Synthetic Completeness for a Terminating Seligman-Style Tableau System

Asta Halkjær From, Ugo de'Liguoro, Stefano Berardi, Thorsten Altenkirch
2021
Hybrid logic extends modal logic with nominals that name worlds. Seligman-style tableau systems for hybrid logic divide branches into blocks named by nominals to achieve a local proof style. We present a Seligman-style tableau system with a formalization in the proof assistant Isabelle/HOL. Our system refines an existing system to simplify formalization and we claim termination from this relationship. Existing completeness proofs that account for termination are either analytic or based on
more » ... lation, but synthetic proofs have been shown to generalize to richer logics and languages. Our main result is the first synthetic completeness proof for a terminating hybrid logic tableau system. It is also the first formalized completeness proof for any hybrid logic proof system.
doi:10.4230/lipics.types.2020.5 fatcat:5rufwgyngvdabmdn7z42dqu7oq