4,329 research outputs found
Characterizing and Extending Answer Set Semantics using Possibility Theory
Answer Set Programming (ASP) is a popular framework for modeling
combinatorial problems. However, ASP cannot easily be used for reasoning about
uncertain information. Possibilistic ASP (PASP) is an extension of ASP that
combines possibilistic logic and ASP. In PASP a weight is associated with each
rule, where this weight is interpreted as the certainty with which the
conclusion can be established when the body is known to hold. As such, it
allows us to model and reason about uncertain information in an intuitive way.
In this paper we present new semantics for PASP, in which rules are interpreted
as constraints on possibility distributions. Special models of these
constraints are then identified as possibilistic answer sets. In addition,
since ASP is a special case of PASP in which all the rules are entirely
certain, we obtain a new characterization of ASP in terms of constraints on
possibility distributions. This allows us to uncover a new form of disjunction,
called weak disjunction, that has not been previously considered in the
literature. In addition to introducing and motivating the semantics of weak
disjunction, we also pinpoint its computational complexity. In particular,
while the complexity of most reasoning tasks coincides with standard
disjunctive ASP, we find that brave reasoning for programs with weak
disjunctions is easier.Comment: 39 pages and 16 pages appendix with proofs. This article has been
accepted for publication in Theory and Practice of Logic Programming,
Copyright Cambridge University Pres
Estimations of expectedness and potential surprise in possibility theory
This note investigates how various ideas of 'expectedness' can be captured in the framework of possibility theory. Particularly, we are interested in trying to introduce estimates of the kind of lack of surprise expressed by people when saying 'I would not be surprised that...' before an event takes place, or by saying 'I knew it' after its realization. In possibility theory, a possibility distribution is supposed to model the relative levels of mutually exclusive alternatives in a set, or equivalently, the alternatives are assumed to be rank-ordered according to their level of possibility to take place. Four basic set-functions associated with a possibility distribution, including standard possibility and necessity measures, are discussed from the point of view of what they estimate when applied to potential events. Extensions of these estimates based on the notions of Q-projection or OWA operators are proposed when only significant parts of the possibility distribution are retained in the evaluation. The case of partially-known possibility distributions is also considered. Some potential applications are outlined
A linear algorithm for multi-target tracking in the context of possibility theory
We present a modelling framework for multi-target tracking based on
possibility theory and illustrate its ability to account for the general lack
of knowledge that the target-tracking practitioner must deal with when working
with real data. We argue that the flexibility of this approach decreases the
risks of misspecification and facilitates the modelling of complex phenomena.
We also introduce and study variants of the notions of point process and
intensity function, which lead to the derivation of an analogue of the
probability hypothesis density (PHD) filter. The gains provided by the
considered modelling framework in terms of flexibility lead to the loss of some
of the abilities that the PHD filter possesses; in particular the estimation of
the number of targets by integration of the intensity function. Yet, the
proposed recursion displays a number of advantages such the availability of
proper observation-driven birth schemes as well as the ability to perform
multi-sensor fusion in a natural way
Nonmonotonic Desires: A Possibility Theory Viewpoint
International audienceIf an agent desires that ϕ and desires that ψ, this agent often also desires that ϕ and ψ hold at the same time (ϕ ∧ ψ). However, there are cases where ϕ ∧ ψ may be found less satisfactory for the agent than each of ϕ or ψ alone.This paper is a first attempt at modeling such nonmonotonic desires. The approach is developed in the setting of possibility theory, since it has been recently pointed out that guaranteed (or strong) possibility measures are a good candidate for modeling graded desires. Although nonmonotonic reasoning has been studied extensively for knowledge, and that preferential nonmonotonic consequence relations can be faithfully represented in the possibilistic setting, nonmonotonic desires appear to require a different approach
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
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