Semantics for a Logic of Presuppositions

TL;DR

This paper develops a semantics for a logic of presuppositions by connecting it to truth-relevant logic, extending it to polyadic cases, and discussing its implications within a propositional framework.

Contribution

It demonstrates that truth-relevant logic is a propositional form of the logic of presuppositions and extends the semantics to polyadic logic.

Findings

Truth-relevant logic is a propositional version of the logic of presuppositions.

A semantics for the logic of presuppositions is constructed using truth-relevant logic.

The semantics is extended to polyadic logic with discussed consequences.

Abstract

In 1952 P. F. Strawson proposed a logic of presuppositions. It is an interpretation of Aristotelian logic, i.e. of the logic of the traditional syllogism. In 1981 Richard Diaz published a monograph in which he presented truth-relevant logic. This paper shows that truth-relevant logic is but a propositional version of the logic of presuppositions. A semantics of the logic of presuppositions is developed using truth-relevant logic. The semantics is then further extended to polyadic logic and some consequences discussed.