Lectures:
The notion of relation: Homogeneous and heterogeneous relations. Binary relations and their types. Reflexivity, ireflexivity, symmetry, antisymmetry, asymmetry, tranzitivity.
Mapping as a special type of relation. Complete, total, partial mapping. Surjection, injection, bijection. Semantic exposition of propositional and 1st-order predicate logic.
Basic principles of logical calculi and theories. The notion of a proof, axiom and theorem.
Rezolution method of proving logical validity and validity of an argument. Robinson's unification algorithm. Logical programming.
The natural deduction system (Gentzen). Proof in the system. Soundness and completeness.
Hilbert-like proof calculus. The notion of a proof in the calculus. Theorem of deduction, soundness and completeness.
Axiomatic theories and their properties.
The set theory, relational and algebraic theories. Robinson and Peano arithmetic. (In)completeness, decidability, models.
Gödel theorems and their importance in computer science.
Closure of a relation, equivalence, factor set.
Ordering Relations (partial, complete, quasi-ordering, linear).
General notion of an operation. Algebras and their morphisms.
Fundamentals of the lattice theory.
Exercises:
Deductively valid arguments
Naive theory of sets
Propositional logic, language and semantics
Resolution method in propositional logic
First-order predicate logic, language and semantics
Relation, function, countable and uncountable sets
Semantic tableau
Aristotelova logika
Resolution method in 1st-order predicate logic
Proof calculi: natural deduction and Hilbert calculus
Theory of relations, functions, algebras
Projects:
Solving a given problem by natural deduction and resolution methods
The notion of relation: Homogeneous and heterogeneous relations. Binary relations and their types. Reflexivity, ireflexivity, symmetry, antisymmetry, asymmetry, tranzitivity.
Mapping as a special type of relation. Complete, total, partial mapping. Surjection, injection, bijection. Semantic exposition of propositional and 1st-order predicate logic.
Basic principles of logical calculi and theories. The notion of a proof, axiom and theorem.
Rezolution method of proving logical validity and validity of an argument. Robinson's unification algorithm. Logical programming.
The natural deduction system (Gentzen). Proof in the system. Soundness and completeness.
Hilbert-like proof calculus. The notion of a proof in the calculus. Theorem of deduction, soundness and completeness.
Axiomatic theories and their properties.
The set theory, relational and algebraic theories. Robinson and Peano arithmetic. (In)completeness, decidability, models.
Gödel theorems and their importance in computer science.
Closure of a relation, equivalence, factor set.
Ordering Relations (partial, complete, quasi-ordering, linear).
General notion of an operation. Algebras and their morphisms.
Fundamentals of the lattice theory.
Exercises:
Deductively valid arguments
Naive theory of sets
Propositional logic, language and semantics
Resolution method in propositional logic
First-order predicate logic, language and semantics
Relation, function, countable and uncountable sets
Semantic tableau
Aristotelova logika
Resolution method in 1st-order predicate logic
Proof calculi: natural deduction and Hilbert calculus
Theory of relations, functions, algebras
Projects:
Solving a given problem by natural deduction and resolution methods