1,142 research outputs found
Nonmonotonic Probabilistic Logics between Model-Theoretic Probabilistic Logic and Probabilistic Logic under Coherence
Recently, it has been shown that probabilistic entailment under coherence is
weaker than model-theoretic probabilistic entailment. Moreover, probabilistic
entailment under coherence is a generalization of default entailment in System
P. In this paper, we continue this line of research by presenting probabilistic
generalizations of more sophisticated notions of classical default entailment
that lie between model-theoretic probabilistic entailment and probabilistic
entailment under coherence. That is, the new formalisms properly generalize
their counterparts in classical default reasoning, they are weaker than
model-theoretic probabilistic entailment, and they are stronger than
probabilistic entailment under coherence. The new formalisms are useful
especially for handling probabilistic inconsistencies related to conditioning
on zero events. They can also be applied for probabilistic belief revision.
More generally, in the same spirit as a similar previous paper, this paper
sheds light on exciting new formalisms for probabilistic reasoning beyond the
well-known standard ones.Comment: 10 pages; in Proceedings of the 9th International Workshop on
Non-Monotonic Reasoning (NMR-2002), Special Session on Uncertainty Frameworks
in Nonmonotonic Reasoning, pages 265-274, Toulouse, France, April 200
Probabilistic Default Reasoning with Conditional Constraints
We propose a combination of probabilistic reasoning from conditional
constraints with approaches to default reasoning from conditional knowledge
bases. In detail, we generalize the notions of Pearl's entailment in system Z,
Lehmann's lexicographic entailment, and Geffner's conditional entailment to
conditional constraints. We give some examples that show that the new notions
of z-, lexicographic, and conditional entailment have similar properties like
their classical counterparts. Moreover, we show that the new notions of z-,
lexicographic, and conditional entailment are proper generalizations of both
their classical counterparts and the classical notion of logical entailment for
conditional constraints.Comment: 8 pages; to appear in Proceedings of the Eighth International
Workshop on Nonmonotonic Reasoning, Special Session on Uncertainty Frameworks
in Nonmonotonic Reasoning, Breckenridge, Colorado, USA, 9-11 April 200
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
Coping with the Limitations of Rational Inference in the Framework of Possibility Theory
Possibility theory offers a framework where both Lehmann's "preferential
inference" and the more productive (but less cautious) "rational closure
inference" can be represented. However, there are situations where the second
inference does not provide expected results either because it cannot produce
them, or even provide counter-intuitive conclusions. This state of facts is not
due to the principle of selecting a unique ordering of interpretations (which
can be encoded by one possibility distribution), but rather to the absence of
constraints expressing pieces of knowledge we have implicitly in mind. It is
advocated in this paper that constraints induced by independence information
can help finding the right ordering of interpretations. In particular,
independence constraints can be systematically assumed with respect to formulas
composed of literals which do not appear in the conditional knowledge base, or
for default rules with respect to situations which are "normal" according to
the other default rules in the base. The notion of independence which is used
can be easily expressed in the qualitative setting of possibility theory.
Moreover, when a counter-intuitive plausible conclusion of a set of defaults,
is in its rational closure, but not in its preferential closure, it is always
possible to repair the set of defaults so as to produce the desired conclusion.Comment: Appears in Proceedings of the Twelfth Conference on Uncertainty in
Artificial Intelligence (UAI1996
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
A Plausibility Semantics for Abstract Argumentation Frameworks
We propose and investigate a simple ranking-measure-based extension semantics
for abstract argumentation frameworks based on their generic instantiation by
default knowledge bases and the ranking construction semantics for default
reasoning. In this context, we consider the path from structured to logical to
shallow semantic instantiations. The resulting well-justified JZ-extension
semantics diverges from more traditional approaches.Comment: Proceedings of the 15th International Workshop on Non-Monotonic
Reasoning (NMR 2014). This is an improved and extended version of the
author's ECSQARU 2013 pape
Numerical Representations of Acceptance
Accepting a proposition means that our confidence in this proposition is
strictly greater than the confidence in its negation. This paper investigates
the subclass of uncertainty measures, expressing confidence, that capture the
idea of acceptance, what we call acceptance functions. Due to the monotonicity
property of confidence measures, the acceptance of a proposition entails the
acceptance of any of its logical consequences. In agreement with the idea that
a belief set (in the sense of Gardenfors) must be closed under logical
consequence, it is also required that the separate acceptance o two
propositions entail the acceptance of their conjunction. Necessity (and
possibility) measures agree with this view of acceptance while probability and
belief functions generally do not. General properties of acceptance functions
are estabilished. The motivation behind this work is the investigation of a
setting for belief revision more general than the one proposed by Alchourron,
Gardenfors and Makinson, in connection with the notion of conditioning.Comment: Appears in Proceedings of the Eleventh Conference on Uncertainty in
Artificial Intelligence (UAI1995
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