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 -Resolution principle based on lattice-valued propositional logic LP(X) |
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| Authors: | Yang Xu Da Ruan Etienne E. Kerre Jun Liu |
| Affiliation: | a Department of Applied Mathematics, Southwest Jiaotong University, Chengdu 610031, Sichuan, People's Republic of China b Belgian Nuclear Research Centre (SCK-CEN), Boeretang 200, B-2400, Mol, Belgium c Department of Applied Mathematics and Computer Science, University of Gent, Gent, Belgium |
| Abstract: | In the present paper, resolution-based automated reasoning theory in an L-type fuzzy logic is focused. Concretely, the -resolution principle, which is based on lattice-valued propositional logic LP(X) with truth-value in a logical algebra – lattice implication algebra, is investigated. Finally, an -resolution principle that can be used to judge if a lattice-valued logical formula in LP(X) is always false at a truth-valued level (i.e., -false), is established, and the theorems of both soundness and completeness of this -resolution principle are also proved. This will become the theoretical foundation for automated reasoning based on lattice-valued logical LP(X). |
| Keywords: | Automated reasoning Multi-valued logic Resolution principle Lattice-valued logic Lattice implication algebras |
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