Accepted Beliefs, Revision and Bipolarity in the Possibilistic Framework

Dubois, Didier; Prade, Henri

doi:10.1007/978-1-4020-9198-8_7

Cited by 4 publications

(4 citation statements)

References 46 publications

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“…So, in this section, we provide some basic knowledge. For details about probabilistic belief revision and update, one may refer to (Gärdenfors 1988) and (Dubois and Prade 1993). In the probabilistic framework, a belief state is represented by a probability measure P (or a probability function p) on the set Ω of possible worlds.…”

Section: Preliminariesmentioning

confidence: 99%

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Two Views of Constrained Differential Privacy: Belief Revision and Update

Likang

Sun

Zhou

et al. 2023

AAAI

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In this paper, we provide two views of constrained differential private (DP) mechanisms. The first one is as belief revision. A constrained DP mechanism is obtained by standard probabilistic conditioning, and hence can be naturally implemented by Monte Carlo algorithms. The other is as belief update. A constrained DP is defined according to l2-distance minimization postprocessing or projection and hence can be naturally implemented by optimization algorithms. The main advantage of these two perspectives is that we can make full use of the machinery of belief revision and update to show basic properties for constrained differential privacy especially some important new composition properties. Within the framework established in this paper, constrained DP algorithms in the literature can be classified either as belief revision or belief update. At the end of the paper, we demonstrate their differences especially in utility on a couple of scenarios.

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Section: Preliminariesmentioning

confidence: 99%

“…Example 3 Here we adopt an example from Section 2.3 in (Dubois and Prade 1993) to illustrate the difference between belief revision and update. There is either an apple (a) or a banana (b) in a box.…”

Section: Preliminariesmentioning

confidence: 99%

Two Views of Constrained Differential Privacy: Belief Revision and Update

Likang

Sun

Zhou

et al. 2023

AAAI

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“…3 However, degrees of belief can also be formalized in non-probabilistic frameworks, such as possibility theory and ranking theory (Dubois and Prade, 2009;Spohn, 2009). …”

Section: The Lockean Thesismentioning

confidence: 99%

Contemporary Epistemic Logic and the Lockean Thesis

Demey

2012

Found Sci

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“…This is because when an agent discovers new desires, it enlarges the number of desirable situations, while accumulating beliefs reduces the number of possible worlds. This difference of behavior between desire and belief has been pointed out by Casali et al (2011), which led them to propose possibility theory as a setting appropriate for modeling desires in terms of guaranteed possibilities, while beliefs can be represented in terms of necessity measures in this setting (Dubois and Prade 2009a). This point of view was then investigated by Dubois et al (2013), revisiting the representation of positive preferences proposed earlier on by Benferhat et al (2006).…”

Section: Introductionmentioning

confidence: 96%

The Strength of Desires: A Logical Approach

2017

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The aim of this paper is to propose a formal approach to reasoning about desires, understood as logical propositions which we would be pleased to make true, also acknowledging the fact that desire is a matter of degree. It is first shown that, at the static level, desires should satisfy certain principles that differ from those to which beliefs obey. In this sense, from a static perspective, the logic of desires is different from the logic of beliefs. While the accumulation of beliefs tend to reduce the remaining possible worlds they point at, the accumulation of desires tends to increase the set of states of affairs tentatively considered as satisfactory. Indeed beliefs are expected to be closed under conjunctions, while, in the positive view of desires developed here, one can argue that endorsing u _ w as a desire means to desire u and to desire w. However, desiring u and :u at the same time is not usually regarded as rational, since it does not make much sense to desire one thing and its contrary at the same time. Thus when a new desire is added to the set of desires of an agent, a revision process may be necessary. Just as belief revision relies on an epistemic entrenchment relation, desire revision is based on a hedonic entrenchment relation satisfying other properties, due to the different natures of belief and desire. While epistemic entrenchment relations are known to be qualitative necessity relations (in the sense of possibility theory), hedonic relations obeying a set of reasonable postulates correspond to another set-function in possibility theory, called guaranteed possibility, that drive well-behaved desire revision operations. Then the general framework of possibilistic logic provides a syntactic

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Accepted Beliefs, Revision and Bipolarity in the Possibilistic Framework

Cited by 4 publications

References 46 publications

Two Views of Constrained Differential Privacy: Belief Revision and Update

Two Views of Constrained Differential Privacy: Belief Revision and Update

Contemporary Epistemic Logic and the Lockean Thesis

The Strength of Desires: A Logical Approach

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