P ROBABILISTIC L OGIC UNDER C OHERENCE : C OMPLEXITY AND A LGORITHMS Veronica BIAZZO Thomas LUKASIEWICZ Angelo GILIO Giuseppe SANFILIPPO

We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore the relationship between coherence-based and classical model-theoretic probabilistic logic. Interestingly, 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. Using these results, we analyze the computational complexity of probabilistic reasoning under coherence. Moreover, we present new algorithms for deciding g-coherence and for computing tight g-coherent intervals, which reduce these tasks to standard reasoning tasks in modeltheoretic probabilistic logic. Thus, efficient techniques for model-theoretic probabilistic reasoning can immediately be applied for probabilistic reasoning under coherence, for example, column generation techniques. We then describe two other interesting techniques for efficient model-theoretic probabilistic reasoning in the conjunctive case. 1Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Città Universitaria, Viale A. Doria 6, 95152 Catania, Italy. E-mail: fvbiazzo, [email protected]. 2Dipartimento di Metodi e Modelli Matematici, Università “La Sapienza”, Via A. Scarpa 16, 00161 Roma, Italy. E-mail: [email protected]. 3Institut und Ludwig Wittgenstein Labor für Informationssysteme, TU Wien, Favoritenstraße 9-11, 1040 Vienna, Austria. E-mail: [email protected]. Acknowledgements: This work has been partially supported by a DFG grant and by the Austrian Science Fund under project N Z29-INF. Copyright c 2001 by the authors 2 INFSYS RR 1843-01-04