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Rational Lukasiewicz logic and DMV-algebras

Brunella Gerla

Abstract

In this paper we present some results on the variety of divisible MV-algebras. Any free divisible MV-algebra is an algebra of continuous piecewise linear functions with rational coefficients. Correspondingly, Rational Łukasiewicz logic is defined.

Rational Lukasiewicz logic and DMV-algebras

Abstract

In this paper we present some results on the variety of divisible MV-algebras. Any free divisible MV-algebra is an algebra of continuous piecewise linear functions with rational coefficients. Correspondingly, Rational Łukasiewicz logic is defined.

Paper Structure

This paper contains 8 sections, 17 theorems, 27 equations.

Table of Contents

  1. Introduction
  2. Basic notions: MV--al-ge-bras
  3. DMV-algebras
  4. Varieties and quasi-varieties of DMV-algebras
  5. Rational Łukasiewicz logic
  6. Free DMV-algebras
  7. Pavelka-style Completeness
  8. Complexity Issues

Key Result

Proposition 3.2

Let $A$ be a DMV-algebra, let $A^*$ be its MV-reduct and let $(G,u)$ be the unique l-group with strong unit $u$ such that ${\bf \Gamma}(G,u)=A^*$. Then, for every $x\in A$,

Theorems & Definitions (27)

  • Definition 2.1: Changcigdotmun
  • Definition 3.1: Mundici
  • Proposition 3.2
  • Proposition 3.3
  • Definition 3.4
  • Definition 3.5
  • Proposition 3.6
  • Proposition 3.7
  • Proposition 3.8
  • Theorem 3.9
  • ...and 17 more