An Extended Syllogistic Logic for Automated Reasoning

Abstract

In this work, we generalise the categorical syllogistic logic in several dimensions to a relatively expressive logic that is sufficiently powerful to encompass a wider range of linguistic semantics. The generalisation is necessary in order to eliminate the existential ambiguity of the quantifiers and to increase expressiveness, practicality, and adaptivity of the syllogisms. The extended semantics is expressed in an extended syntax such that an algorithmic solution of the extended syllogisms can be processed. Our algorithmic approach for deduction in this logic allows for automated reasoning directly with quantified propositions, without reduction of quantifiers.