Content

Propositional logic: combinatorial problems as propositional problems. Methods for efficient solution and representation of propositional problems (Davis–Putnam, BDDs).
Modal logic: possible worlds semantics, Kripke models.
Interpretations of modal logic: Temporal logic and epistemic logic. Applications in model checking.
Equational logic: terms, unification, universal algebra, equational reasoning, term rewriting.
Predicate logic and proof search: the completeness theorem, proof search in some calculi (tableaux, resolution).
Solvable and unsolvable problems: complete and decidable theories, quantifier elimination, Gödel’s incompleteness theorem (without proof).
Constructive logic and type theory: lambda calculus, simple type theory, intuitionistic logic, Martin-Löf type theory, propositions-as-types, program extraction from proofs, logical frameworks, proof support systems (Coq, Hol, Isabelle or Agda).

Instructions

Lectures and problem solving sessions.

Assessment

Written and, possibly, oral examination at the end of the course. Moreover, compulsory assignments may be given during the course.