Lectures:
Introduction to logic: What is the subject matter of logic? Where and how can logic be helpful for us. Logic as the theory of correct argumentation, logical entailment (consequence).
The language of propositional logic. Definition of truth-value connectives.
The analysis of natural language statements in the language of propositional logic. The semantics of propositional logic: valuation, truth-value functions, tautology, contradiction, satisfaction.
Consequence relation in propositional logic. Semantic methods of justifying arguments in propositional logic.
Complete system of connectives. Normal forms, functional completeness, logical consequences of a set of formulae.
Resolution in propositional logic and its using.
Correct arguments that are not analysable in propositional logic. Language of 1st-order predicate logic, free and bound variables, collisionlessly substituting terms for variables.
Semantics of the 1st-order predicate logic, the notions of interpretation and model. Analysis of natural language expressions in the language of 1st-order predicate logic.
Satisfaction of formulae, formulae true in an interpretation, logically true formulae, contradictions, the consequence relation in the 1st-order predicate logic.
Semantic methods of proving justified arguments. Traditional (Aristotelian) logic.
Deduction in the 1st-order predicate logic, semantic tableau. The set of logically true formulae is not decidable.
Formal systems. Characteristics and features of formal systems. The set of axioms and theorems. The notion of a proof in a formal system. Completeness of 1st-order predicate logic.
Theoretical fundamentals of logic programming. Prenex normal forms, Skolem's clausal forms, Herbrand's procedure - the basic resolution method.
General resolution method and Robinson's unification algorithm.
Exercises:
Examples of arguments formulated in natural language
The analysis of sentences in the language of propositional logic
Negation of sentences
Semantic methods of justifying arguments in propositional logic
Normal forms of formulae in propositional logic
Logical consequences of the set of formulae
Resolution method in propositional logic and its using
The analysis of natural language sentences in the predicate logic
Negation of sentences, equivalent transformations
Interpretation of formulae, models
Semantic methos of justifying arguments in predicate logic
Scolem's clausal forms
Resolution in predicate logic
Proof in a formal system. Gentzen's natural deduction
Introduction to logic: What is the subject matter of logic? Where and how can logic be helpful for us. Logic as the theory of correct argumentation, logical entailment (consequence).
The language of propositional logic. Definition of truth-value connectives.
The analysis of natural language statements in the language of propositional logic. The semantics of propositional logic: valuation, truth-value functions, tautology, contradiction, satisfaction.
Consequence relation in propositional logic. Semantic methods of justifying arguments in propositional logic.
Complete system of connectives. Normal forms, functional completeness, logical consequences of a set of formulae.
Resolution in propositional logic and its using.
Correct arguments that are not analysable in propositional logic. Language of 1st-order predicate logic, free and bound variables, collisionlessly substituting terms for variables.
Semantics of the 1st-order predicate logic, the notions of interpretation and model. Analysis of natural language expressions in the language of 1st-order predicate logic.
Satisfaction of formulae, formulae true in an interpretation, logically true formulae, contradictions, the consequence relation in the 1st-order predicate logic.
Semantic methods of proving justified arguments. Traditional (Aristotelian) logic.
Deduction in the 1st-order predicate logic, semantic tableau. The set of logically true formulae is not decidable.
Formal systems. Characteristics and features of formal systems. The set of axioms and theorems. The notion of a proof in a formal system. Completeness of 1st-order predicate logic.
Theoretical fundamentals of logic programming. Prenex normal forms, Skolem's clausal forms, Herbrand's procedure - the basic resolution method.
General resolution method and Robinson's unification algorithm.
Exercises:
Examples of arguments formulated in natural language
The analysis of sentences in the language of propositional logic
Negation of sentences
Semantic methods of justifying arguments in propositional logic
Normal forms of formulae in propositional logic
Logical consequences of the set of formulae
Resolution method in propositional logic and its using
The analysis of natural language sentences in the predicate logic
Negation of sentences, equivalent transformations
Interpretation of formulae, models
Semantic methos of justifying arguments in predicate logic
Scolem's clausal forms
Resolution in predicate logic
Proof in a formal system. Gentzen's natural deduction