Rozhodnutelné podtřídy formulí predikátového počtu 1. řádu

Abstract

Complete and, of course, indisputable proof calculi exist for the first-order predicate logic. By Kurt Gödel’s completeness theorem, a calculus (such as the Hilbert Calculus) with the following property can be developed: Each logical true formula is provable and (by the stronger version of the completeness theorem) if a given formula logically follows from given axioms, then it is provable from these axioms. There are not, however, any calculi where it would be possible to decide whether or not a given formula is logically true or whether it is the consequence of a given set of axioms. This is one of the implications of Gödelov’s first incompleteness theorem. Therefore, we say in short that the first-order predicate logic is undecidable. There are however a large number of predicate calculus formulae subclasses that have the desirable property of being decidable. The goal of this diploma thesis has been to compile a synoptic study of such first-order predicate logic formulae subclasses and put it into the form of a webpage so that the results are accessible for teaching the subjects of select parts of mathematical logic. These results can also find further application in the theory and practice of automated proving of theorems.