Probabilistic Logic under Coherence, Model-theoretic Probabilistic Logic, and Default Reasoning in System Probabilistic Logic under Coherence, Model-theoretic Probabilistic Logic, and Default Reasoning in System

We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore how probabilistic reasoning under coherence is related to model-theoretic probabilistic reasoning and to default reasoning in System . In particular, we show that the notions of g-coherence and of g-coherent entailment can be expressed by combining notions in model-theoretic probabilistic logic with concepts from default reasoning. Moreover, we show that probabilistic reasoning under coherence is a generalization of default reasoning in System . That is, we provide a new probabilistic semantics for System , which neither uses infinitesimal probabilities nor atomic bound (or big-stepped) probabilities. These results also provide new algorithms for probabilistic reasoning under coherence and for default reasoning in System , and they give new insight into default reasoning with conditional objects. 1Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Città Universitaria, Viale A. Doria 6, 95152 Catania, Italy; email: vbiazzo, gsanfilippo @dmi.unict.it. 2Dipartimento di Metodi e Modelli Matematici, Università di Roma “La Sapienza”, Via A. Scarpa 16, 00161 Roma, Italy; email: [email protected]. 3Dipartimento di Informatica e Sistemistica, Università di Roma “La Sapienza”, Via Salaria 113, 00198 Roma, Italy; email: [email protected]. Alternate address: Institut für Informationssysteme, Technische Universität Wien, Favoritenstraße 9-11, 1040 Wien, Austria; email: [email protected]. Acknowledgements: This work has been partially supported by a DFG grant, a European Community Marie Curie Individual Fellowship (Disclaimer: The authors are solely responsible for information communicated and the European Commission is not responsible for any views or results expressed), and the Austrian Science Fund Project N Z29-INF. We are thankful to the reviewers of the ECSQARU-2001 version of this paper, whose constructive comments helped to improve this paper. Copyright c 2002 by the authors 2 INFSYS RR 1843-01-03