Thirty seven years ago, Richard Greechie and Stanley Gudder wrote a paper entitled Is a Quantum Logic a Logic? [1] in which they strengthen a previous negative result of Josef Jauch and Constantin Piron. [2] “Jauch and Piron have considered a possibility that a quantum propositional system is an infinite valued logic. . . and shown that standard propositional systems (that is, ones that are iso...

$top$-filters can be used to define $top$-convergence spaces in the lattice-valued context. Connections between $top$-convergence spaces and lattice-valued convergence spaces are given. Regularity of a $top$-convergence space has recently been defined and studied by Fang and Yue. An equivalent characterization is given in the present work in terms of convergence of closures of $top$-filters.  M...

A prospective study of the use of ordered multi-lattices as underlying sets of truth-values for a generalised framework of logic programming is presented. Specifically, we investigate the possibility of using multi-lattice-valued interpretations of logic programs and the theoretical problems that this generates with regard to its fixed point semantics.

In this paper, at first we define the concepts of response function and accessible states of a complete residuated lattice-valued (for simplicity we write $mathcal{L}$-valued) tree automaton with a threshold $c.$ Then, related to these concepts, we prove some lemmas and theorems that are applied in considering some decision problems such as finiteness-value and emptiness-value of recognizable t...

Gentzen systems are introduced for Spinks and Veroff’s substructural logic corresponding to constructive logic with strong negation, and some logics in its vicinity. It has been shown by Spinks and Veroff in [9], [10] that the variety of Nelson algebras, the algebras of constructive logic with strong negation N, is term-equivalent to a certain variety of bounded commutative residuated lattices ...

Thirty-seven years ago, Richard Greechie and Stanley Gudder wrote a paper entitled Is a Quantum Logic a Logic? [Greechie and Gudder, 1971] in which they strengthen a previous negative result of Josef Jauch and Constantin Piron. [Jauch and Piron, 1970] “Jauch and Piron have considered a possibility that a quantum propositional system is an infinite valued logic. . . and shown that standard propo...

The classical approach to the study of xed point semantics of deenite logic programs P utilises two main facts : (1) The set I J L of all interpretations of the underlying language L based on a given preinterpretation J forms a complete lattice under the partial order of set inclusion. (2) The immediate consequence map T P deened on I J L is lattice continuous. An application is then made of a ...

This paper describes our multi-valued symbolic modelchecker χChek. χChek is a generalization of an existing symbolic model-checking algorithm for a multi-valued extension of the temporal logic CTL. Multi-valued modelchecking supports reasoning with values other than just TRUE and FALSE. Multi-valued logics are useful in software engineering because they support explicit modeling of uncertainty,...