Abstract:
A t-norm fuzzy logic is presented, in which a triangular norm (t-norm) plays the role of a graduated conjunction operator. Based on this fuzzy logic we develop methods for fuzzy reasoning in which antecedents and consequents involve fuzzy conditional propositions of the form “If x is A then y is B”, with A and B being fuzzy concepts (fuzzy sets). In this study, we present a systemic approach toward fuzzy logic formalization for approximate reasoning. We examine statistical characteristics of the proposed fuzzy logic. As the matter of practical interest, we construct a set of fuzzy conditional inference rules on the basis of the proposed fuzzy logic. Important features of these rules are investigated.

Resolution is an useful tool for mechanical theorem proving in modelling the refutation proof procedure, which is mostly used in constructing a “proof” of a “theorem”. An attempt is made to utilize approximate reasoning methodology in fuzzy resolution. Approximate reasoning is a methodology which can deduce a specific information from general knowledge and specific observation. It is dependent on the form of general knowledge and the corresponding deductive mechanism. In ordinary approximate reasoning, we derive from A→B and by some mechanism. In inverse approximate reasoning, we conclude from A→B and using an altogether different mechanism. An important observation is that similarity is inherent in fuzzy set theory. In approximate reasoning methodology-

Abstract:
Based on the truth degree of the formula, conditional truth degree and the implicative truth degree respectively, we gain the new numerical studying method of the severity of the systems and the approximate reasoning problems in the two-valued propositionallogic. Furthermore, we also concentrate on the relationship among the truth degree, conditional truth degree and the implicative truth degree in approximate reasoning mode. According to the truth degree in this paper, we obtain the definition of the implication measure-ment in the two-valued propositional logic system. Using the truth degree expressions of the implication measurement, we show the implication measurement expressions of the pseudo mertic which are resulted separately from the truth degree, conditional truth degree and implicative truth degree. These expressions are all relative to the finite theory. Hence we have achieved the transformation from the problems of approximate reasoning based on the tree kind of truth degrees as above to the approximate reasoning based on the implication measurement. Meanwhile, we have mastered the applications of approximate reasoning in implication measurement. So these studies could become the numetrical identification of approximate reasoning which is based on the different kinds of truth degree in two-valused propositional logic.

Abstract:
The paper introduces novel residuum-based reasoning systems in a pseudo—analysis based uninorm environment. Based on the definitions and theorems for lattice ordered monoids and left continuous uninorms and t-norms, certain distance-based operators are focused on, with the help of which the uninorm-residuum based approximate reasoning system becomes possible in Fuzzy Logic Control (FLC) systems, but as it will be shown, this type of the reasoning partially satisfies the conditions for approximate reasoning and inference mechanism for FLC systems.

Abstract:
Fuzzy set systems can be used to solve the problem with uncertain knowledge, and default logic can be used to solve the problem with incomplete knowledge, in some sense. In this paper, based on interval-valued fuzzy sets we introduce a method of inference which combines approximate reasoning and default logic, and give the procedure of transforming monotonic reasoning into default reasoning.

Abstract:
The article presents a simple way how knowledge represented via RDF triples provides an easier method of inference, managing and finding interrelations between knowledge objects than that an approach based on OWL language. The authors of the article come out of the T. Richards inference system of the Clausal Form Logic (CFL) based on the formal manipulation with conditional if-then statements, and an idea of RDF extended model (with quantifiers) of knowledge representation to propose an inference mechanism RDF RR working over knowledge bases of RDF triples.

Abstract:
The concept of logic proposition induced functions is proposed in the present paper, then the concept of relative truth degree of propositions with respect to a logic theory is introduced by means of infinite product of evenly distributed probability spaces and integrated semantics respectively w.r.t. discrete and continuous situations, and a graded approximate reasoning theory is established. Next, theory of consistency degrees of finite logic theories is also proposed. Finally, the simple application of graded fuzzy logic in fuzzy inference is given by examples.

Abstract:
Similarity-based Logic Programming (briefly, SLP ) has been proposed to enhance the LP paradigm with a kind of approximate reasoning which supports flexible information retrieval applications. This approach uses a fuzzy similarity relation R between symbols in the program's signature, while keeping the syntax for program clauses as in classical LP. Another recent proposal is the QLP(D) scheme for Qualified Logic Programming, an extension of the LP paradigm which supports approximate reasoning and more. This approach uses annotated program clauses and a parametrically given domain D whose elements qualify logical assertions by measuring their closeness to various users' expectations. In this paper we propose a more expressive scheme SQLP(R,D) which subsumes both SLP and QLP(D) as particular cases. We also show that SQLP(R,D) programs can be transformed into semantically equivalent QLP(D) programs. As a consequence, existing QLP(D) implementations can be used to give efficient support for similarity-based reasoning.

Abstract:
Fuzzy logic dates back to 1965 and it is related not only to current areas of knowledge, such as Control Theory and Computer Science, but also to traditional ones, such as Philosophy and Linguistics. Like any logic, fuzzy logic is concerned with argumentation, but unlike other modalities, which focus on the crisp reasoning of Mathematics, it deals with common sense reasoning; i.e., with approximate reasoning. Although the teaching of logic has formed part of mainstream education for many years, fuzzy logic is a much more recent inclusion. In this paper we emphasize the desirability of having illustrative examples related to students’ everyday activities, such as sports, in order to introduce fuzzy logic in higher education. Taking an example from cycling, we show, step by step, how to model an approximate reasoning regarding the choice of a ratio (a combination of freewheel and chainring) in order to advance more or less with each rotation of the pedals. Led by this example, a number of alternatives attending to the formal representation of the premises and the ways of inferring a plausible conclusion are analyzed. The choices made between alternatives are justified. We show that the conclusion inferred in the example is consistent with the models selected for premises and fuzzy inference and similar to that concluded by a human being.

Abstract:
The approximate reasoning is perceived as a derivation of new formulas with the corresponding temporal attributes, within a fuzzy theory defined by the fuzzy set of special axioms. For dynamic management applications, the reasoning is evolutionary because of unexpected events which may change the state of the expert system. In this kind of situations it is necessary to elaborate certain mechanisms in order to maintain the coherence of the obtained conclusions, to figure out their degree of reliability and thetime domain for which these are true. These last aspects stand as possible further directions of development at a basic logic level. The purpose of this paper is to characterise an extended fuzzy logic system with modal operators, attained by incorporating the basic elements of a first-degree fuzzy logic and certain elements oftemporal logic.