A lattice of the paracomplete calculi-Reference-Cited by-同舟云学术

A lattice of the paracomplete calculi

Published:2020-08-08 Issue:1 Volume:26 Page:110-123
ISSN:2413-2713
Container-title:Logical Investigations
language:
Short-container-title:LI

Author:

Ciuciura Janusz

Abstract

Paracomplete logic is intended to cope with the problem of vagueness, or uncertain and incomplete data. It deals with the situation when some propositions and their negations are allowed to be simultaneously false, which is obviously impossible in the classical and many non--classical propositional logics. In paracomplete logic, such classical laws as tertium non datur or consequentia mirabilis are not generally accepted. This implies that the logic is defined negatively. In this paper, we introduce a family of the paracomplete calculi that will be defined in a Hilbert-style formalization. We propose the so-called bi--valuational semantics and prove the key metatheorems for the calculi. We also discuss a generalization of the paracomplete calculus $QD^{1}$ to the hierarchy of related calculi.

Publisher

Institute of Philosophy, Russian Academy of Sciences

Subject

Applied Mathematics

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