Terminating Hybrid Tableaus for Ordered Models

TL;DR

This paper introduces terminating tableau calculi for hybrid logic with nominals, specifically designed for models with various types of partial orders, enabling effective reasoning about properties like irreflexivity and anti-symmetry.

Contribution

It presents new terminating tableau methods tailored for hybrid logic over different classes of partially ordered models, ensuring completeness and practical applicability.

Findings

Tableau calculi are complete for models with strict partial orders.

Calculi terminate for unbounded strictly partial ordered models.

Effective reasoning about properties like irreflexivity and anti-symmetry is enabled.

Abstract

Hybrid logic extends modal logic with special propositions called nominals, each of which is true at only one state in a model. This enables us to describe some properties of binary relations, such as irreflexivity and anti-symmetry, which are essential to treat partial orders. We present terminating tableau calculi complete with respect to models whose accessibility relations are strictly partially ordered, unbounded strictly partially ordered, and partially ordered.