Filter-based resolution principle for lattice-valued propositional logic LP(X) |
| |
Authors: | Jun Ma Wenjiang Li Yang Xu |
| |
Affiliation: | a Department of Mathematics, Southwest Jiaotong University, Chengdu 610031, PR China b Faculty of Information Technology, University of Technology, Sydney, P.O. Box 123, Broadway, NSW 2007, Australia c School of Electric Engineering, Southwest Jiaotong University, Chengdu 610031, PR China d Belgian Nuclear Research Centre (SCK•CEN) Boeretang 200, Mol 2400, Belgium e Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), Gent 9000, Belgium |
| |
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. |
| |
Keywords: | Resolution principle Filter Lattice-valued logic Automated reasoning Simple generalized clause Complex generalized clause |
本文献已被 ScienceDirect 等数据库收录! |
|