A Hierarchy of Modal Event Calculi: Expressiveness and Complexity
We consider a hierarchy of modal event calculi to represent and reason about partially ordered events. These calculi are based on the model of time and change of Kowalski and Sergot’s Event Calculus (EC): given a set of event occurrences, EC allows the derivation of the maximal validity intervals (MVIs) over which properties initiated or terminated by those events hold. The formalisms we analyze extend EC with operators from modal logic. They range from the basic Modal Event Calculus (MEC), that computes the set of all current MVIs (MVIs computed by EC) as well as the sets of MVIs that are true in some/every refinement of the current partial ordering of events (◊-/□;-MVIs), to the Generalized Modal Event Calculus (GMEC),that extends MEC by allowing a free mix of boolean connectives and modal operators. We analyze and compare the expressive power and the complexity of the proposed calculi, focusing on intermediate systems between MEC and GMEC. We motivate the discussion by using a fault diagnosis problem as a case study.
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- Cervesato, I., L. Chittaro, and A. Montanari: 1995a, ‘A Modal Calculus of Partially Ordered Events in a Logic Programming Framework’. In: L. Sterling (ed.): Proceedings of the Twelfth International Conference on Logic Programming — ICLP’95. Kanagawa, Japan, pp. 299–313.Google Scholar
- Cervesato, I., L. Chittaro, and A. Montanari: 1995b, ‘Speeding up temporal reasoning by exploiting the notion of kernel of an ordering relation’. In: S. Goodwin and H. Hamilton (eds.): Proceedings of the Second International Workshop on Temporal Representation and Reasoning — TIME’95. Melbourne Beach, FL, pp. 73–80.Google Scholar
- Cervesato, I., L. Chittaro, and A. Montanari: 1996, ‘A General Modal Framework for the Event Calculus and its Skeptical and Credulous Variants’. In: W. Wahlster (ed.): Proceedings of the Twelfth European Conference on Artificial Intelligence — ECAI’96. Budapest, Hungary, pp. 33–37. Extended and revised version submitted for publication, July 1996.Google Scholar
- Cervesato, I., A. Montanari, and A. Provetti: 1993, ‘On the Non-Monotonic Behavior of the Event Calculus for Deriving Maximal Time Intervals’. International Journal on Interval Computations 2, 83–119.Google Scholar
- Franceschet, M.: 1996, ‘Una Gerarchia di Calcoli Modali degli Eventi: Espressività e Complessità (in Italian)’. Tesi di Laurea in Informatica, Università di Udine, Italy. To appear as a Research Report in English.Google Scholar
- Garey, M. and D. Johnson: 1979, Computing and Intractability: A Guide to the Theory of NP-Completeness. Freeman & Cie.Google Scholar
- Nökel, K.: 1991, Temporarily Distributed Symptoms in Technical Diagnosis. Springer-Verlag.Google Scholar
- Segerberg, K.: 1971, ‘An Essay in Classical Modal Logic’. Uppsala Filosofiska Studier.Google Scholar