First-order friendliness

TL;DR

This paper introduces a first-order logic counterpart to propositional 'logical friendliness', creating a new consequence relation that retains some properties despite lacking compactness and interpolation.

Contribution

It develops a novel consequence relation for predicate logic inspired by propositional 'logical friendliness', extending the concept to first-order models.

Findings

Compactness and interpolation fail dramatically in the new relation.

Some properties from propositional logic are preserved in the first-order case.

The new consequence relation offers a different perspective on logical inference in predicate logic.

Abstract

In this note we study a counterpart in predicate logic of the notion of 'logical friendliness', introduced into propositional logic in Makinson (2007). The result is a new consequence relation for predicate languages using first-order models. Although compactness and interpolation fail dramatically, other properties are preserved from the propositional case.