40,893 research outputs found
Precise Propagation of Upper and Lower Probability Bounds in System P
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
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
In this paper we explore relaxations of (Williams) coherent and convex
conditional previsions that form the families of -coherent and -convex
conditional previsions, at the varying of . We investigate which such
previsions are the most general one may reasonably consider, suggesting
(centered) -convex or, if positive homogeneity and conjugacy is needed,
-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 -convex or, respectively, -coherent natural extension.
The role of these extensions is analogous to that of the natural extension for
coherent lower previsions. On the contrary, -convex and -coherent
previsions with 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 -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 -convex. In the final
part, we determine the rationality requirements of -convexity and
-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
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
- …