Tensed Ontology Based on Simple Partial Logic

Simple partial logic (=SPL) is, broadly speaking, an extensional logic which allows for the truth-value gap. First I give a system of propositional SPL by partializing classical logic, as well as extending it with several non-classical truth-functional operators. Second I show a way based on SPL to construct a system of tensed ontology, by representing tensed statements as two kinds of necessary statements in a linear model that consists of the present and future worlds. Finally I compare that way with other two ways based on à Lukasiewicz’s threevalued logic and branching temporal logic. 1 Simple Partial Logic SPL is a system of truth-functional logic that generalizes (propositional) classical logic (=CL) by allowing for the truth-value gap. At the same time the SPL given in this paper is an extension of CL by adding several non-classical truth-functional operators which are reducible to one. Here I restrict my arguments to its syntax and semantics, omitting its proof theory. There are two kinds of logical operators in SPL: the basic operators, which are also included in the syntax of CL, and the modal operators, which are not included. I show the operators and their semantics in the following tables: Table 1: Basic operators A ∼A