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