750 --> 00:31:53.705 Well, first of all-- 00:31:53.705 --> 00:31:54.580 AUDIENCE: [INAUDIBLE] 00:31:59.130 --> 00:32:00.880 MARK SEIFTER: First of all, interestingly, 00:32:00.880 --> 00:32:05.537 if it says x is not ambitious-- literally like that. 00:32:05.537 --> 00:32:06.870 And I'm not being pedantic here. 00:32:06.870 --> 00:32:08.245 This is one of the tricks someone 00:32:08.245 --> 00:32:11.060 played in a previous quiz. 00:32:11.060 --> 00:32:13.050 You can have that and x is ambitious 00:32:13.050 --> 00:32:16.340 both in the list because it's a dumb rules-based system it 00:32:16.340 --> 00:32:19.190 doesn't know that you can't have both of those on the list. 00:32:19.190 --> 00:32:22.760 So if you have a positive assertion in a consequent, 00:32:22.760 --> 00:32:25.990 x is not ambitious in a consequent, x is not ambitious, 00:32:25.990 --> 00:32:29.000 it'll be happy to add Millicent is not ambitious 00:32:29.000 --> 00:32:31.730 while Millicent ambitious this is already there, 00:32:31.730 --> 00:32:33.020 because it's stupid. 00:32:33.020 --> 00:32:35.490 Now if it had delete Millicent is 00:32:35.490 --> 00:32:37.740 ambitious in the consequent and deleted something that 00:32:37.740 --> 00:32:44.110 was previously there, that would be an interesting problem. 00:32:44.110 --> 00:32:46.406 It could cause mistakes. 00:32:46.406 --> 00:32:47.780 Your back chaining would probably 00:32:47.780 --> 00:32:49.196 make the mistake of allowing this. 00:32:49.196 --> 00:32:53.580 However, this is exactly what we do not, I believe as a policy, 00:32:53.580 --> 00:32:55.795 do not have DELETE statements on the quizzes. 00:32:58.496 --> 00:32:59.870 At least previous quizzes did not 00:32:59.870 --> 00:33:02.170 have them, except for in a hypothetical 00:33:02.170 --> 00:33:04.480 of what happens if we add a DELETE statement here. 00:33:04.480 --> 00:33:06.480 I don't think we've ever made people work things 00:33:06.480 --> 00:33:07.610 through with the delete. 00:33:07.610 --> 00:33:10.910 Delete would possibly cause some issues. 00:33:10.910 --> 00:33:12.460 Question in the back? 00:33:12.460 --> 00:33:13.930 AUDIENCE: So, just to check this, 00:33:13.930 --> 00:33:16.053 we're doing backwards chaining, we 00:33:16.053 --> 00:33:18.350 don't actually add assertions to your [INAUDIBLE]. 00:33:18.350 --> 00:33:20.230 MARK SEIFTER: Never add assertions in backward chain 00:33:20.230 --> 00:33:21.188 to the assertion table. 00:33:21.188 --> 00:33:22.840 It's dumb. 00:33:22.840 --> 00:33:23.890 The system is dumb. 00:33:23.890 --> 00:33:25.850 I'm not saying it's a dumb idea to do this. 00:33:25.850 --> 00:33:28.040 It's actually pretty fast to do it this way. 00:33:28.040 --> 00:33:29.840 But the system is dumb. 00:33:29.840 --> 00:33:32.204 The question is, do you add assertions 00:33:32.204 --> 00:33:33.370 or you don't add assertions? 00:33:33.370 --> 00:33:34.610 You do not. 00:33:34.610 --> 00:33:37.350 You simply go through, checking all the things on your goal 00:33:37.350 --> 00:33:40.050 tree until the goal tree is either proven or disproven, 00:33:40.050 --> 00:33:42.530 then you're out of here. 00:33:42.530 --> 00:33:44.660 So, cool so far, everyone? 00:33:44.660 --> 00:33:46.080 Good questions from everyone. 00:33:46.080 --> 00:33:47.790 These are all questions that are things 00:33:47.790 --> 00:33:49.300 that often trip people up. 00:33:49.300 --> 00:33:51.190 So, our next thing, Millicent is ambitious. 00:33:51.190 --> 00:33:53.259 We sort of-- the cat is out of the bag 00:33:53.259 --> 00:33:55.300 because there is a question mentioning that there 00:33:55.300 --> 00:33:57.130 is an assertion that says that. 00:33:57.130 --> 00:34:01.290 But I direct you guys to our favorite rule, rule two. 00:34:01.290 --> 00:34:03.000 Shouldn't we use rule two to prove 00:34:03.000 --> 00:34:05.480 that Millicent is ambitious? 00:34:05.480 --> 00:34:08.010 The answer is if you want to lose four points or however 00:34:08.010 --> 00:34:09.420 many points, then yes. 00:34:09.420 --> 00:34:11.130 But if you don't want to lose points, 00:34:11.130 --> 00:34:22.280 then this is already correct by virtue of assertion one. 00:34:22.280 --> 00:34:26.250 So I guess I should write, also, that this over here, 00:34:26.250 --> 00:34:33.840 Millicent studies a lot rule, this rule is rule four. 00:34:33.840 --> 00:34:36.210 Yeah, that's rule four [INAUDIBLE] and protagonist. 00:34:36.210 --> 00:34:40.980 Down here to prove that she studies a lot is rule three. 00:34:40.980 --> 00:34:48.989 And then at the bottom here we have what rules here? 00:34:48.989 --> 00:34:52.870 We have the protagonist rule, which is one, 00:34:52.870 --> 00:34:55.610 and the villain rule which is two. 00:34:58.330 --> 00:35:01.250 This is correct virtue of A0. 00:35:04.500 --> 00:35:06.390 OK, great. 00:35:06.390 --> 00:35:08.670 So we've proved this whole AND node. 00:35:08.670 --> 00:35:10.700 We know that Millicent studies a lot. 00:35:10.700 --> 00:35:12.824 But now we're going to have to go a little bit more 00:35:12.824 --> 00:35:16.080 quickly based on time, and so I will do the remaining things. 00:35:16.080 --> 00:35:18.270 Anyone who has not been called on is off the hook. 00:35:18.270 --> 00:35:19.760 But that doesn't mean not to pay attention 00:35:19.760 --> 00:35:22.100 because there's some interesting stuff still to come. 00:35:22.100 --> 00:35:24.350 So, Millicent is a protagonist. 00:35:24.350 --> 00:35:27.460 Well, good news, everyone. 00:35:27.460 --> 00:35:29.770 There's one other reason that I can do this 00:35:29.770 --> 00:35:32.500 and that's that you've already told me what I need to do. 00:35:32.500 --> 00:35:37.810 Most is a protagonist, you use rule one, rule one. 00:35:37.810 --> 00:35:40.580 And check if she lives in Gryffindor tower. 00:35:40.580 --> 00:35:43.031 Now, will it do it again? 00:35:43.031 --> 00:35:44.340 Yes it will. 00:35:44.340 --> 00:35:47.715 It hasn't cached that it's already tried that. 00:35:47.715 --> 00:35:49.840 Now, hash table not withstanding, caching something 00:35:49.840 --> 00:35:52.810 you've already tried may be a good idea with backward 00:35:52.810 --> 00:35:55.070 chaining, but we do not do that in this class. 00:35:55.070 --> 00:35:56.610 That's an implementation detail. 00:35:56.610 --> 00:35:58.672 It's another idea of something you can do. 00:35:58.672 --> 00:36:00.630 We don't catch things that we've already tried. 00:36:00.630 --> 00:36:03.250 We try them again, dammit. 00:36:03.250 --> 00:36:06.170 And when we try it again, maybe it'll work this time. 00:36:06.170 --> 00:36:07.390 No, it never works. 00:36:07.390 --> 00:36:09.725 It never works this time. 00:36:09.725 --> 00:36:10.490 This fails. 00:36:10.490 --> 00:36:12.000 This AND node fails. 00:36:12.000 --> 00:36:13.880 The whole thing fails. 00:36:13.880 --> 00:36:15.820 They're not friends at all. 00:36:15.820 --> 00:36:19.310 They're bitter enemies. 00:36:19.310 --> 00:36:22.120 Millicent does not become Hermione's friend. 00:36:22.120 --> 00:36:24.510 So now they ask us a few questions 00:36:24.510 --> 00:36:28.020 which are pretty easy to answer based on the ordeal we've just 00:36:28.020 --> 00:36:28.950 been through. 00:36:28.950 --> 00:36:32.580 So, determine the minimum number of additional assertions 00:36:32.580 --> 00:36:34.450 that we would need to add for Millicent 00:36:34.450 --> 00:36:38.180 to become Hermione's friend. 00:36:38.180 --> 00:36:40.740 But you're not allowed to add an assertion that 00:36:40.740 --> 00:36:43.820 matches a consequent of a rule. 00:36:43.820 --> 00:36:47.060 You can only add an assertion-- in other words, 00:36:47.060 --> 00:36:51.030 you can't add an assertion that will prove some other rules. 00:36:51.030 --> 00:36:55.090 You have to add an assertion that directly-- yeah, 00:36:55.090 --> 00:36:56.880 that's basically the rule here. 00:36:56.880 --> 00:36:58.820 Because there's a lot of choices. 00:36:58.820 --> 00:37:01.440 But he wanted one particular answer. 00:37:01.440 --> 00:37:03.105 And so can anyone think of an assertion 00:37:03.105 --> 00:37:06.650 that doesn't match any consequent of any rule that 00:37:06.650 --> 00:37:11.560 will make her be Hermione's friend. 00:37:11.560 --> 00:37:13.680 A lot of people say Millicent lives in Gryffindor. 00:37:13.680 --> 00:37:14.304 That's correct. 00:37:14.304 --> 00:37:16.640 So, part three, your solution to part two 00:37:16.640 --> 00:37:18.650 causes an uncommon situation. 00:37:18.650 --> 00:37:21.140 What is the uncommon situation? 00:37:21.140 --> 00:37:23.780 And what should you do to the list of assertions 00:37:23.780 --> 00:37:24.770 to solve this problem? 00:37:27.207 --> 00:37:29.040 Does anyone know what the uncommon situation 00:37:29.040 --> 00:37:31.300 would be if we added that she lives in Gryffindor? 00:37:31.300 --> 00:37:32.330 Hand is raised up here. 00:37:32.330 --> 00:37:33.935 What is your answer? 00:37:33.935 --> 00:37:36.687 [INAUDIBLE] That's true. 00:37:36.687 --> 00:37:38.270 She lives in Gryffindor and Slytherin. 00:37:38.270 --> 00:37:41.742 So how would you fix that? 00:37:41.742 --> 00:37:46.090 [INAUDIBLE] Yes, you could take out 00:37:46.090 --> 00:37:49.270 Slytherin from the assertions and say that she only 00:37:49.270 --> 00:37:50.540 lived in Gryffindor. 00:37:50.540 --> 00:37:54.159 A lot of people gave the answer to this question, 00:37:54.159 --> 00:37:55.700 which is a perfectly reasonable thing 00:37:55.700 --> 00:37:57.270 to do in a rules-basis system. 00:37:57.270 --> 00:37:59.440 They said, well, we can add a rule that 00:37:59.440 --> 00:38:06.060 says that if you live in x and y is different than x, then 00:38:06.060 --> 00:38:08.040 you can't live in y. 00:38:08.040 --> 00:38:10.520 The problem with that, among other things, 00:38:10.520 --> 00:38:13.290 is that we asked for a way to change the assertions and not 00:38:13.290 --> 00:38:13.850 the rules. 00:38:13.850 --> 00:38:15.340 And you gave us a way to change the assertions. 00:38:15.340 --> 00:38:16.340 That's the right answer. 00:38:22.310 --> 00:38:25.210 There was another backward chaining problem, 00:38:25.210 --> 00:38:32.030 this is 2009 quiz one, and I will leave it off 00:38:32.030 --> 00:38:32.800 for the moment. 00:38:32.800 --> 00:38:35.110 You guys should take a look at it, 00:38:35.110 --> 00:38:37.550 in particular with variable binding. 00:38:37.550 --> 00:38:40.150 Because remember, you always have to bind 00:38:40.150 --> 00:38:42.171 the variable that's relevant to you. 00:38:42.171 --> 00:38:43.920 But that doesn't mean that you always have 00:38:43.920 --> 00:38:45.460 to bind all of the variables. 00:38:45.460 --> 00:38:47.270 For instance, let's say that we wanted 00:38:47.270 --> 00:38:49.290 to prove that Millicent has a bad term, which 00:38:49.290 --> 00:38:51.081 as it turns out, is what we wanted to prove 00:38:51.081 --> 00:38:52.490 in the other backward chaining. 00:38:52.490 --> 00:38:57.549 Very quickly and without doing the problem, can anyone who 00:38:57.549 --> 00:38:59.840 thinks they're very clever at backward chaining tell me 00:38:59.840 --> 00:39:03.860 exactly what things would be added to the goal tree 00:39:03.860 --> 00:39:05.590 to prove that Millicent has a bad term? 00:39:05.590 --> 00:39:06.256 Raise your hand. 00:39:06.256 --> 00:39:08.350 I won't pick out a victim because I'm asking 00:39:08.350 --> 00:39:09.955 this to happen pretty quickly. 00:39:12.750 --> 00:39:13.330 No one? 00:39:18.190 --> 00:39:20.732 All right. 00:39:20.732 --> 00:39:25.405 AUDIENCE: You would add the three antecedents to rule-- 00:39:25.405 --> 00:39:26.530 MARK SEIFTER: To rule five. 00:39:26.530 --> 00:39:28.580 So what would you add specifically? 00:39:28.580 --> 00:39:30.282 AUDIENCE: For anyone, variable-wise, 00:39:30.282 --> 00:39:32.365 you would just have to show that there is at least 00:39:32.365 --> 00:39:34.160 one person who matches. 00:39:34.160 --> 00:39:36.860 MARK SEIFTER: So can you just sort of read out, 00:39:36.860 --> 00:39:39.580 what would the first thing say with the snogs? 00:39:39.580 --> 00:39:44.200 AUDIENCE: X snogs-- or Millicent snogs anyone. 00:39:44.200 --> 00:39:47.200 MARK SEIFTER: Yeah, Millicent snogs y. 00:39:47.200 --> 00:39:48.120 That's crucial. 00:39:48.120 --> 00:39:49.910 Some people did a lot of different things. 00:39:49.910 --> 00:39:51.660 Some people put Seamus in already. 00:39:51.660 --> 00:39:53.140 You can't do that. 00:39:53.140 --> 00:39:55.970 The system is stupid, it doesn't know that the person is Seamus. 00:39:55.970 --> 00:39:57.860 Also, some people said it worked, 00:39:57.860 --> 00:39:59.610 because look, they're snogging each other, 00:39:59.610 --> 00:40:03.130 but it's the wrong snoggle direction up there. 00:40:05.650 --> 00:40:07.460 Because we have Seamus snogging Millicent, 00:40:07.460 --> 00:40:08.710 not Millicent snogging Seamus. 00:40:08.710 --> 00:40:09.418 But yes, exactly. 00:40:09.418 --> 00:40:11.440 It would be Millicent snogs y. 00:40:11.440 --> 00:40:12.980 Millicent lives in Gryffindor tower. 00:40:12.980 --> 00:40:15.160 y lives in Slytherin dungeon. 00:40:15.160 --> 00:40:19.930 So, let's give forward chaining all the attention it deserves, 00:40:19.930 --> 00:40:22.895 about eight minutes, which will be more than enough. 00:40:26.410 --> 00:40:28.570 OK, we still got all these rules. 00:40:28.570 --> 00:40:30.410 We've still got all these assertions. 00:40:30.410 --> 00:40:33.345 Instead of doing that horrible backward chaining-- well, 00:40:33.345 --> 00:40:35.640 it's not that horrible-- but we'll do forward chaining. 00:40:35.640 --> 00:40:36.880 It'll be really easy. 00:40:36.880 --> 00:40:38.900 We'll just add new assertions as they go. 00:40:38.900 --> 00:40:41.260 Remember the tiebreak order. 00:40:41.260 --> 00:40:43.400 Rules in order from 0 to 5. 00:40:43.400 --> 00:40:46.490 And if the same rule could fire off 00:40:46.490 --> 00:40:48.530 with multiple different assertions, 00:40:48.530 --> 00:40:51.160 we'll use the assertions in order from 0 to 3. 00:40:51.160 --> 00:40:55.160 So let's see. 00:40:55.160 --> 00:40:59.530 We don't have much time, but with our four assertions, 00:40:59.530 --> 00:41:01.310 let's see, what rules possibly could 00:41:01.310 --> 00:41:04.110 match with our four assertions? 00:41:04.110 --> 00:41:06.390 Well, I'll figure out for you. 00:41:06.390 --> 00:41:09.100 Do we have an assertion about an ambitious person? 00:41:09.100 --> 00:41:09.600 Yes. 00:41:09.600 --> 00:41:10.720 But they're not a squib. 00:41:10.720 --> 00:41:11.917 So not rule zero. 00:41:11.917 --> 00:41:13.750 Do we have someone that lives in Gryffindor? 00:41:13.750 --> 00:41:14.580 We absolutely do. 00:41:14.580 --> 00:41:16.019 Rule one is matches. 00:41:16.019 --> 00:41:17.810 Do we have someone that lives in Slytherin? 00:41:17.810 --> 00:41:18.560 We do. 00:41:18.560 --> 00:41:19.550 Rule two matches. 00:41:19.550 --> 00:41:21.850 Do we have a protagonist or a villain? 00:41:21.850 --> 00:41:23.680 We don't have any protagonist or villain. 00:41:23.680 --> 00:41:26.500 Rule three is not going to match because it's in an "and." 00:41:26.500 --> 00:41:28.440 do we have someone who studies a lot? 00:41:28.440 --> 00:41:30.149 We do not have someone who studies a lot. 00:41:30.149 --> 00:41:31.481 Rule four is not going to match. 00:41:31.481 --> 00:41:32.730 Do we have some snogging? 00:41:32.730 --> 00:41:34.220 We do have some snogging. 00:41:34.220 --> 00:41:36.500 So rule one, two, and five match. 00:41:36.500 --> 00:41:40.810 So m for matching, we have one, two and five. 00:41:40.810 --> 00:41:43.180 Everyone, which one wins the tiebreak between one, two, 00:41:43.180 --> 00:41:44.350 and five? 00:41:44.350 --> 00:41:47.070 One, because it comes first numerically. 00:41:47.070 --> 00:41:50.740 Which one is rule one if x lives in Gryffindor tower? 00:41:50.740 --> 00:41:52.980 The only binding for x is Seamus. 00:41:52.980 --> 00:41:54.810 Seamus lives in Gryffindor tower. 00:41:54.810 --> 00:41:57.520 We're firing off rule one. 00:41:57.520 --> 00:42:01.260 So new assertions, the first assertion that we'll add 00:42:01.260 --> 00:42:06.075 is Seamus is it a protagonist. 00:42:06.075 --> 00:42:06.575 Great. 00:42:09.380 --> 00:42:12.060 Now, there's one other thing, and it's 00:42:12.060 --> 00:42:16.590 the main thing I wanted to tell you about in forward chaining. 00:42:16.590 --> 00:42:19.420 About our old friend, rule one, now that we've done this, 00:42:19.420 --> 00:42:22.940 does rule one still match an assertion in the database? 00:42:26.430 --> 00:42:27.450 Yes. 00:42:27.450 --> 00:42:28.590 It does. 00:42:28.590 --> 00:42:32.186 But what's going to stop us from constantly doing rule one 00:42:32.186 --> 00:42:33.810 every time because it comes numerically 00:42:33.810 --> 00:42:35.650 before the other rules? 00:42:35.650 --> 00:42:38.260 What stops us there is a part of our implementation. 00:42:38.260 --> 00:42:40.840 And it's a very important part that people sometimes forget. 00:42:40.840 --> 00:42:44.240 It's what I like to call the no-impotent rules 00:42:44.240 --> 00:42:45.240 implementation detail. 00:42:45.240 --> 00:42:47.220 That is, if a rule is completely, 00:42:47.220 --> 00:42:51.190 100% impotent, it would do absolutely nothing. 00:42:51.190 --> 00:42:52.505 Then you do not fire it. 00:42:52.505 --> 00:42:53.990 You go to the next one. 00:42:53.990 --> 00:42:55.200 That's pretty important. 00:42:55.200 --> 00:42:57.350 Let's say that you possibly had a delete, which 00:42:57.350 --> 00:42:59.660 you won't have on the quiz. 00:42:59.660 --> 00:43:02.630 That means that if the thing to delete is missing, 00:43:02.630 --> 00:43:03.520 it's impotent. 00:43:03.520 --> 00:43:05.720 If the thing to delete is there, it's not impotent 00:43:05.720 --> 00:43:07.200 because you can delete. 00:43:07.200 --> 00:43:09.990 Let's say you have 500,000 things that you're going 00:43:09.990 --> 00:43:11.700 to add to your assertions. 00:43:11.700 --> 00:43:15.670 499,999 are already in your database. 00:43:15.670 --> 00:43:16.740 One of them is missing. 00:43:16.740 --> 00:43:18.390 Is it an impotent rule? 00:43:18.390 --> 00:43:19.090 No, it's not. 00:43:19.090 --> 00:43:20.360 You have to fire it anyway. 00:43:20.360 --> 00:43:23.060 You can't be like, oh, it's mostly impotent rule. 00:43:23.060 --> 00:43:23.560 No. 00:43:23.560 --> 00:43:27.147 You have fire off the rule if it will do anything. 00:43:27.147 --> 00:43:29.730 But right now rule one won't do anything because we've already 00:43:29.730 --> 00:43:31.590 added Seamus is a protagonist. 00:43:31.590 --> 00:43:34.260 So what rules match down? 00:43:34.260 --> 00:43:37.510 Well, Seamus becoming a protagonist is nice and all, 00:43:37.510 --> 00:43:40.620 but he's not ambitious, so we still don't match rule three. 00:43:40.620 --> 00:43:43.230 We still match rules one, two, and five. 00:43:43.230 --> 00:43:45.460 As I basically just got finished telling you, 00:43:45.460 --> 00:43:48.930 the one that we're going to fire off now is two. 00:43:48.930 --> 00:43:50.000 That's right. 00:43:50.000 --> 00:43:54.240 So, rule two is if x lives in Slytherin dungeon 00:43:54.240 --> 00:43:57.130 our only [? binding ?] for that is Millicent. 00:43:57.130 --> 00:43:59.950 And that will show that she's a villain and she's ambitious. 00:43:59.950 --> 00:44:04.372 So what assertions will we add? 00:44:04.372 --> 00:44:05.330 Millicent is a villain. 00:44:05.330 --> 00:44:06.570 And people stopped. 00:44:06.570 --> 00:44:07.380 That's right. 00:44:07.380 --> 00:44:08.410 Good job, everyone. 00:44:08.410 --> 00:44:10.350 You remembered that Millicent is already 00:44:10.350 --> 00:44:15.080 ambitious from assertion one, so we don't have to add them both. 00:44:15.080 --> 00:44:16.340 A lot of people did. 00:44:16.340 --> 00:44:17.580 They were wrong. 00:44:17.580 --> 00:44:21.550 So Millicent is a villain. 00:44:21.550 --> 00:44:24.020 The other part of that rule doesn't do anything. 00:44:24.020 --> 00:44:26.420 But it's not an impotent rule because one of the things 00:44:26.420 --> 00:44:27.410 is not on there. 00:44:27.410 --> 00:44:29.740 Great. 00:44:29.740 --> 00:44:31.890 So, what rules match now? 00:44:31.890 --> 00:44:34.150 Well, as it turns out, now that Millicent 00:44:34.150 --> 00:44:37.700 is a villain and ambitious, we match rule three as well. 00:44:37.700 --> 00:44:41.370 So we match one, two, three, and five. 00:44:41.370 --> 00:44:43.710 What rule are we going to fire, everyone? 00:44:43.710 --> 00:44:44.210 Three. 00:44:44.210 --> 00:44:47.470 Because one and two are impotent rules. 00:44:47.470 --> 00:44:48.890 We'll fire rule three. 00:44:48.890 --> 00:44:50.800 Well, Millicent is a villain. 00:44:50.800 --> 00:44:51.770 She's also ambitious. 00:44:51.770 --> 00:44:53.890 She's our only match for three. 00:44:53.890 --> 00:44:57.250 Therefore, what assertion do we add? 00:44:57.250 --> 00:44:58.250 Millicent studies a lot. 00:44:58.250 --> 00:44:58.791 That's right. 00:45:05.030 --> 00:45:07.220 So, Millicent studies a lot. 00:45:07.220 --> 00:45:08.820 However, she's not a protagonist. 00:45:08.820 --> 00:45:12.180 We still don't match rule four. 00:45:12.180 --> 00:45:14.520 Oh well, we figured that out already ourselves 00:45:14.520 --> 00:45:17.400 from backward chaining that we were never going to match that. 00:45:17.400 --> 00:45:19.210 So what matches? 00:45:19.210 --> 00:45:21.200 It's still one, two, three, and five. 00:45:21.200 --> 00:45:22.950 Seeing as one, two and three are impotent, 00:45:22.950 --> 00:45:26.695 the only match is five. 00:45:26.695 --> 00:45:28.570 So the only match we care about, the only one 00:45:28.570 --> 00:45:30.970 we're going to fire is five. 00:45:30.970 --> 00:45:32.220 And the result? 00:45:32.220 --> 00:45:33.280 Let's see. 00:45:33.280 --> 00:45:34.180 x snogs y. 00:45:34.180 --> 00:45:36.020 That's Seamus snogs Millicent. 00:45:36.020 --> 00:45:39.010 x lives in Gryffindor, that's Seamus. 00:45:39.010 --> 00:45:41.130 y lives in Slytherin, that's Millicent. 00:45:41.130 --> 00:45:43.870 So what do we add? 00:45:43.870 --> 00:45:45.360 Seamus has a bad term. 00:45:56.660 --> 00:46:00.000 Simple, painless, it works out. 00:46:00.000 --> 00:46:00.860 We're done. 00:46:00.860 --> 00:46:03.430 And we got 100 on this quiz. 00:46:03.430 --> 00:46:05.180 Hopefully you guys will, too. 00:46:05.180 --> 00:46:06.000 Question? 00:46:06.000 --> 00:46:09.640 The question is, if you have a new assertion which matches 00:46:09.640 --> 00:46:11.520 a rule but it's really high number, 00:46:11.520 --> 00:46:14.150 it's all the way down at the bottom of the rules, 00:46:14.150 --> 00:46:16.350 but it's new and it has new stuff, 00:46:16.350 --> 00:46:20.220 should we do that first, maybe, because it's new? 00:46:20.220 --> 00:46:23.075 Oh, you mean that it has a lower number, a lower number? 00:46:23.075 --> 00:46:23.950 AUDIENCE: [INAUDIBLE] 00:46:23.950 --> 00:46:25.630 MARK SEIFTER: OK, so the question 00:46:25.630 --> 00:46:29.270 is, if a rule-- let's say that rule three made Millicent 00:46:29.270 --> 00:46:30.920 be a squib. 00:46:30.920 --> 00:46:33.090 Then yes, you'd immediately not only match 00:46:33.090 --> 00:46:36.715 zero-- zero would immediately fire because numerically 00:46:36.715 --> 00:46:37.900 it comes first. 00:46:37.900 --> 00:46:39.790 You'll see that on some of the old quizzes. 00:46:39.790 --> 00:46:41.604 And you may see that in tutorial. 00:46:41.604 --> 00:46:44.270 If you guys want to do some more practice problems in tutorials, 00:46:44.270 --> 00:46:46.356 your TAs will have that available as one 00:46:46.356 --> 00:46:47.355 opportunity in tutorial. 00:46:47.355 --> 00:46:48.930 But yeah, that's exactly right. 00:46:48.930 --> 00:46:50.930 It happened that it went in order this time, 00:46:50.930 --> 00:46:53.130 but it will definitely hop anywhere 00:46:53.130 --> 00:46:57.217 it can in order to get to the lowest numbered assertion.