This paper is a continuation of Part I [9]. First, the extension of fuzzy theories is studied and the important deduction theorem is proved which is a generalisation of the corresponding classical one. In Section 7.3, algebraic properties of the set of formulae are studied. This section serves as a preparation for the proofs of the most important theorems in this paper which are the completenes...

The paper deals with fuzzy logic in the narrow sense of Lukasiewicz style, i.e. a special kind of many-valued logic which is aimed at modeling of vagueness phenomenon. This logic is a generalization of Lukasiewicz logic with many interesting properties (for example, generalization of the deduction and completeness theorems hold in it). Our aim is to prepare the background for the resolution in ...

The basic aim of our study is to give a possible model for handling uncertain information. This model is worked out in the framework of DATALOG. The concept of multivalued knowledgebase will be defined as a quadruple of any background knowledge; a deduction mechanism; a connecting algorithm, and a function set of the program, which help us to determine the uncertainty levels of the results. At ...

This is an extended abstract of the published paper “Approximate Similarity and Poincaré Paradox to be published in Notre Dame Journal of Formal Logic, 49, 2008”. The startin point is an observation by De Cock and Kerre, in which, in considering Poincaré paradox, one observes that the intuitive notion of “approximate similarity” cannot be adequately represented by the fuzzy equivalence relation...

We formulate a unified display calculus proof theory for the four principal varieties of bunched logic by combining display calculi for their component logics. Our calculi satisfy cut-elimination, and are sound and complete with respect to their standard presentations. We show how to constrain applications of display-equivalence in our calculi in such a way that an exhaustive proof search need ...

Processing information in fuzzy rule-based systems generally employs one of two patterns of inference: composition or compatibility modification. Composition originated as a generalization of binary logical deduction to fuzzy logic, while compatibility modification was developed to facilitate the evaluation of rules by separating the evaluation of the input from the generation of the output. Th...

In this paper we prove the strong standard completeness of interval-valued monoidal t-norm based logic (IVMTL) and some of its extensions. For other extensions we show that they are not strong standard complete. We also give a local deduction theorem for IVMTL and other extensions of interval-valued monoidal logic. Similar results are obtained for interval-valued fuzzy logics expanded with Baaz...

A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The proposed semantics is based on fuzzy sets of interpretations. It is tolerant to partial inconsistency. Satisfiability is extended from interpretations to fuzz...

The basic question of our study is how we can give a possible model for handling uncertain information. This model is worked out in the framework of DATALOG. The concept of fuzzy knowledge-base will be defined as a quadruple of any background knowledge; a deduction mechanism; a connecting algorithm, and a decoding set of the program, which help us to determine the uncertainty level of the resul...

By means of theory of truth degrees of formulas, according to deduction theorems and completeness theorems, the new concepts of consistency degrees and polar index for general theories in Łukasewicz fuzzy and n-valued propositional logic systems are introduced. Moreover, sufficient and necessary conditions for a theory Γ to be consistent, inconsistent, and fully divergent are obtained. Finally,...