Shallow models for non-iterative modal logics

Lutz Schröder; Dirk Pattinson

In: Andreas Dengel; Karsten Berns; Thomas Breuel; Frank Bomarius; Thomas Roth-Berghofer (Hrsg.). Proc. German Conference on Artificial Intelligence (KI 2008). German Conference on Artificial Intelligence (KI-2008), 31st Annual German Conference on AI, September 23-26, Kaiserslautern, Germany, Pages 324-331, Lecture Notes in Artificial Intelligence (LNAI), Vol. 5243, Springer, 2008.


Modal logics see a wide variety of applications in artificial intelligence, e.g. in reasoning about knowledge, belief, uncertainty, agency, defaults, and relevance. From the perspective of applications, the attractivity of modal logics stems from a combination of expressive power and comparatively low computational complexity. Compared to the classical treatment of modal logics with relational semantics, the use of modal logics in AI has two characteristic traits: Firstly, a large and growing variety of logics is used, adapted to the concrete situation at hand, and secondly, these logics are often non-normal. Here, we present a shallow model construction that witnesses PSPACE bounds for a broad class of mostly non-normal modal logics. Our approach is both uniform and generic: rather than investigating the complexity of logics one at a time, we present general criteria that uniformly apply to and are easily checked in large numbers of examples. In this way, we not only re-prove known complexity bounds for a wide variety of structurally different logics and obtain previously unknown PSPACE-bounds, e.g. for Elgesem's logic of agency, but also lay the foundations upon which the complexity of newly emerging logics can be determined.

Deutsches Forschungszentrum für Künstliche Intelligenz
German Research Center for Artificial Intelligence