On the Axiomatization of Finite-Valued Logical Calculi

Abstract

We analyze the two-kaon Bose-Einstein correlation in the reactions of 160A GeV/c P b t P b within an event generator URASiMA. The apparent radius of kaon-source is extracted. The theoretical result agrees quite well with the preliminary data of NA44.

Von Wright’s truth-logic and around

“…As a result, we obtain an entirely new class of many-valued logics which I suggest to call 'Wright's many-valued logics' and a new class algebras which I suggest to call 'Wright's algebras'. Then again it follows from [1] that for such logics we have adequate first-order axiomatization. 4 Properties of a truth-operator T and the twin truth operators…”

On Finite-Valued Propositional Logical Calculi

“…The main result of our joint papers [2] and [5] is the specification of a general, effective method for constructing Hilbert-type first-order calculi for any truthcomplete C-extending well-quantified logic. (Note that the condition of being wellquantified is not necessary for constructing propositional calculi.)…”

“…(Note that the condition of being wellquantified is not necessary for constructing propositional calculi.) Further, in the final sections of [2] and [5], we describe a general effective method to construct so-called "quasi-Hilbert"-type first-order calculi for arbitrary finite-valued logics. A general computational scheme for two-termed sequents in finite-valued logics is given in our papers [3] and [4].…”

“…(Examples include the Łoś ultraproduct theorem, Maltsev's compactness theorem, and others.) In this connection, at least the following papers should also be mentioned: [2], [3], [4], [5], D'Ottaviano [40], [41], and [42], along with the abstracts [6] and [52].…”

“…is functionally equivalent to the basic signature σ 1 . In Section 4 we shall briefly discuss (along the lines of [2] and [5]) the possibility of extending our results to other classes of finite-valued logics. In Section 5 we shall describe L n -derivable formulas of a truth-complete C-extending finite-valued propositional calculus L n in an algebraic language.…”