Logics from $\sqrt{^{\prime}}$ Quasi-MV Algebras

Abstract

The purpose of the present article is to extend the scope of some investigations about abstract logics arising quite naturally out of Quasi-MV algebras (for short, qMV algebras) also to √ qMV algebras. We will therefore introduce, mutually compare and (in some cases) axiomatise several logics arising out of the variety of √ qMV algebras and out of some important subclasses of such. Subsequently, we will investigate the same logics by resorting to the methods and techniques of abstract algebraic logic.

Holistic Type Extension for Classical Logic via Toffoli Quantum Gate

“…In this way, the input and the output of quantum circuits are labeled by density operators and possible notions of logical consequence are defined by relations between the input and the output of circuits. Several families of quantum computational logics arise from these extensions [ 5 , 6 , 24 ]. These families of logics have a common semantics based on probability-values introduced in Equation ( 5 ).…”