5,343 research outputs found
Belief Revision with Uncertain Inputs in the Possibilistic Setting
This paper discusses belief revision under uncertain inputs in the framework
of possibility theory. Revision can be based on two possible definitions of the
conditioning operation, one based on min operator which requires a purely
ordinal scale only, and another based on product, for which a richer structure
is needed, and which is a particular case of Dempster's rule of conditioning.
Besides, revision under uncertain inputs can be understood in two different
ways depending on whether the input is viewed, or not, as a constraint to
enforce. Moreover, it is shown that M.A. Williams' transmutations, originally
defined in the setting of Spohn's functions, can be captured in this framework,
as well as Boutilier's natural revision.Comment: Appears in Proceedings of the Twelfth Conference on Uncertainty in
Artificial Intelligence (UAI1996
A New Rational Algorithm for View Updating in Relational Databases
The dynamics of belief and knowledge is one of the major components of any
autonomous system that should be able to incorporate new pieces of information.
In order to apply the rationality result of belief dynamics theory to various
practical problems, it should be generalized in two respects: first it should
allow a certain part of belief to be declared as immutable; and second, the
belief state need not be deductively closed. Such a generalization of belief
dynamics, referred to as base dynamics, is presented in this paper, along with
the concept of a generalized revision algorithm for knowledge bases (Horn or
Horn logic with stratified negation). We show that knowledge base dynamics has
an interesting connection with kernel change via hitting set and abduction. In
this paper, we show how techniques from disjunctive logic programming can be
used for efficient (deductive) database updates. The key idea is to transform
the given database together with the update request into a disjunctive
(datalog) logic program and apply disjunctive techniques (such as minimal model
reasoning) to solve the original update problem. The approach extends and
integrates standard techniques for efficient query answering and integrity
checking. The generation of a hitting set is carried out through a hyper
tableaux calculus and magic set that is focused on the goal of minimality.Comment: arXiv admin note: substantial text overlap with arXiv:1301.515
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
Plausible inference: A multi-valued logic for problem solving
A new logic is developed which permits continuously variable strength of belief in the truth of assertions. Four inference rules result, with formal logic as a limiting case. Quantification of belief is defined. Propagation of belief to linked assertions results from dependency-based techniques of truth maintenance so that local consistency is achieved or contradiction discovered in problem solving. Rules for combining, confirming, or disconfirming beliefs are given, and several heuristics are suggested that apply to revising already formed beliefs in the light of new evidence. The strength of belief that results in such revisions based on conflicting evidence are a highly subjective phenomenon. Certain quantification rules appear to reflect an orderliness in the subjectivity. Several examples of reasoning by plausible inference are given, including a legal example and one from robot learning. Propagation of belief takes place in directions forbidden in formal logic and this results in conclusions becoming possible for a given set of assertions that are not reachable by formal logic
An Ordinal View of Independence with Application to Plausible Reasoning
An ordinal view of independence is studied in the framework of possibility
theory. We investigate three possible definitions of dependence, of increasing
strength. One of them is the counterpart to the multiplication law in
probability theory, and the two others are based on the notion of conditional
possibility. These two have enough expressive power to support the whole
possibility theory, and a complete axiomatization is provided for the strongest
one. Moreover we show that weak independence is well-suited to the problems of
belief change and plausible reasoning, especially to address the problem of
blocking of property inheritance in exception-tolerant taxonomic reasoning.Comment: Appears in Proceedings of the Tenth Conference on Uncertainty in
Artificial Intelligence (UAI1994
Syntactic Computation of Hybrid Possibilistic Conditioning under Uncertain Inputs
International audienceWe extend hybrid possibilistic conditioning to deal with inputs consisting of a set of triplets composed of propositional formulas, the level at which the formulas should be accepted, and the way in which their models should be revised. We characterize such conditioning using elementary operations on possibility distributions. We then solve a difficult issue that concerns the syntactic computation of the revision of possibilistic knowledge bases, made of weighted formulas, using hybrid conditioning. An important result is that there is no extra computational cost in using hybrid possibilistic conditioning and in particular the size of the revised possibilistic base is polynomial with respect to the size of the initial base and the input
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