Návrh algoritmu pro rozhodování vybraných podtříd predikátové logiky 1. řádu

Abstract

The problem in predicate logic is that the logical truthfulness of formulas is undecidable. This means that there is no general algorithm that should always be decided with absolute certainty whether a given formula of predicate logic tautology, contradiction or only achievable. However, there are large areas where the problem is successfully mastered and those are decidable subclasses. These subclasses have been introduced in the diploma thesis of Radim Vasicek from 2012 called "Decidable subclass of predicate logic formulas of the first order." This thesis presents gradually these subclasses. Designs and implements an algorithm for decision making. The result is a program that accepts input formula of predicate logic verifies that meets some of the subclasses and by implementing proving calculus, this subclass decides.