Many-Valued logics have been developed to represent mathematical model of imprecision, vagueness, uncertainty and ambiguity in the information. In real world each and every species is vague, human knowledge and the natural languages have a bunch of vagueness or imprecise information. This paper attempts to present three main theories of many-valued logics to treat the vagueness: Fuzzy Logic, Va...

MUltlog is a system which takes as input the specification of a finitely-valued first-order logic and produces a sequent calculus, a natural deduction system, and a calculus for transforming a many-valued formula to clauses suitable for many-valued resolution. All generated rules are optimized regarding their branching degree. The output is in the form of a scientific paper, written in LTEX.

We introduce a fibrational semantics for many-valued logic programming, use it to define an SLD-resolution for annotation-free many valued logic programs as defined by Fitting, and prove a soundness and completeness result relating the two. We show that fibrational se­ mantics corresponds with the traditional declarative (ground) semantics and deduce a soundness and completeness result for our ...

In this paper we compare the expressive power of elementary representation formats for vague, incomplete or conflicting information. These include Boolean valuation pairs introduced by Lawry and Gonzalez-Rodriguez, orthopairs of sets of variables, Boolean possibility and necessity measures, three-valued valuations, supervaluations. We make explicit their connections with strong Kleene logic and...

Several interpretations can be given to the third truth value in three-valued logics. Here, we consider the case when it refers to the epistemic notion of contradictory, or both true and false at the same time. We study several paraconsistent threevalued logics that carry this concern and show that they can be translated into a fragment of a simple epistemic logic where modalities can only appe...

This paper addresses the problem of probabilistic reasoning as it applies to Truth Maintenance Systems. A Belief Maintenance System hal! been constructed which manages a current set of probabilistic beliefs in much the same way that a TMS manages a set of true/false beliefs. Such a system may be thought of as a generalization of a. Truth Maintenance System. It enables one to reason using normal...

Bilattices and d-frames are two different kinds of structures with a four-valued interpretation. Whereas d-frames were introduced with their topological semantics in mind, the theory of bilattices has a closer connection with logic. We consider a common generalisation of both structures and show that this not only still has a clear bitopological semantics, but that it also preserves most of the...

We investigate some finitely-valued generalizations of propositional dynamic logic with tests. We start by introducing the n+ 1valued Kripke models and a corresponding language based on a modal extension of Łukasiewicz many-valued logic. We illustrate the definitions by providing a framework for an analysis of the Rényi Ulam searching game with errors. Our main result is the axiomatization of t...

A common standard for the interpretation of classical propositional logic is set by the functionally complete collection of 2-valued truth-tables. The structure of the free algebra of formulas is faithfully mirrored in the semantics: In each admissible model, each sentential letter freely ranges over the set of truth-values, and to each n-ary logical constant there corresponds a convenient n-ar...

Motivated by aspects of reasoning in theories of physics, Robin Giles defined a characterization of infinite valued Lukasiewicz logic in terms of a game that combines Lorenzen-style dialogue rules for logical connectives with a scheme for betting on results of dispersive experiments for evaluating atomic propositions. We analyze this game and provide conditions on payoff functions that allow us...