Tentative Syllabus
Here is an overview of the material that I would like to cover. I
reserve the right to make modifications based on the interests of
the class and/or time constraints.
- Propositional Logic
- Syntax, semantics & theories
- Compactness
- Complexity: hardness results & efficiently decidable cases, including 2SAT & HORNSAT
- BDDs (Boolean Decision Diagrams)
- Davis-Putnam-Loveland-Logemann SAT algorithm
- First-Order Logic
- Syntax, semantics & model theory for FOL
- Proof theory & its soundness
- Completeness of FOL
- Compactness, Lowenheim-Skolem, & related theorems
- FOL as the foundations of mathematics
- Undecidability of FOL & arithmetic
- Godel's incompleteness theorems
- Decision Procedures
- Uninterpreted functions & equality
- Presburger arithmetic
- Linear arithmetic
- Combining decision procedures with SMT
- ACL2 (A Computational Logic for Applicative Common Lisp)
- The ACL2 programming language
- The ACL2 logic, recursion and induction
- Effective use of the ACL2 theorem prover & applications
- Selected topics in mechanized reasoning