Mathematical Logic via Foundational Algorithms CS 410/510 Mathematical Logic via Foundational Algorithms
Winter term, 2011
CRN 44342 (CS 410) and 44343 (CS 510)
Tuesday / Thursday 14:00-15:50
Fourth Avenue Building (FAB), room 150.

Day Date Notes Topic Readings Exercises Problem sets Due Today
T1 Jan 4 Propositional Logic: definition, natural deduction proofs
MCECS Innovation Proposal announcement.
Read: HR 1.1-3 outline.pdf 1 Exercise 1. Natural Deduction forward style Proofs.
H1 Jan 6 Prop logic: truth, validity, satisfiability, tautology, soundness HR 1.4 outline.pdf 2 Exercise 2. Natural Deduction in HR style P1. Write a tautology checker. Exercise 1.
T2 Jan 11 Prop logic: Tableau proof

HR 1.4 - 1.6
(Fitting Chapter 3) outline.pdf 3

Exercise 3: Proofs in tableau style and L style   Exercise 2
H2 Jan 13 Prop logic: completeness, deciding truth, normal forms,   Exercise 4. Using minisat to test tautologies.
Installing MiniSat on Windows
.
Installing MiniSat on Mac
P2. Write a toCNF function P1 - Tautology. Exercise 3
T3 Jan 18 SAT solvers. Applications of SAT solvers. Representing and asking questions about finite sets. The FiniteSet module Exercise 5. An algebra of sets.   Exercise 4
H3 Jan 20 Applications of SAT solvers.   predicate logic word problems P3. 4x4 Soduko Solver.
Minisat library. Installing MiniSat on Windows. Installing MiniSat on Mac
P2 - CNF.
T4 Jan 25 SAT solver internals HR 1.6, outline.pdf 6 Exercise 6: Reassembling the cubic solver (link coming soon)   Exercise 5.
H4 Jan 27 Predicate Logic: Introduction, Syntax, Substitution, Semantics HR 2.1 -- 2.4, outline.pdf 7   outline.pdf 7.4

P3 - Soduko Solver

Exercise 6

T5 Feb 1 Tableau proofs; Herbrand models; Model existance theorem

outline.pdf 8,
(Fitting Chapter 5)

H5 Feb 3 NK, LK, and Tableau proof systems. Soundness and completeness.   Exercise 7: A prover for LK   outline.pdf 7.4
T6 Feb 8 Automating proof systems, Skolem functions, unification     outline.pdf Problem Set 10.3: unification and tableau prover
H6 Feb 10 SMT provers
T7 Feb 15 Path coverage using SMT       outline.pdf 10.3
H7 Feb 17
T8 Feb 22 Higher-order logics outline.pdf 11
H8 Feb 24 Propositions as Types outline.pdf 12 Some examples of Curry-Howard in Haskell
T9 Mar 1 Temporal Logic and model checking: Intro, Examples, NuSMV HR 3.1 -- 3.5 Download NuSMV (Mac ports for mac; http://nusmv.fbk.eu/ for Linux and Windows)
H9 Mar 3 Foundations: Process language; Kripke Models; Semantics; A Model checking algorithm HR 3.5 -- 3.7 (Clarke, Grumberg, and Peled 2, 3, 4)     Share Experiences with NuSMV
T10 Mar 8 BDDs Chapter 6
H10 Mar 10

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