Monotonicity and Persistence in Preferential Logics

TL;DR

This paper investigates monotonicity and persistence properties in preferential logics, characterizing formulae that preserve or respect these properties, with implications for improving theorem prover efficiency.

Contribution

It introduces a syntactic characterization of monotonic and conservative formulae in preferential logics, linking them to truth-value preservation along the ordering.

Findings

Identifies classes of formulae respecting monotonicity and persistence.

Provides syntactic characterization results for preferential logics.

Potentially improves theorem prover efficiency for preferential logics.

Abstract

An important characteristic of many logics for Artificial Intelligence is their nonmonotonicity. This means that adding a formula to the premises can invalidate some of the consequences. There may, however, exist formulae that can always be safely added to the premises without destroying any of the consequences: we say they respect monotonicity. Also, there may be formulae that, when they are a consequence, can not be invalidated when adding any formula to the premises: we call them conservative. We study these two classes of formulae for preferential logics, and show that they are closely linked to the formulae whose truth-value is preserved along the (preferential) ordering. We will consider some preferential logics for illustration, and prove syntactic characterization results for them. The results in this paper may improve the efficiency of theorem provers for preferential logics.