Cylindric algebras of De Morgan-valued logic

TL;DR

This paper develops a De Morgan algebra-valued logic with quantifiers, establishing a representation theorem for its cylindric algebra and proving a completeness theorem, generalizing previous results in the field.

Contribution

It introduces a new De Morgan algebra-valued logic with quantifiers and proves a representation and completeness theorem, extending prior work in algebraic logic.

Findings

Representation theorem for cylindric algebra of the logic

Completeness theorem for De Morgan algebra-valued logic

Generalization of previous algebraic logic results

Abstract

We construct a De Morgan algebra-valued logic with quantifiers, where the truth values are in a finite De Morgan algebra, We show that there is a representation theorem of the cylindric algebra of this logic from which a completeness theorem for De Morgan algebra-valued logic follows. This is a generalization of the results in [2].