Free Quantification in Four-Valued and Fuzzy Bilattice-Valued Logics
Abstract
We introduce a variant of free logic (i.e., a logic admitting terms with nonexistent referents) that accommodates truth-value gluts as well as gaps. Employing a suitable expansion of the Belnap-Dunn four-valued logic, we specify a dual-domain semantics for free logic, in which propositions containing non-denoting terms can be true, false, neither true nor false, or both true and false. In each model, the dual domain semantics separates existing and non-existing objects into two subdomains, making it possible to quantify either over all objects or existing objects only. We also outline a fuzzy variant of the dual-domain semantics, accommodating non-denoting terms in fuzzy contexts that can be partially indeterminate or inconsistent.
Cite
@article{arxiv.2306.13079,
title = {Free Quantification in Four-Valued and Fuzzy Bilattice-Valued Logics},
author = {Libor Behounek and Martina Dankova and Antonin Dvorak},
journal= {arXiv preprint arXiv:2306.13079},
year = {2023}
}
Comments
12 pages, to appear in the proceedings of the IUKM 2023 Conference. Version 2: minor corrections and terminology changes