24.241
Logic I
Fall 2009
Topics
- Basic notions of logic; arguments; the connectives
- Truth-functionality; introduction to sentential logic (SL) syntax and semantics; translation
- Translation continued; problems with conditionals and other phenomena of natural language; truth-tables
- Truth-tables and logical properties of compound sentences
- Entailment and validity with truth-tables
- Derivations in sentential logic (SD)
- Derivations in SD/SD+
- Theorem-proving, review
- Introduction to meta-theory; mathematical induction
- Soundness of SD/SD+
- Completeness of SD/SD+
- Introduction to predicate logic: quantifiers, variables, constants, predicates, universe of discourse
- Open sentences; free vs. bound variables; scope, multiply quantified sentences; definite descriptions; properties of relations
- Identity; functions, translation to and from predicate logic (PL)
- Translation to and from PL/PLE; “most”; donkey sentences
- Informal PL/PLE semantics: Interpretations, substitutions, quantification truth, falsity, consistency, and equivalence, quantificational argument validity
- Formal PL/PLE semantics: Extensions, interpretations, variable assignments, satisfaction, truth and falsity under interpretations and variable assignments
- Formal PL/PLE semantics continued; review
- Derivations in PD
- Derivations in PD+/PDE
- Derivations in PDE continued; preliminaries for meta-theory
- Meta-theory: Soundness of PD, PD+, PDE
- Meta-theory: Completeness of PD
- Meta-theory: Completeness continued; PD+; PDE
Readings
- The required text is: Bergmann, Merrie, James Moor, and Jack Nelson. The Logic Book . 5th ed. New York, NY: McGraw-Hill, 2008. ISBN: 9780073535630.
- Reading assignments are from the required textbook: Bergmann, Merrie, James Moor, and Jack Nelson. The Logic Book . 5th ed. New York, NY: McGraw-Hill, 2008. ISBN: 9780073535630.
- LEC #: 2 · TOPICS: Truth-functionality; introduction to sentential logic (SL) syntax and semantics; translation · READINGS: Chapter 1
- LEC #: 3 · TOPICS: Translation continued; problems with conditionals and other phenomena of natural language; truth-tables · READINGS: Chapter 2
- LEC #: 4 · TOPICS: Truth-tables and logical properties of compound sentences · READINGS: Chapter 3
- LEC #: 7 · TOPICS: Derivations in SD/SD+ · READINGS: Chapter 5
- LEC #: 8 · TOPICS: Theorem-proving, review · READINGS: Chapter 6.1-6.2
- LEC #: 9 · TOPICS: Introduction to meta-theory; mathematical induction · READINGS: Chapter 6.3
- LEC #: 11 · TOPICS: Completeness of SD/SD+ · READINGS: Chapter 6.3-6.4
- LEC #: 14 · TOPICS: Identity; functions, translation to and from predicate logic (PL) · READINGS: Chapter 7.1-7.7
- LEC #: 16 · TOPICS: Informal PL/PLE semantics: Interpretations, substitutions, quantification truth, falsity, consistency, and equivalence, quantificational argument validity · READINGS: Chapter 7.8, 8.1-8.4
- LEC #: 17 · TOPICS: Formal PL/PLE semantics: Extensions, interpretations, variable assignments, satisfaction, truth and falsity under interpretations and variable assignments · READINGS: Chapter 7.9, 8.6
- LEC #: 18 · TOPICS: Formal PL/PLE semantics continued; review · READINGS: Chapter 8.7
- LEC #: 20 · TOPICS: Derivations in PD+/PDE · READINGS: Chapter 10.1-10.2
- LEC #: 21 · TOPICS: Derivations in PDE continued; preliminaries for meta-theory · READINGS: Chapter 10.4
- LEC #: 23 · TOPICS: Meta-theory: Completeness of PD · READINGS: Chapter 11.3-11.4
- LEC #: 24 · TOPICS: Meta-theory: Completeness continued; PD+; PDE · READINGS: Chapter 11.1-11.4
Sources
- Course catalogue ↗Historical OpenCourseWare
- MIT OCW calendar ↗
- MIT OCW syllabus ↗
- MIT OCW readings ↗
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.