TY - JOUR
AB - 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. © 2006 Elsevier Inc. All rights reserved.
AU - Ma, J
AU - Li, W
AU - Ruan, D
AU - Xu, Y
DA - 2007/02/15
DO - 10.1016/j.ins.2006.07.027
EP - 1062
JO - Information Sciences
PY - 2007/02/15
SP - 1046
TI - Filter-based resolution principle for lattice-valued propositional logic LP(X)
VL - 177
Y1 - 2007/02/15
Y2 - 2019/09/19
ER -