fuzzy logic; deduction; resolution;

The thesis presents refutational resolution theorem proving system for both the classical and many-valued logics based on the general (non-clausal) resolution rule. There is also presented a unification algorithm handling existentiality without the need of skolemization. This formalism integrates properties especially suitable for description logic and for fuzzy predicate logic. The problem of automated reasoning concerning fuzzy logic requires more complex methods in contrast to classical logic. Presented formalism overcomes the key unsolvable obstacle - clausal normal form generation (in fuzzy logic) - by introduction of generally applicable inference rule (working with general formulas not only clauses). Additionally we present several inference strategies for efficient theorem proving in fuzzy logic based on Detection of Consequent Formulas algorithm.

The thesis presents refutational resolution theorem proving system for both the classical and many-valued logics based on the general (non-clausal) resolution rule. There is also presented a unification algorithm handling existentiality without the need of skolemization. This formalism integrates properties especially suitable for description logic and for fuzzy predicate logic. The problem of automated reasoning concerning fuzzy logic requires more complex methods in contrast to classical logic. Presented formalism overcomes the key unsolvable obstacle - clausal normal form generation (in fuzzy logic) - by introduction of generally applicable inference rule (working with general formulas not only clauses). Additionally we present several inference strategies for efficient theorem proving in fuzzy logic based on Detection of Consequent Formulas algorithm.