40,893 research outputs found

    ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

    Get PDF
    B

    Precise Propagation of Upper and Lower Probability Bounds in System P

    Full text link
    In this paper we consider the inference rules of System P in the framework of coherent imprecise probabilistic assessments. Exploiting our algorithms, we propagate the lower and upper probability bounds associated with the conditional assertions of a given knowledge base, automatically obtaining the precise probability bounds for the derived conclusions of the inference rules. This allows a more flexible and realistic use of System P in default reasoning and provides an exact illustration of the degradation of the inference rules when interpreted in probabilistic terms. We also examine the disjunctive Weak Rational Monotony of System P+ proposed by Adams in his extended probability logic.Comment: 8 pages -8th Intl. Workshop on Non-Monotonic Reasoning NMR'2000, April 9-11, Breckenridge, Colorad

    Probabilistic entailment in the setting of coherence: The role of quasi conjunction and inclusion relation

    Full text link
    In this paper, by adopting a coherence-based probabilistic approach to default reasoning, we focus the study on the logical operation of quasi conjunction and the Goodman-Nguyen inclusion relation for conditional events. We recall that quasi conjunction is a basic notion for defining consistency of conditional knowledge bases. By deepening some results given in a previous paper we show that, given any finite family of conditional events F and any nonempty subset S of F, the family F p-entails the quasi conjunction C(S); then, given any conditional event E|H, we analyze the equivalence between p-entailment of E|H from F and p-entailment of E|H from C(S), where S is some nonempty subset of F. We also illustrate some alternative theorems related with p-consistency and p-entailment. Finally, we deepen the study of the connections between the notions of p-entailment and inclusion relation by introducing for a pair (F,E|H) the (possibly empty) class K of the subsets S of F such that C(S) implies E|H. We show that the class K satisfies many properties; in particular K is additive and has a greatest element which can be determined by applying a suitable algorithm

    2-coherent and 2-convex Conditional Lower Previsions

    Get PDF
    In this paper we explore relaxations of (Williams) coherent and convex conditional previsions that form the families of nn-coherent and nn-convex conditional previsions, at the varying of nn. We investigate which such previsions are the most general one may reasonably consider, suggesting (centered) 22-convex or, if positive homogeneity and conjugacy is needed, 22-coherent lower previsions. Basic properties of these previsions are studied. In particular, we prove that they satisfy the Generalized Bayes Rule and always have a 22-convex or, respectively, 22-coherent natural extension. The role of these extensions is analogous to that of the natural extension for coherent lower previsions. On the contrary, nn-convex and nn-coherent previsions with n3n\geq 3 either are convex or coherent themselves or have no extension of the same type on large enough sets. Among the uncertainty concepts that can be modelled by 22-convexity, we discuss generalizations of capacities and niveloids to a conditional framework and show that the well-known risk measure Value-at-Risk only guarantees to be centered 22-convex. In the final part, we determine the rationality requirements of 22-convexity and 22-coherence from a desirability perspective, emphasising how they weaken those of (Williams) coherence.Comment: This is the authors' version of a work that was accepted for publication in the International Journal of Approximate Reasoning, vol. 77, October 2016, pages 66-86, doi:10.1016/j.ijar.2016.06.003, http://www.sciencedirect.com/science/article/pii/S0888613X1630079

    Credence for Epistemic Discourse

    Get PDF
    Many recent theories of epistemic discourse exploit an informational notion of consequence, i.e. a notion that defines entailment as preservation of support by an information state. This paper investigates how informational consequence fits with probabilistic reasoning. I raise two problems. First, all informational inferences that are not also classical inferences are, intuitively, probabilistically invalid. Second, all these inferences can be exploited, in a systematic way, to generate triviality results. The informational theorist is left with two options, both of them radical: they can either deny that epistemic modal claims have probability at all, or they can move to a nonstandard probability theory
    corecore