Study On Uncertainty Reasoning In Lattice-Valued First-Order Logic L_vfl Based On Lattice Implication Algebra

Uncertainty reasoning is one of important directions in the research field of artificial intelligence. To study uncertainty reasoning based on logic is one of scientific methodologies. Lattice-valued logic is an important kind of non-classical logic in that it can not only depict totally ordered information, but also non-totally ordered (noncoma-parable) information. Based on many related research works, the current dissertation studies lattice implication algebra and uncertainty reasoning based on lattice-valued first-order logic, which takes lattice implication algebra as its truth-valued field, and achieved the following results:Part One. The study of lattice implication algebra1. It is proved that the set of the product of LI-ideals for two lattice implication algebras is equal to the set of LI-ideals of the lattice implication product algebra of these two lattice implication algebras. While the subalgebras of the lattice implication product algebra of two lattice implication algebras take other forms (chain type), besides the product of subalgebras for these two lattice implication algebras.2. The concepts of normal fuzzy filters, maximal fuzzy filters and completely normal fuzzy filters of lattice implication algebras are proposed, and some of their properties are discussed. It is shown that every maximal fuzzy filter of a lattice implication algebra is completely normal.3. The notions of intuitionistic fuzzy filters and intuitionistic fuzzy lattice dual ideals in lattice implication algebra are introduced. It is shown that every intuitionistic fuzzy filter is an intuitionistic fuzzy lattice dual ideal. Some characterizations of intuitionistic fuzzy filters are also established.4. It is proved that LI-ideals of lattice implication algebras are not closed w.r.t. operations → and (?). A topological space based on LI-ideals of a lattice implication algebra is constructed, and its topological properties, such as separability, compactness and connectedness are discussed. It is shown that the product topology of two LI-ideal spaces for two lattice implication algebras is identical to the LI-ideal topology of the lattice implication product algebra of these two lattice implication algebras.Part Two. The study of uncertainty reasoning based on lattice-valued first-order logic Lvfl1. A kind of multiple and multi-dimensional uncertainty reasoning theory and method based on lattice-valued first-order logic Lvfl is proposed, which has not onlysound semantic interpretation, but also strict syntactical proof. The definitions of representability of rule in a uncertainty reasoning model and regularity of a uncertainty reasoning model are introduced, and some conditions for uncertainty reasoning models to be representable and regular are given.2. For some representative uncertainty reasoning models, some concrete methods for selecting appropriate parameters during the uncertainty reasoning process based on lattice-valued first-order logics Luj are proposed.3. For some representative uncertainty reasoning models, some concrete methods for selecting appropriate parameters during the uncertainty reasoning process based on lattice-valued first-order logics #5/ are proposed.4. For some representative uncertainty reasoning models, some concrete methods for selecting appropriate parameters during the uncertainty reasoning process based on lattice-valued first-order logics JZ^f are proposed.5. For some representative uncertainty reasoning models, some concrete methods for selecting appropriate parameters during the uncertainty reasoning process based on lattice-valued first-order logics J&nf are proposed.