Open AccessFixed-point models for paradoxical predicates
Author(s) -
Luca Castaldo
Publication year - 2021
Publication title -
australasian journal of logic
Language(s) - English
Resource type - Journals
ISSN - 1448-5052
DOI - 10.26686/ajl.v18i7.6576
Subject(s) - fixed point , consistency (knowledge bases) , kripke semantics , semantics (computer science) , kripke structure , mathematics , fixed point theorem , point (geometry) , computer science , discrete mathematics , algorithm , artificial intelligence , model checking , intermediate logic , description logic , mathematical analysis , programming language , geometry
This paper introduces a new kind of fixed-point semantics, filling a gap within approaches to Liar-like paradoxes involving fixed-point models à la Kripke (1975). The four-valued models presented below, (i) unlike the three-valued, consistent fixed-point models defined in Kripke (1975), are able to differentiate between paradoxical and pathological-but-unparadoxical sentences, and (ii) unlike the four-valued, paraconsistent fixed-point models first studied in Visser (1984) and Woodruff (1984), preserve consistency and groundedness of truth.Keywords: Semantic Paradoxes · Fixed-point semantics · Many-valued logic · Kripke’s theory oftruth