24.241 | Fall 2009 | Undergraduate

# Logic I

## Calendar

LEC # TOPICS KEY DATES
1 Basic notions of logic; arguments; the connectives
2 Truth-functionality; introduction to sentential logic (SL) syntax and semantics; translation
3 Translation continued; problems with conditionals and other phenomena of natural language; truth-tables
4 Truth-tables and logical properties of compound sentences Problem set 1 due
5 Entailment and validity with truth-tables
6 Derivations in sentential logic (SD) Problem set 2 due
7 Derivations in SD/SD+
8 Theorem-proving, review Problem set 3 due
9 Introduction to meta-theory; mathematical induction
10 Soundness of SD/SD+ Problem set 4 due
11 Completeness of SD/SD+
12 Introduction to predicate logic: quantifiers, variables, constants, predicates, universe of discourse
13 Open sentences; free vs. bound variables; scope, multiply quantified sentences; definite descriptions; properties of relations Problem set 5 due
14 Identity; functions, translation to and from predicate logic (PL)
15 Translation to and from PL/PLE; “most”; donkey sentences Problem set 6 due
16 Informal PL/PLE semantics: Interpretations, substitutions, quantification truth, falsity, consistency, and equivalence, quantificational argument validity
17 Formal PL/PLE semantics: Extensions, interpretations, variable assignments, satisfaction, truth and falsity under interpretations and variable assignments Problem set 7 due
18 Formal PL/PLE semantics continued; review
19 Derivations in PD Problem set 8 due
20 Derivations in PD+/PDE
21 Derivations in PDE continued; preliminaries for meta-theory Problem set 9 due
22 Meta-theory: Soundness of PD, PD+, PDE
23 Meta-theory: Completeness of PD Problem set 10 due
24 Meta-theory: Completeness continued; PD+; PDE
25 Review

## Course Info

Fall 2009
##### Learning Resource Types
Problem Sets with Solutions
Exams
Lecture Notes