[alpha]-Resolution principle based on first-order lattice-valued logic LF (X) (original) (raw)
Related papers
α-Resolution principle based on lattice-valued propositional logic LP( X)
Information Sciences - ISCI, 2000
In the present paper, resolution-based automated reasoning theory in an L-type fuzzy logic is focused. Concretely, the α-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 α-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 α (i.e., α-false), is established, and the theorems of both soundness and completeness of this α-resolution principle are also proved. This will become the theoretical foundation for automated reasoning based on lattice-valued logical LP(X).
Linguistic truth-valued lattice implication algebra and its properties
Computational Engineering in Systems …, 2006
The subject of this work is to establish a mathematical framework that provides the basis and tool for automated reasoning and uncertainty reasoning based on linguistic information. This paper focuses on a flexible and realistic approach, i.e., the use of linguistic terms, specially, the symbolic approach acts by direct computation on linguistic terms. An algebra model with linguistic terms, which is based on a logical algebraic structure, i.e., lattice implication algebra, is constructed and applied to represent imprecise information and deal with both comparable and incomparable linguistic terms (i.e., non-ordered linguistic terms). Some properties and its substructures of this algebraic model are discussed.
Resolution-based Theorem Proving for SHn-Logics (Extended Abstract)
2007
In this paper we illustrate by means of an example, namely SHn-logics, a method for translation to clause form and automated theorem proving for first-order manyvalued logics based on distributive lattices with operators. 1 Introduction The main goal of this paper is to present a method for translation to clause form and automated theorem proving in finitely-valued logics having as algebras of truth values distributive lattices with certain types of operators. Many non-classical logics that occur in practical applications fall in this class. One of the advantages of distributive lattices (with well-behaved operators) is the existence, in such cases, of good representation theorems, such as the Priestley representation theorem. The method for translation to clause form we present uses the Priestley dual of the algebra of truth values. The ideas behind this method are very natural, even if the algebraic notions used may at first sight seem involved. This is why in this paper we illust...
Uncertainty Reasoning Based on Lattice-Valued Propositional Logic L6
Computational Engineering in Systems …, 2006
Uncertainty reasoning is one of important directions in the research field of artificial intelligence. Uncertainty reasoning theory and methods based on lattice-valued logic is sound in its strict logical foundation. In this paper, some methods for selecting appropriate parameters in the uncertainty reasoning process based on lattice-valued propositional logic Y6 are proposed.
Journal of Symbolic Computation, 2003
We establish a link between the satisfiability of universal sentences with respect to classes of distributive lattices with operators and their satisfiability with respect to certain classes of relational structures. This justifies a method for structure-preserving translation to clause form of universal sentences in such classes of algebras. We show that refinements of resolution yield decision procedures for the universal theory of some such classes. In particular, we obtain exponential space and time decision procedures for the universal clause theory of (i) the class of all bounded distributive lattices with operators satisfying a set of (generalized) residuation conditions, and (ii) the class of all bounded distributive lattices with operators, and a doubly-exponential time decision procedure for the universal clause theory of the class of all Heyting algebras.
On the content of lattices of logics. Part I
For every consequence (or closure) operator Cn on a set S, the family C of all Cn-closed sets, partially ordered by set inclusion, forms a complete lattice, called the lattice of logics. If the lattice C is distributive, then, it forms a Heyting algebra, since it has the zero element Cn(0) and is complete. Logics determined by this Heyting algebra is studied in the second part. In Part I it is shown (for Cn finitary or compact) that the lattice C is distributive iff its dual space is topological. Moreover a representation theorem for lattices of logics is given.
Uncertainty reasoning based on lattice-valued first-order logic Lvfl
Systems, Man and Cybernetics, 2004 IEEE …, 2004
Uncertainty reasoning is one of important directions in the research field of artificial intelligence. Uncertainty reasoning theory and methods based on lattice-valued logic is sound in its strict logical foundation. In this paper, some methods for selecting appropriate parameters in the uncertainty reasoning process based on lattice-valued propositional logic Y6 are proposed.
A linguistic truth-valued uncertainty reasoning model based on Lattice-Valued Logic
Fuzzy Systems and Knowledge Discovery, 2005
The subject of this work is to establish a mathematical framework that provide the basis and tool for uncertainty reasoning based on linguistic information. This paper focuses on a flexible and realistic approach, i.e., the use of linguistic terms, specially, the symbolic approach acts by direct computation on linguistic terms. An algebra model with linguistic terms, which is based on a logical algebraic structure, i.e., lattice implication algebra, is applied to represent imprecise information and deals with both comparable and incomparable linguistic terms (i.e., non-ordered linguistic terms). Within this framework, some inferential rules are analyzed and extended to deal with these kinds of lattice-valued linguistic information.
A resolution framework for finitely-valued first-order logics
Journal of Symbolic Computation, 1992
In this paper we propose a resolution proof framework on the basis of which automated proof systems for finitely-valued first-order logics (F FO logics) can be introduced and studied. \Ve define the notion of a first-order resolution proof system and we show that for every disjunctive F FO logic a refutationally complete resolution proof system can be constructed. Moreover, we discuss two theorem proving strategies, the polarity and set of support strategies, and we prove their completeness.
The Beth property and interpolation in lattice-based algebras and logics
Algebra and Logic, 2008
We deal with logics based on lattices with an additional unary operation. Interrelations of different versions of interpolation, the Beth property, and amalgamation, as they bear on modal logics and varieties of modal algebras, superintuitionistic logics and varieties of Heyting algebras, positive logics and varieties of implicative lattices, have been studied in many works. Sometimes these relations can and sometimes cannot be extended to the logics without implication considered in the paper.