Showing papers on "Paraconsistent logic published in 1975"

Stochastic and fuzzy logics

Abstract: It is shown that it is possible to regard stochastic and fuzzy logics as being derived from two different constraints on a probability logic: statistical independence (stochastic) and logical implication (fuzzy). To contrast the merits of the two logics, some published data on a fuzzy-logic controller is reanalysed using stochastic logic and it is shown that no significant difference results in the control policy.

Stalnaker conditionals and quantum logic

Abstract: Since Birkhoff and von Neumann [l] first proposed that the logic appropriate to the elementary propositions of quantum mechanics (QM) is nonclassical, a considerable amount of research has been pursued on the quantum logical foundations of QM and on the mathematical structures associated with quantum logic (QL). Birkhoff and von Neumann singled out the distributive law of classical logic as suspect, replacing it by the weaker modular law. More recently, even the modular law has been abandoned in favor of the still weaker law of orthomodularity (weak modularity or quasimodularity). This move has resulted from the fact that the lattice of subspaces of an infinite dimensional Hilbert space, which provides the concrete model for QL, is orthomodular but not modular. In many respects the algebraic study of QL has been subsumed under the general study of orthomodular lattices and, in some cases, orthomodular partially ordered sets (posets). It is commonplace for mathematicians to appropriate terms from ordinary discourse and confer upon them esoteric technical meanings which have little in common with the ordinary meanings. In most cases, it is useless to question the mathematicians’ usage; for example, it seems quite inappropriate to ask whether the mathematicians’ ‘field’ is ‘really’ a field. Along the same lines, as a simple matter of technical definition, one need not dispute employing the term ‘logic’ to refer to certain lattices and posets. On the other hand, claims concerning these abstract ‘quantum logic? are often intended to have a peculiar relevance to logic, as ordinarily construed, in a way quite unlike the intended relevance of the mathematical theory of fields to cornfields, wheatfields, or electromagnetic fields. Accordingly, it does seem appropriate to ask whether ‘quantum logic’ is really a logic. More specifically, the question is whether it is proper to regard the lattice of QM, or more generally the class of orthomodular lattices (posets), as a logic as opposed to merely a class of algebraic structures only formally analogous to logic properly so called. Doubts along these lines have in particular been