The Study Of Approximate Reasoning In Lattice-Valued Logic Based On Lattice Implication Algebra

Human intelligence actions are always involved with acquiring, refining, judgment, reasoning and decision-making about uncertainty information. Uncertainty reasoning plays the key role in the intelligence activities of humankind. It is also the important subject of computer science and artificial intelligence technology. After Zadeh's fuzzy reasoning method proposed, so many uncertainty reasoning methods and theories are proposed. Naturally, the multi-valued logic and fuzzy logic become the foundation of uncertainty reasoning. They are expanding of classical logic whose valuation field from two-valued to multi-valued or Infinitive valued. But they can only deal with the order or comparability information with their linear-valued field. The lattice is a kind of important algebraic structure. Many non-comparability phenomena can be described by lattice in real word. Lattice-valued logic which valuation field is lattice can deal with not only order information but also non-order information. Therefore, it can deal with the reasoning of comparability and non comparability information. Xu Yang proposed the Lattice Implication Algebra, and put the logic on it, such as LP(X), LF(X), Lvpl and Lvfl.Based on lattice-valued propositional logic systems LP(X), Lvpl and lattice-valued first-order logic systems LF(X), Lvfl, the author studied the rules of uncertainty reasoning, the uncertainty reasoning with generalized quantifier, and probed syntax properties andα-resolution principle. The main specific contents are as follow1. We proved the reasoning rules of FMP, FMT and their restoration theorems in the lattice-valued propositional logics and lattice-valued first-order logics.2. We gave the definition of generalized quantifier in the lattice-valued first-order logic LF(X) and Lvfl. We also gave the inclusion relation, union and product operation of generalized quantifiers and proved reasoning results with them.3. We gave the extended definition of closed L-type fuzzy set with the generalized quantifier in lattice-valued first-order logic LF(X). We studied syntax and also proved the soundness theorem and weak completion theorem with generalized quantifier.4. We gave the definition of generalized quantifier prenex stander form , generalized-Skolem standard form and H-interpretation, and proved the Herbrand theorem which was theoretic prepare ofα-resolution with generalized quantifier in LF(X).