Terminating Hybrid Tableaus for Ordered Models
This work addresses a foundational issue in automated reasoning for hybrid logic, focusing on partial orders, but it is incremental as it builds on existing tableau methods for modal logic.
The paper tackled the problem of developing terminating tableau calculi for hybrid logic to handle models with strictly partially ordered, unbounded strictly partially ordered, and partially ordered accessibility relations, achieving completeness for these specific relational properties.
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.