A fuzzy and intuitionistic fuzzy account of the Liar paradox

Abstract

The Liar paradox, or the sentence "What I am now saying is false." and its various guises have been attracting the attention of logicians and linguists since ancient times. A commonly accepted treatment of the Liar paradox [7,8] is by means of Situation semantics, a powerful approach to natural language analysis. It is based on the machinery of non-well-founded sets developed in [1]. In this paper we show how to generalize these results including elements of fuzzy and intuitionistic fuzzy logic [3,4]. Basing on the results, a way is proposed towards solving the problem of modelling the two levels of Situation theory -- infons and propositions -- with a single one retaining the specific features of the two-levels logics.