Recently, a propositional logic modeling of analogical proportions, i.e., statements of the form “A is to B as C is to D”, has been proposed, and has then led to introduce new related proportions in a general setting. This framework is well-suited for analogical reasoning and classification tasks about situations described by means of Boolean properties. There is a clear need for extending this...

This paper generalises the tree-based data structure of ∆tree to be applied to signed propositional formulas. The ∆-trees allow a compact representation for signed formulas as well as for a number of reduction strategies in order to consider only those occurrences of literals which are relevant for the satisfiability of the input formula. The conversions from signed formulas to ∆-trees and vice...

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...

This paper presents arithmetic operations, including addition and multiplication, in the ternary Galois field through carbon nanotube field-effect transistors (CNTFETs). Ternary logics have received considerable attention among all the multiple-valued logics. Multiple-valued logics are an alternative to common-practice binary logic, which mostly has been expanded from ternary (three-valued) log...

A b s t r a c t. The paper deals with functional properties of three-valued logics. We consider the family of regular three-valued Kleene's logics (strong, weak, intermediate) and it's extensions by adding an implicative connectives (" natural " implications). The main result of our paper is the lattice that describes the relations between implicative extensions of regular logics. In this paper...

Multiple-valued logics are useful for dealing with uncertainty and imprecision in Knowledge-Based Systems. Different problems can require different logics. Then we need mechanisms to translate the information exchanged between two problems with different logics. In this paper, we introduce the logical foundations of such logics and the communication mechanisms that preserve some deductive prope...

We continue a series of papers on a family of many-valued modal logics, a family whose Kripke semantics involves many-valued accessibility relations. Earlier papers in the series presented a motivation in terms of a multiple-expert semantics. They also proved completeness of sequent calculus formulations for the logics, formulations using a cut rule in an essential way. In this paper a novel cu...

Multiple-valued logics are useful for dealing with uncertainty and imprecision in knowledge-based systems. In this paper, we present the foundations of QMORPH: a tool that assists users in the declaration of such logics and in the declaration of the communication mechanism between two of these different logics by preserving inference.

The polyadic algebras that arise from the algebraization of the first-order extensions of a SIC are characterized and a representation theorem is proved. Standard implicational calculi (SIC)’s were considered by H. Rasiowa [19] and include classical and intuitionistic logic and their various weakenings and fragments, the many-valued logics of Post and Lukasiewicz, modal logics that admit the ru...

We introduce a general recipe for presenting non-classical logics in a modular and uniform way as labelled deduction systems. Our recipe is based on a labelling mechanism where labels are general entities that are present, in one way or another, in all logics, namely truth-values. More specifically, the main idea underlying our approach is the use of algebras of truth-values, whose operators re...