A many-valued approach to quantum computational logics

A note on many valued quantum computational logics

The standard theory of quantum computation relies on the idea that the basic information quantity is represented by a superposition of elements of the canonical basis and the notion of probability naturally follows from the Born rule. In this work we consider three valued quantum computational logics. More specifically, we will focus on the Hilbert space C3, we discuss extensions of several gat...

Many-Valued Logics

The paper considers the fundamental notions of manyvalued logic together with some of the main trends of the recent development of infinite valued systems, often called mathematical fuzzy logics. Besides this logical approach also a more algebraic approach is discussed. And the paper ends with some hints toward applications which are based upon actual theoretical considerations about infinite v...

Many-valued modal logics

Two families of many-valued modal logics are investigated. Semantically, one family is characterized using Kripke models that allow formulas to take values in a finite many-valued logic, at each possible world. The second family generalizes this to allow the accessibility relation between worlds also to be many-valued. Gentzen sequent calculi are given for both versions, and soundness and compl...

Many - Valued Logics

Prolog Extensions to Many{Valued Logics

The aim of this paper is to show that a restriction of a logical language to clauses like Horn clauses, as they are used in Prolog, applied to 0,1]{valued logics leads to calculi with a sound and complete proof theory. In opposition to other models where generally the set of axioms as well as the deduction schemata are enriched we restrict ourselves to a simple modiication of the deduction rule...