First-Order Resolution Methods for Modal Logics

Abstract

Abstract. In this paper we give an overview of results for modal logic which can be shown using techniques and methods from first-order logic and resolution. Because of the breadth of the area and the many applications we focus on the use of first-order resolution methods for modal logics. In addition to traditional propositional modal logics we consider more expressive PDL-like dynamic modal logics which are closely related to description logics. Without going into too much detail, we survey different ways of translating modal logics into first-order logic, we explore different ways of using first-order resolution theorem provers, and we discuss a variety of results which have been obtained in the setting of first-order resolution.

Efficient Local Reductions to Basic Modal Logic

“…For the relational and semi-functional translation for K, KB, KD, and KT we thereby obtain a decision procedure, while for the other logics we do not. For K4 and K5, the fragment of first-order clausal logic corresponding to the semi-functional translation of modal formula and their background theories is decidable by ordered resolution with selection [25]. However, the non-trivial ordering and selection function required is not currently implemented in SPASS.…”

Modal Satisfiability via SMT Solving

“…In particular, Hustadt and Schmidt [10,16,21] systematically explored techniques based on translations to first-order logic and the use of resolution and superposition provers. Our work starts from the same encodings in first-order languages but relies on ground decision procedures for suitable fragments of first-order logic.…”

Automated Reasoning in Deontic Logic

“…Nonetheless, numerous approaches to translate modal logics into (decidable fragments of) first-order predicate logics are stated in the literature. A nice overview including many relevant references is given in [19].…”