This paper studies the linguistic truth value domain (AX) based on finite monotonous hedge algebra and then we extend lukasiewicz algebra on [0, 1] to linguistic lukasiewicz algebra on linguistic truth value domain (AX), in an attempt to propose a general resolution for linguistic many-valued logic based on hedge moving rules and linguistic lukasiewicz algebra for linguistic reasoning. Its theo...

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The fundamentals of à Lukasiewicz-Moisil logic algebras and their applications to complex genetic network dynamics and highly complex systems are presented in the context of a categorical ontology theory of levels, Medical Bioinformatics and self-organizing, highly complex systems. Quantum Automata were defined in refs.[2] and [3] as generalized, probabilistic automata with quantum state spaces...

This paper looks at logic programming with three kinds of negation: default, weak and strict negations. A 3-valued logic model theory is discussed for logic programs with three kinds of negation. The procedure is constructed for negations so that a soundness of the procedure is guaranteed in terms of 3-valued logic model theory.

In this paper we discuss some generalizations of Rényi-Ulam game with lies: some of them are simply probabilistic variants of it, some others differ from it by the presence of more than one number to guess. In the last part of the paper, we also discuss the relationship between such variants and many-valued logic. This paper is just a survey of known results, but in its last part it also contai...

The state of the art in coherent structure theory is driven by two assertions, both of which are limiting: (1) all units of a system can exist in one of two states, failed or functioning; and (2) at any point in time, each unit can exist in only one of the above states. In actuality, units can exist in more than two states, and it is possible that a unit can simultaneously exist in more than on...

In recent years, interest in many-valued logics for computer science has increased considerably, and there is certainly a need for good and thorough textbooks on the subject geared towards that potential area of application, namely, computer science. The authors of the volume Many-valued Logics 1 , Leonard Bolc and Piotr Borowik, have set out to do just that. The volume under review here is the...

In this paper we compare the two versions of knowledge invariant transformations of the original Many-valued logic programs: the strict Annotated logic programs and the ’meta’ logic programs obtained by the ontological encapsulation [1]. We show that the first one has the higher-order Herbrand interpretations, while the last can be seen as the flattening of the first one. These two knowledge in...

Łukasiewicz three-valued logic Ł3 is often understood as the set of 3-valued valid formulas according to Łukasiewicz’s 3-valued matrices. Following Wojcicki, in addition, we shall consider two alternative interpretations of Ł3: “well-determined” Ł3a and “truth-preserving” Ł3b defined by two different consequence relations on the 3-valued matrices. The aim of this paper is to provide (by using D...

This paper describes relations between a trilattice and corresponding meet-distributive lattices. The three meet-distributive lattices illustrate the five information levels, five logical levels and five levels of constructivity respectively. While the trilattice shows connections among the sexteen truth values in general, the three meetdistributive lattices visualize specific information about...