相关论文: Classical Bivalent Logic as a Particular Case of C…

Bipolar fuzzy relation equations arise as a generalization of fuzzy relation equations considering unknown variables together with their logical connective negations. The occurrence of a variable and the occurrence of its negation…

The propositional logic is generalized on the real numbers field. The logical analog of the Bernoulli independent tests scheme is constructed. The variant of the nonstandard analysis is adopted for the definition of the logical function,…

The propositional logic is generalized on the real numbers field. the logical function with all properties of the classical probability function is obtained. The logical analog of the Bernoulli independent tests scheme is constructed. The…

We investigate the possibility of extending the non-functionally complete logic of a collection of Boolean connectives by the addition of further Boolean connectives that make the resulting set of connectives functionally complete. More…

The present article is a brief informal survey of computability logic --- the game-semantically conceived formal theory of computational resources and tasks. This relatively young nonclassical logic is a conservative extension of classical…

We define a stable model semantics for fuzzy propositional formulas, which generalizes both fuzzy propositional logic and the stable model semantics of classical propositional formulas. The syntax of the language is the same as the syntax…

We study a conservative extension of classical propositional logic distinguishing between four modes of statement: a proposition may be affirmed or denied, and it may be strong or classical. Proofs of strong propositions must be…

In this article we investigate the notion and basic properties of Boolean algebras and prove the Stone's representation theorem. The relations of Boolean algebras to logic and to set theory will be studied and, in particular, a neat proof…

In this talk a brief survey of basic ideas of Idempotent Mathematics is presented. Relations between this theory and the theory of fuzzy sets as well as the possibility theory and some applications (including computer applications) are…

Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…

In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…

We review the close relationship between abstract machines for (call-by-name or call-by-value) lambda-calculi (extended with Felleisen's C) and sequent calculus, reintroducing on the way Curien-Herbelin's syntactic kit expressing the…

Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts…

The paper explores categorical interconnections between lattice-valued Relational systems and algebras of Fitting's lattice-valued modal logic. We define lattice-valued boolean systems, and then we study co-adjointness, adjointness of…

In this paper we present, by way of case studies, a proof of concept, based on a prototype working on a automotive data set, aimed at showing the potential usefulness of using formulas of {\L}ukasiewicz propositional logic to query…

Interpolation is an important property of classical and many non classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the propositional version of the…

In this paper, we present a propositional sequent calculus containing disjoint copies of classical and intuitionistic logics. We prove a cut-elimination theorem and we establish a relation between this system and linear logic.

This paper develops a category-theoretic approach to uncertainty, informativeness and decision-making problems. It is based on appropriate first order fuzzy logic in which not only logical connectives but also quantifiers have fuzzy…

Fuzzy set theory opens new vistas in computability theory and here I show this by defining a new computational metaphor--the fuzzy chemical metaphor. This metaphor is an extension of the chemical metaphor. In particular, I introduce the…

Justification Logics provide a framework for reasoning about justifications and evidences. Most of the accounts of justification logics are crisp in the sense that agent's justifications for a statement is convincing or is not. In this…