Neighbourhood completeness for quantified pretransitive modal logics

TL;DR

This paper proves that quantified pretransitive Horn modal logics are complete not only with respect to predicate Kripke frames with expanding domains but also with respect to neighbourhood frames with constant domains.

Contribution

It establishes the completeness of these logics with respect to neighbourhood frames, extending known results beyond Kripke frames.

Findings

Completeness with respect to neighbourhood frames with constant domains.

Extension of known completeness results to a broader class of frames.

Advancement in understanding the semantics of quantified pretransitive Horn modal logics.

Abstract

We consider quantified pretransitive Horn modal logic. It is known that such logics are complete with respect to predicate Kripke frames with expanding domains. In this paper we prove that they are also complete with respect to neighbourhood frames with constant domains.