Filter-based resolution principle for lattice-valued propositional logic LP(X)

  • Authors:

  • Jun Ma;Wenjiang Li;Da Ruan;Yang Xu

  • Affiliations:

  • Department of Mathematics, Southwest Jiaotong University, Chengdu 610031, PR China and Faculty of Information Technology, University of Technology, Sydney, P.O. Box 123, Broadway, NSW 2007, Austra ...;School of Electric Engineering, Southwest Jiaotong University, Chengdu 610031, PR China;Belgian Nuclear Research Centre (SCKCEN) Boeretang 200, Mol 2400, Belgium and Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), Gent 9000, Belgium;Department of Mathematics, Southwest Jiaotong University, Chengdu 610031, PR China

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2007

Quantified Score

Hi-index 0.11

Visualization

Abstract

As one of most powerful approaches in automated reasoning, resolution principle has been introduced to non-classical logics, such as many-valued logic. However, most of the existing works are limited to the chain-type truth-value fields. Lattice-valued logic is a kind of important non-classical logic, which can be applied to describe and handle incomparability by the incomparable elements in its truth-value field. In this paper, a filter-based resolution principle for the lattice-valued propositional logic LP(X) based on lattice implication algebra is presented, where filter of the truth-value field being a lattice implication algebra is taken as the criterion for measuring the satisfiability of a lattice-valued logical formula. The notions and properties of lattice implication algebra, filter of lattice implication algebra, and the lattice-valued propositional logic LP(X) are given firstly. The definitions and structures of two kinds of lattice-valued logical formulae, i.e., the simple generalized clauses and complex generalized clauses, are presented then. Finally, the filter-based resolution principle is given and after that the soundness theorem and weak completeness theorems for the presented approach are proved.