A Framework for Automated Reasoning in Multiple-Valued Logics

The integration of knowledge for multiple sources is an important aspect of automated reasoning systems. When different knowledge bases are used to store knowledge provided by multiple sources, we are faced with the problem of integrating multiple knowledge bases: Under these circumstances, we are also confronted with the prospect of inconsistency. In this paper we present a uniform theoretical framework, based on annotated logics , for amalgamating multiple knowledge bases when these knowledge bases (possibly) contain inconsistencies, uncertainties, and nonmonotonic modes of negation. We show that annotated logics may be used, with some modifications, to mediate between different knowledge bases. The multiple knowledge bases are amalgamated by a transformation of the individual knowledge bases into new annotated logic programs, together with the addition of a new axiom scheme. We characterize the declarative semantics of such amalgamated knowledge bases and study how the semantics of the amalgam is related to the semantics of the individual knowledge bases being combined. —Author's Abstract

This paper presents a new method of rule based fuzzy logic inferencing solely based on a many-valued logic, Lukasiewicz many-valued logic. Fuzzy logic can be considered as an extended set many-valued logic. Many-valued logic is extended from two-valued logic but differs from it in that each has different sets of primitives. The authors believe that fuzzy logic should be solely based on many-valued logic. In this paper, an implication connective of Lukasiewicz many-valued logic is proposed to be a basis of the conditional proposition in a new fuzzy logic inferencing method. Corresponding to this implication connective, a max-/spl delta/ composition is derived from Lukasiewicz many-valued logic and it is shown to fit human intuition. The advantage of the new fuzzy logic inferencing, over other fuzzy logic inferencing, is that it provides a solid theoretical basis for further study of its inferencing behavior when used in a certain application, such as in a fuzzy controller. An example, using machine vision to detect surface flaws of machined parts, is given. >

In this short paper we will discuss on saturated and κ-saturated models of many-valued (t-norm based fuzzy) logics. Using these peculiar structures we show a representation theorem à la Di Nola for several classes of algebras including MV, Gödel, product, BL, NM and WNM-algebras. Then, still using (κ)-saturated algebras, we finally show that some relevant subclasses of algebras related to many-valued logics also enjoy the joint embedding property and the amalgamation property.

In Knowledge-Based Systems, experts should model human knowledge as faithful as possible to reality. In this way, it is essential to consider knowledge imperfection. Several approaches have dealt with this kind of data. The most known are fuzzy logic and multi-valued logic. These latter propose a linguistic modeling using linguistic terms that are uniformly distributed on a scale. However, in some cases, we need to assess qualitative aspects by means of variables using linguistic term sets which are not uniformly distributed. We have noticed, in the literature, that in the context of fuzzy logic many researchers have dealt with these term sets. However, it is not the case for multi-valued logic. Thereby, in our work, we aim to establish a methodology to represent and manage this kind of data in the context of multi-valued logic. Two aspects are treated. The first one concerns the representation of terms within an unbalanced multi-set. The second deals with the use of symbolic modifiers within such kind of imperfect knowledge.

We outline a method for proving theorems in first-order logic with equality using some equational logics and their associated multiple-valued propositional logics, and describe an application of the method that makes use of the automated theorem-prover Otter to prove a range of theorems from the TPTP library of problems in first-order logic with equality.

Fuzzy logic is a multivalued logic. The membership function and linguistic variables characterize it. It is closer to human intuitive thinking. It offers easy, cheap and accurate solutions. In general, it is suitable for complex, continuous and nonlinear processes. The present paper deals with application of fuzzy logic in channel equalization.

Fuzzy logic is a multi-valued logic which is obtained from fuzzy set theory. It deals with human resourcing which is approximate than ‘very unlikely’, when compared to the traditional binary sets the truth value ranges in degree between 0 and 1. The main concept of fuzzy logic is that it provides a practical way of approach to automate the complex data analysis, fusion and inference processes which is usually performed by human experts with extensive experiences. COPRAS-G and COPRAS (Venkatesan et al. in Performance analysis of mobile agent failure recovery in e-service applications 32(1–2):38–43, 2005, Licata in Employing fuzzy logic in the diagnosis of a clinical case, 2010) decision-making methods are separately used in various applications to illustrate the approximate evaluation of attributes. This helps in selecting the best thing. It can be used to select best websites, company, project manager, etc. It can also be used to select the location for constructing warehouse, underground dam, etc. We propose the case study to compare both COPRAS and COPRAS-G (Aruldoss et al. in A survey on multi criteria decision making methods and its applications, 2013, Dhavachelvan et al. in A new approach in development of distributed framework for automated software testing using agents, 2006) decision making fuzzy methods for finding the rate of diseases occurring to children, teenagers and old aged people. That is, what are the diseases may occur at certain age can be accurately predicted through this project. Two methods Simplified COPRAS and COPRAS-G are implemented with the same input to obtain the best and the worst alternative. The ranking of the Simplified COPRAS-G and COPRAS method are compared by the parameters. Each parameter is applied in both the method in order to find the better method.

Fuzzy logic (FL) is a mathematical technique for dealing with imprecise data and problems that have many solutions rather than one. Although it is implemented in digital computers which ultimately make only yesno decisions, FL works with ranges of values, solving problems in a way that more resembles human logic. FL is a multi-valued (as opposed to binary) logic developed to deal with imprecise or vague data. Classical logic holds that everything can be expressed in binary terms: 0 and 1, black and white, yes or no; in terms of Boolean algebra, everything is in one set or another but not in both. FL allows for partial membership in asset values between 0 and 1, shades of gray, and introduces the concept of the “fuzzy set.” When the approximate reasoning of FL (Zadeh, 1965) is used with an expert system, logical inferences can be drawn from imprecise relationships. FL theory was developed by Lofti A. Zadeh at the University of California in the mid 1960s. However, it was not applied commercially until 1987 when the Matsushita Industrial Electric Co. used it to automatically optimize the wash cycle of a washing machine by sensing the load size, fabric mix, and quantity of detergent and has applications in the control of passenger elevators, household applications, and so forth.

Resolution-based Theorem Proving for Many-valued Logics

We have already developed some kinds of paraconsistent annotated logic programs. In this paper we propose the paraconsistent process order control method based on a paraconsistent annotated logic program called before–after extended vector annotated logic program with strong negation (bf-EVALPSN) with a small example of pipeline process order verification. Bf-EVALPSN can deal with before–after relations between two processes (time intervals) in its annotations, and its reasoning system consists of two kinds of inference rules called the basic bf-inference rule and the transitive bf-inference rule. We introduce how the bf-EVALPSN-based reasoning system can be applied to the safety verification for process order.

This issue represents a collection of selected “pieces” created by “masters” in the area of logic design. Although relatively few people in the world participate in the research on artificial intelligence aspects of digital design, this is no impairment to the truly original research. We believe that artificial intelligence approach is an important aspect of digital systems design, because it includes advanced theory (such as multiple-valued logic, fuzzy logic and evolutionary algorithms) and is flexible to advanced and new technologies that could have far-reaching effects on future computers and information systems.

Finite lattices are fundamental structures which can be found in many fields of information science and computational intelligence: data analysis, data mining, multiple-valued logics, fuzzy logics, hierarchical modelling, graph theory, combinatorics, etc. Surprisingly, not much attention has been paid to structural properties of finite lattices. In this paper we study properties of finite lattices up to eleven elements. We present algorithms for generating non-isomorphic finite lattices up to a given size. We propose heuristic tests of non-isomorphism of finite lattices and examine their performance. We present a summary of selected properties of finite lattices

The goal of a new area of Computing with Words (CWW) is solving computationally tasks formulated in a natural language (NL). The extreme uncertainty of NL is the major challenge to meet this ambitious goal requiring computational approaches to handle NL uncertainties. Attempts to solve various CWW tasks lead to the methodological questions about rigorous and heuristic formulations and solutions of the CWW tasks. These attempts immediately reincarnated the long-time discussion about different methodologies to model uncertainty, namely: Probability Theory, Multi-valued logic, Fuzzy Sets, Fuzzy Logic, and the Possibility theory. The main forum of the recent discussion was an on-line Berkeley Initiative on Soft Computing group in 2014. Zadeh claims that some computing with words tasks are in the province of the fuzzy logic and possibility theory, and probabilistic solutions are not appropriate for these tasks. In this work we propose a useful constructive probabilistic approach for CWW based on sets of specialized K-Measure (Kolmogorov’s measure) probability spaces that differs from the random sets. This work clarifies the relationships between probability and possibility theories in the context of CWW.

Soft and neutrosophic sets are used in this chapter as tools for introducing a multi-valued logic for ethics. The introduction of a multi-valued logic in ethics is not a new idea, but there is not any integrated proposal about this reported in the literature until now. The target is not to add another theory about ethics, but instead to create a new basis enabling a modern approach to the subject. The chapter starts by examining the role of human logic and statistical thinking for the creation and evolution of ethics. A brief historical account of the development of ethics follows with emphasis to the moral dilemmas, the existence of which motivates the application of a multi-valued logic. The basic information about fuzzy sets, fuzzy logic, soft sets, and neutrosophic sets, needed for the understanding of the rest of the chapter, are also presented before using soft and neutrosophic sets for a mathematical representation of the ethical rules and in extension of the moral theories.

This paper presents a unified treatment of the propositional and first-order many-valued logics through the method of tableaux. It is shown that several important results on the proof theory and model theory of those logics can be obtained in a general way.We obtain, in this direction, abstract versions of the completeness theorem, model existence theorem (using a generalization of the classical analytic consistency properties), compactness theorem and Löwenheim-Skolem theorem.The paper is completely self-contained and includes examples of application to particular many-valued formal systems.