Logics from sqrt MV-algebras

PAOLI, LEDDA, SPINKS, FREYTES, GIUNTINI

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS

SPRINGER/PLENUM PUBLISHERS

Año: 2011 vol. 50 p. 3882 - 3902

0020-7748

The study of qMV algebras and p0 qMV algebras has its roots in an inquiry into the structure of quantum computational circuits  and thus, to all intents and purposes, in a problem that is logical rather than algebraic { the work referred to so far sidesteps, as it were, the logical aspects connected with these structures. On the other hand, contains a detailed investigation into some abstract logics arising quite naturally out of qMV algebras. The purpose of the present article is to extend the scope of this investigation to p0 qMValgebras. We will therefore introduce, mutually compare and (in some cases) axiomatise several logics arising from the variety of p0 qMV algebras and from some of its important subclasses; subsequently, we will investigate the same logics by resorting to the methods and techniques of abstract algebraic logic.p0 qMV algebras has its roots in an inquiry into the structure of quantum computational circuits  and thus, to all intents and purposes, in a problem that is logical rather than algebraic { the work referred to so far sidesteps, as it were, the logical aspects connected with these structures. On the other hand, contains a detailed investigation into some abstract logics arising quite naturally out of qMV algebras. The purpose of the present article is to extend the scope of this investigation to p0 qMValgebras. We will therefore introduce, mutually compare and (in some cases) axiomatise several logics arising from the variety of p0 qMV algebras and from some of its important subclasses; subsequently, we will investigate the same logics by resorting to the methods and techniques of abstract algebraic logic.