A Model Theoretic Semantics for Quantum Logic

Abstract

The purpose of this contribution is to consider a model theoretic semantics of quantum logic. The quantum logic to which we refer here comprises the system of sequential quantum logic (Stachow 1980b). This system establishes the implication relation with respect to logically connected propositions and also with respect to the more general class of sequentially connected propositions of the language of quantum physics.A dialogic semantics for logically connected sentences is developed in Stachow (1976, p. 203), where it is shown that a logical system, usually called the system of quantum logic, is complete and sound with respect to the dialogic semantics. The dialogic semantics is extended to sequentially connected sentences in Stachow (1980b) and to modal sentences in Mittelstaedt (1979, p. 479).In comparison with other approaches to a language for science, the dialogic approach is developed from a pragmatic and methodological point of view (Stachow 1980a).