Uncertainty Reasoning Based on Lattice-Valued Propositional Logic L6 (original) (raw)

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.

Parameterized uncertain reasoning approach based on a lattice-valued logic

Symbolic and Quantitative …, 2011

This paper presents a parameterized reasoning approach with uncertainty based on a lattice-valued logic system. In this uncertain reasoning approach, some parameters are used to represent uncertainty arising from different sources, which is a common phenomenon in rule-based systems. In our system, reasoning with different parameter values means reasoning with different levels of belief and consistency. Some methods are presented for selecting appropriate parameter values during the uncertain reasoning process which allow us to find suitable parameter values to meet the diverse practical and theoretical requirements.

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.

Review of some uncertain reasoning methods

Most artificial intelligence applications, especially expert systems, have to reason and make decisions based on uncertain data and uncertain models. For this reason, several methods have been proposed for reasoning with different kinds of uncertainty. This paper discusses and illustrates some of the reasoning methods proposed by the artificial intelligence research community to deal with uncertainty.

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).

Treatment of Uncertainties with Algorithms of the Paraconsistent Annotated Logic

The method presented in this work is based on the fundamental concepts of Paraconsistent Annotated Logic with annotation of 2 values (PAL2v). The PAL2v is a non-classic Logics which admits contradiction and in this paper we perform a study using mathematical interpretation in its representative lattice. This studies result in algorithms and equations give an effective treatment on signals of information that represent situations found in uncertainty knowledge database. From the obtained equations, algorithms are elaborated to be utilized in computation models of the uncertainty treatment Systems. We presented some results that were obtained of analyses done with one of the algorithms that compose the paraconsistent analyzing system of logical signals with the PAL2v Logic. The paraconsistent reasoning system built according to the PAL2v methodology notions reveals itself to be more efficient than the traditional ones, because it gets to offer an appropriate treatment to contradictory information. Treatment of Uncertainties with Algorithms of the Paraconsistent Annotated Logic 145 P (, λ) : T = Inconsistent = P (1, 1) , F = False = P (0, 1) , t = True = P (1, 0) ,  = Indeterminate = P (0, 0) Figure 1. Four-vertex lattice.

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.

Fuzzy reasoning and the logics of uncertainty

International Symposium on Multiple-Valued Logic, 1976

This paper is concerned with the foundations of fuzzy reasoning and its relationships with other logics of uncertainty. The definitions of fuzzy logics are first examined and the role of fuzzification discussed. It is shown that fuzzification of PC gives a known multivalued logic but with inappropriate semantics of implication and various alternative forms of implication are discussed. In the main section the discussion is broadened to other logics of uncertainty and it is argued that there are close links, both formal and semantic, between fuzzy logic and probability logics. A basic multivalued logic is developed in terms of a truth function over a lattice of propositions that encompasses a wide range of logics of uncertainty. Various degrees of truth functionality are then defined and used to derive specific logics including probability logic and Lukasiewicz infinitely valued logic. Quantification and modal operators over the basic logic are introduced. Finally, a semantics for the basic logic is introduced in terms of a population (of events, or people, or neurons) and the semantic significance of the constraints giving rise to different logics is discussed.

A robust logic for rule-based reasoning under uncertainty

1992

Abstract A symbolically quantified logic is presented for reasoning under uncertainty that is based upon the concept of rough sets. This mathematical model provides a simple yet sound basis for a robust reasoning system. A rule of inference analogous to modus ponens is described, and it is shown how it might be used by a reasoning system to determine the most likely outcome under conditions of uncertain knowledge. An analysis of the robustness of the logic in rule-based reasoning is also presented.<>

A note on truth value in uncertain logic

Expert Systems with Applications, 2011

Uncertain logic is a generalization of classical logic for dealing with uncertain knowledge via uncertainty theory. The truth value is defined as the uncertain measure that a proposition is true. In this paper, a numerical method for calculating the truth value of uncertain formulas is proposed and some examples are presented.