Two modellings for theory change

Grove, Adam J.

doi:10.1007/bf00247909

Cited by 503 publications

(370 citation statements)

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“…4 One can show that Lewis' 'sphere models' are an example of conditional models. The later modification due to Grove [18], in order to model belief revision, is also a special case; interestingly, the appropriate selection function is suggested by Grove himself in [18] p. 159. As we will show, our clauses are weaker than the semantic requirements of conditional doxastic logic.…”

Section: Lemma 3 Cautious Transitivity Entails the Left-to-right Incmentioning

confidence: 99%

Bisimulation for Conditional Modalities

Baltag

Cinà

2017

Stud Logica

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Abstract.We give a definition of bisimulation for conditional modalities interpreted on selection functions and prove the correspondence between bisimilarity and modal equivalence, generalizing the Hennessy-Milner Theorem to a wide class of conditional operators. We further investigate the operators and semantics to which these results apply. First, we show how to derive a solid notion of bisimulation for conditional belief, behaving as desired both on plausibility models and on evidence models. These novel definitions of bisimulations are exploited in a series of undefinability results. Second, we treat relativized common knowledge, underlining how the same results still hold for a different modality in a different semantics. Third, we show the flexibility of the approach by generalizing it to multi-agent systems, encompassing the case of multi-agent plausibility models.

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Section: Lemma 3 Cautious Transitivity Entails the Left-to-right Incmentioning

confidence: 99%

Bisimulation for Conditional Modalities

Baltag

Cinà

2017

Stud Logica

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“…Starting from relations that are linked, one can use the method of constructing knowledge and belief relations by means of the regular operations that was presented in the previous section to construct 'preference models' in the style of Grove [14], Board [9], and Baltag and Smets [3; 4] (who call them 'multi-agent plausibility frames').…”

Section: Belief Revision With Linked Preference Relationsmentioning

confidence: 99%

Multi-agent Belief Revision with Linked Preferences

Eijck

Sietsma

2010

Lecture Notes in Computer Science

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In this paper we forge a connection between dynamic epistemic logics of belief revision on one hand and studies of collective judgement and multi-agent preference change on the other. Belief revision in the spirit of dynamic epistemic logic uses updating with relational substitutions to change the beliefs of individual agents. Collective judgement in social choice theory studies the collective outcomes of individual belief changes.We start out from the logic of communication and change (LCC), which is basically epistemic propositional dynamic logic (PDL) extended with update action modalities. We show how epistemic PDL can be made to handle belief operators. Our new version of epistemic/doxastic PDL does not impose any constraints on the basic relations. Because of this it does not suffer from the drawback of LCC that constraints on epistemic relations, such as transitivity and reflexivity, may get lost under updates that are admitted by the system.After introducing the base system without constraints, we study the effects of imposing a single constraint, namely the constraint that the agent's preference relations are linked. Linkedness is a natural extension of local connectedness to the multi-agent case. It assures that if Alice prefers y to x and Bob prefers z to x, then both Alice and Bob can make up their minds when given a choice between y and z. Since general belief changes may not preserve linkedness, we propose a recipe for belief change that does preserve it.Finally, we show that the resulting framework can be used to model consensus seeking procedures. We focus on the case of plenary Dutch meetings. In Dutch meetings, a belief change (or rather: preference change) is performed for all agents in the meeting if a majority believes (or: is in favour of) the proposition that is under discussion. A special case of these meetings is judgement aggregation, and we apply our framework to the discursive dilemma in 2 this field. Our framework has obvious connections to coalition logic and social choice theory.

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“…A well known method for defining the operations of expansion, revision and contraction in accordance with the Gärdenfors postulates and with entrenchment-based selection rules has been provided by Grove (1988). For the sake of brevity, below we will outline Grove's method only with reference to expansion and revision.…”

Section: The Agm Theory Of Belief Changementioning

confidence: 99%