CST 329

Reasoning and Logic

CST 329: Reasoning and Logic

In this course students learn to develop skill in using logic to describe and assess arguments. Students will learn to write formulas in propositional and first-order logic, and more importantly, to write and check proofs. Students will also learn to write formulas in three-valued and modal logic, know how to choose an appropriate logic, and understand the limitations of logic in capturing human reasoning.

Week 1

Topics

  • Defined The language of logic
  • Built and interpreted logical sentences involving implication and negations
  • Defined arguments

Week 2

Topics

  • Checked the validity of arguments using a truth table
  • Check the validity of arguments using direct proofs

Week 3

Topics

  • Wrote proofs using rules for conjunction
  • Identified top-level operators and used sub-formulas to create a truth table
  • Used conditional derivation in proofs
  • Defined tautology and theorem

Week 4

Topics

  • Wrote proofs using rules for disjunction
  • Used contradictions in proofs

Week 5

Topics

  • Wrote proofs using IFF
  • Introduced to First ORder Logic (FOL)
  • Wrote logic with proper names and predicates
  • Defined universal and existential quantifiers
  • Determined WFF and Sentences
  • Translated sentences from English to FOL

Week 6

Topics

  • Incorporated universal instantiation in proofs
  • Incorporated existential generalization in proofs
  • Used existential instantiation in proofs
  • Used universal derivation in proofs

Week 7

Topics

  • Showed when a FOL argument is invalid
  • Used functions in FOL translations
  • Used identities in translations and proofs

Week 8

Topics

  • Review

Sample Proof

logical proof