Logic for approximate entailment in ordered universes of discourse

TL;DR

This paper introduces a modified logic for approximate entailment that incorporates an order structure on possible worlds, aiming to improve its applicability by enabling conjunctive reasoning.

Contribution

It proposes a new semantic framework for LAE by adding an order structure to the set of possible worlds, addressing its previous limitation in conjunctive reasoning.

Findings

Enhanced semantic framework for LAE with order structure

Potential for improved reasoning in applications

Addresses conjunctive reasoning limitations in LAE

Abstract

The Logic of Approximate Entailment (LAE) is a graded counterpart of classical propositional calculus, where conclusions that are only approximately correct can be drawn. This is achieved by equipping the underlying set of possible worlds with a similarity relation. When using this logic in applications, however, a disadvantage must be accepted; namely, in LAE it is not possible to combine conclusions in a conjunctive way. In order to overcome this drawback, we propose in this paper a modification of LAE where, at the semantic level, the underlying set of worlds is moreover endowed with an order structure. The chosen framework is designed in view of possible applications.