Three Approaches to Iterated Belief Contraction

Ramachandran, Raghav; Nayak, Abhaya C.; Orgun, Mehmet A.

doi:10.1007/s10992-011-9201-7

Cited by 21 publications

(29 citation statements)

References 14 publications

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“…Assume that fulfills (PCP ocf • ), (AGMes-1) -(AGMes-7) and (18). We will now prove that fulfills (IC3) -(IC4) under the given presuppositions.…”

Section: Conditional Preservation For Iterated Propositional Contractionmentioning

confidence: 81%

“…In comparison to iterated belief revision, the case of iterated belief contraction is less examined. Spohn [21], Hansson [10], Nayak et al [17,18], and [2] consider special aspects of iterated belief contraction, but to the best of our knowledge the recent paper by Konieczny and Pino Pérez [16] is the only work on propositional iterated contraction that addresses the general case. Similar to the work of Darwiche and Pearl, Konieczny and Pino Pérez adapt a set of AGM contraction postulates for the propositional case; these propositional contraction postulates where proposed by Caridroit, Konieczny and Marquis [3].…”

Section: Proposition 1 ([4])mentioning

confidence: 99%

“…Among these postulates for Iterated Contraction, the postulates (IC1) and (IC2), called rigidity conditions in [16] and ordered preservation conditions in [18], ensure that the order of worlds does not change if they are equivalent in the perspective of contraction. The postulates (IC3) and (IC4), called non-worsening conditions in [16], enforce that no world that contradicts the contracted information is getting relatively more plausible after the contraction than a world that was already more plausible before and does not contradict the contracted information.…”

Section: Proposition 3 ([16])mentioning

confidence: 99%

“…We first consider c-contractions of the form (14) and directly obtain κ (ω 1 ) < κ (ω 2 ) iff κ(ω 1 ) < κ(ω 2 )+γ + −γ − . Since the prerequisite (18) ensures that γ + − γ − 0, we have if κ(ω 1 ) < κ(ω 2 ) holds then also κ (ω 1 ) < κ (ω 2 ). For every c-contraction of the form (15), κ(A) 0 yields that κ(ω 1 ) < κ(ω 2 ) implies κ(ω 1 ) − κ(A) < κ(ω 2 ) and hence κ (ω 1 ) < κ (ω 2 ).…”

Section: Conditional Preservation For Iterated Propositional Contractionmentioning

confidence: 99%

“…For every c-contraction of the form (15), κ(A) 0 yields that κ(ω 1 ) < κ(ω 2 ) implies κ(ω 1 ) − κ(A) < κ(ω 2 ) and hence κ (ω 1 ) < κ (ω 2 ). So if we have (PCP ocf ), (18), and (AGMes-1) -(AGMes-7) we can derive the axiom (IC3). The proof of (IC4) is analogue.…”

Section: Conditional Preservation For Iterated Propositional Contractionmentioning

confidence: 99%

See 4 more Smart Citations

Iterated contraction of propositions and conditionals under the principle of conditional preservation

Kern-Isberner¹,

Bock²,

Sauerwald³

et al.

EPiC Series in Computing

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Research on iterated belief change has focussed mostly on belief revision, only few papers have addressed iterated belief contraction. Most prominently, Darwiche and Pearl published seminal work on iterated belief revision the leading paradigm of which is the so-called principle of conditional preservation. In this paper, we use this principle in a thoroughly axiomatized form to develop iterated belief contraction operators for Spohn's ranking functions. We show that it allows for setting up constructive approaches to tackling the problem of how to contract a ranking function by a proposition or a conditional, respectively, and that semantic principles can also be derived from it for the purely qualitative case.

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“…Assume that fulfills (PCP ocf • ), (AGMes-1) -(AGMes-7) and (18). We will now prove that fulfills (IC3) -(IC4) under the given presuppositions.…”

Section: Conditional Preservation For Iterated Propositional Contractionmentioning

confidence: 81%

Section: Proposition 1 ([4])mentioning

confidence: 99%

Section: Proposition 3 ([16])mentioning

confidence: 99%

Section: Conditional Preservation For Iterated Propositional Contractionmentioning

confidence: 99%

Section: Conditional Preservation For Iterated Propositional Contractionmentioning

confidence: 99%

See 3 more Smart Citations

Iterated contraction of propositions and conditionals under the principle of conditional preservation

Kern-Isberner¹,

Bock²,

Sauerwald³

et al.

EPiC Series in Computing

View full text Add to dashboard Cite

show abstract

Bringing Belief Base Change into Dynamic Epistemic Logic

Souza

Moreira

2020

Lecture Notes in Computer Science

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AGM's belief revision is one of the main paradigms in the study of belief change operations. In this context, belief bases (prioritised bases) have been primarily used to specify the agent's belief state. While the connection of iterated AGM-like operations and their encoding in dynamic epistemic logics have been studied before, few works considered how well-known postulates from iterated belief revision theory can be characterised by means of belief bases and their counterpart in dynamic epistemic logic. Particularly, it has been shown that some postulates can be characterised through transformations in priority graphs, while others may not be represented that way. This work investigates changes in the semantics of Dynamic Preference Logic that give rise to an appropriate syntactic representation for its models that allow us to represent and reason about iterated belief base change in this logic.

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