Derivation Schemes in Twin Open Set Logic

Abstract

Several logic-like structures have been developed to analyze classical mechanical systems. These phase space logics are examples of a wider class of structures known as derived logics. Many of the derived logics for classical systems are non-Boolean so it is natural to ask about the existence of derivation schemes in these logics. The prime example of a derivation scheme is the one in classical logic given by entailment, implication, and modus ponens. This chapter presents the relation between these three aspects of classical logic and shows that these three exist only when the logic is Boolean. The chapter then considers some possible alternative derivation schemes for the particular derived logic known as twin open set logic. We show how twin open set logic describes a collision model of computation. We then consider this collision model to choose between alternatives for a derivation scheme for twin open set logic when that logic is applied to collision models.