Logic for Computer Scientists I11003

Course content:

Propositional Logic:
The language and its semantics (propositional variables, connectives, formulas). Propositional tautologies.
Disjunctive and conjunctive normal forms.

First-Order Logic:
First-order language (terms and formulas).Free variables of a formula, sentences. Semantics. Satisfability. Examples of first-order tautologies.

Proof Theory of Propositional Logic::
Deductive systems (logical axioms and inference rules, specific axioms). Properties of the logical consequence operation. Deduction and completeness theorems.

Proof Theory of First-Order Logic:
Deductive systems (logical axioms and inference rules, specific axioms).Deduction and completeness theorems.

Logics of Programs:
Hoare Logic,
Algorithmic Logic,
Dynamic Logic.

Learning outcomes:
Students should be acquainted with deductive systems on propositional and first-order levels and logics of programs and produce correctness proofs for simple algorithms.