Download Beyond Two: Theory and Applications of Multiple-Valued Logic by Janusz Brzozowski, Zoltán Ésik, Yaacov Iland (auth.), PDF

By Janusz Brzozowski, Zoltán Ésik, Yaacov Iland (auth.), Professor Dr. Melvin Fitting, Professor Dr. Ewa Orłowska (eds.)

This quantity represents the state-of-the-art for far present study in many-valued logics. fundamental researchers within the box are one of the authors. significant methodological problems with many-valued logics are taken care of, in addition to purposes of many-valued logics to reasoning with fuzzy info. parts coated comprise: Algebras of a number of valued logics and their functions, evidence concept and automatic deduction in a number of valued logics, fuzzy logics and their purposes, and a number of valued logics for keep an eye on conception and rational belief.

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In this paper I try to show how the application of a certain general framework, developed in [16) in the context just introduced, helps in understanding and describing the algebraic behaviour of a certain family of multiplevalued logics defined from truth-value algebras that are subalgebras of the real unit interval endowed with Lukasiewicz's familiar operations. The way these logics are defined from the algebras is a particular instance of the socalled semilattice-based logics l , a general procedure devised in order to formalise a specific view of logics as inference systems preserving degrees of truth.

Abstract Algebraic Logic is a general theory of the algebraization of deductive systems arising as an abstraction of the wellknown Lindenbaum-Tarski process. The notions of logical matrix and of Leibniz congruence are among its main building blocks. Its most successful part has been developed mainly by BLOK, PIGOZZI and CZELAKOWSKI, and obtains a deep theory and very nice and powerful results for the so-called protoalgebraic logics. I will show how the idea (already explored by WOJCKICI and NOWAK) of defining logics using a scheme of "preservation of degrees of truth" (as opposed to the more usual one of "preservation of truth") characterizes a wide class of logics which are not necessarily protoalgebraic and provide another fairly general framework where recent methods in Abstract Algebraic Logic (developed mainly by JANSANA and myself) can give some interesting results.

Hazard-Non-Increasing Gate-Level Optimization Algorithms. Proc. Int. Conf. Computer-Aided Design, IEEE, (1992) 631-634 32. : Hazard Detection by a Quinary Simulation of Logic Devices with Bounded Propagation Delays, MSc Thesis, University of Syracuse (1972) 33. : Transient Behavior of Combinational Logic Circuits. In Redundancy Techniques for Computing Systems. H. C. , Spartan Books, Washington, DC (1962) 9-46 34. : Many-Valued Logic and the Design of Switching Circuits, MSc Thesis, University of Illinois, Urbana (1953) 35.

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