The technique applies also to the formalisation of partial functions as proper type-theoretic functions, rather that relations representing their graphs. In collaboration with Pieter A. M. Seuren and Herman Geuvers . Some of the insights elaborated in this paper have appeared in the literature over the past thirty years, and a number of new developments have resulted from them. The present paper aims at providing an integrated conceptual basis for this new development in semantics. In Section 1 it is argued that the reduction by translation of occasion sentences to eternal sentences, as proposed by Russell and Quine, is semantically and thus logically inadequate.
Natural language is a system of occasion sentences, eternal sentences being merely boundary cases.
The logic has fewer tasks than is standardly assumed, as it excludes semantic calculi, which depend crucially on information supplied by cognition and context and thus belong to cognitive psychology rather than to logic. For sentences to express a proposition and thus be interpretable and informative, they must first be properly anchored in context . A proposition has a truth value when it is, moreover, properly keyed in the world , i.e. is about a situation in the world. Section 2 deals with the logical properties of natural language. It argues that presuppositional phenomena require trivalence and presents the trivalent logic PPC3, with two kinds of falsity and two negations.