SE 212

#class

Logic and Computation

Prereqs: Math 135

1. Course intro
   • George
2. Propositional logic
   • Logic
   • Propositional Logic
   • Formalizing Propositional Logic
   • Proof theories
     • Transformational Proof
       • Simplifying Conditionals
     • Natural Deduction
     • Semantic Tableaux
3. Predicate logic
   • Predicate Logic
   • Formalizing Predicate Logic
   • Proof theories
     • Natural Deduction (Predicate Logic)
     • Semantic Tableaux (Predicate Logic)
4. Theories
   • Hidden Premises
   • Theories
   • Predicate Logic with Equality
   • Theory of Natural Number Arithmetic
     • Gödel's Incompleteness Theorem
   • Satisfiable Modulo Theories Solvers
5. Set Theory
   • Summary of axioms: Set Theory Axioms (SE212)
   • Set Theory
   • Set Builder Notation
   • Subsets
   • Set Equality
   • Power Set
   • Formalizing Set Theory
   • Example Set Theory ND Proof: Subsets#^f65b37
   • Example Set Theory TP Proof: Transformational Proof (Predicate Logic)
   • Counterexamples for Set Theory
   • Russel's Paradox
   • Relations
   • Formalizing Set Theory#Formalizing Relations
6. Formal Specification in Z
   • Formal Specification
   • Z Specification
7. Program correctness
   • Formal Verification
   • Floyd-Hoare Logic
   • The Halting Problem