| 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+ |
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| 12 |
Introduction to predicate logic: quantifiers, variables, constants, predicates, universe of discourse |
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| 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) |
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| 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 |
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| 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 |
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