A Proof System for a Logic of Presuppositions

TL;DR

This paper introduces a derivation system for a logic of presuppositions, extending truth-relevant logic to predicate calculus, and clarifies the conditions under which tautologies are considered truth-relevant.

Contribution

It develops a new derivation system for a logic of presuppositions based on truth-relevant logic, extending previous work to predicate calculus.

Findings

A derivation system for a logic of presuppositions is proposed.

A criterion for truth-relevant tautologies is established.

Extension of truth-relevant logic to predicate calculus is demonstrated.

Abstract

The paper proposes a derivation system for a logic of presuppositions as introduced by P. F. Strawson. It is based on truth-relevant logic described by M. Richard Diaz in 1981. In another paper I outlined a derivation system for t-relevant logic based on truth trees. The conclusion was that a tautology is truth-relevant iff all the variables in a tree are self-contradicted. It is possible that a tree terminates without all the variables self-contradicting themselves. In this case the pertaining formula is still a tautology, but not a truth-relevant tautology. This concept is extended to the predicate calculus, i.e. a logic of presuppositions or a variant thereof.