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REXPANSIONS OF NONDETERMINISTIC MATRICES AND THEIR APPLICATIONS IN NONCLASSICAL LOGICS

Published online by Cambridge University Press:  26 October 2018

ARNON AVRON  and
YONI ZOHAR
ARNON AVRON*
Affiliation:
School of Computer Science, Tel Aviv University
YONI ZOHAR*
Affiliation:
School of Computer Science, Tel Aviv University
*
*SCHOOL OF COMPUTER SCIENCE TEL AVIV UNIVERSITY TEL AVIV, ISRAEL E-mail: aa@cs.tau.ac.il
†SCHOOL OF COMPUTER SCIENCE TEL AVIV UNIVERSITY TEL AVIV, ISRAEL E-mail: yoni.zohar@cs.tau.ac.il
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Abstract

The operations of expansion and refinement on nondeterministic matrices (Nmatrices) are composed to form a new operation called rexpansion. Properties of this operation are investigated, together with their effects on the induced consequence relations. Using rexpansions, a semantic method for obtaining conservative extensions of (N)matrix-defined logics is introduced and applied to fragments of the classical two-valued matrix, as well as to other many-valued matrices and Nmatrices. The main application of this method is the construction and investigation of truth-preserving ¬-paraconsistent conservative extensions of Gödel fuzzy logic, in which ¬ has several desired properties. This is followed by some results regarding the relations between the constructed logics.

Keywords

03B5003B5203B5303B60non-deterministic matricesnon-classical logicsfuzzy logicparaconsistent logics

Information

Type
Research Article
Information
The Review of Symbolic Logic , Volume 12 , Issue 1 , March 2019 , pp. 173 - 200
Copyright
Copyright © Association for Symbolic Logic 2018 

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