2016
DOI: 10.1007/978-3-662-52921-8_6
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Justified Belief and the Topology of Evidence

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Cited by 43 publications
(85 citation statements)
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“…We can further extend our syntax by observation modalities and belief and study the connection between knowledge, belief and observation together in one framework (as in [5]). An extension with the original effort modality of [24] is also of great interest.…”
Section: (X)(i) Then Y Z ∈ D(θ) and Either θ(Y)(i) ⊆ θ(Z)(i) Or θ(Z)mentioning
confidence: 99%
“…We can further extend our syntax by observation modalities and belief and study the connection between knowledge, belief and observation together in one framework (as in [5]). An extension with the original effort modality of [24] is also of great interest.…”
Section: (X)(i) Then Y Z ∈ D(θ) and Either θ(Y)(i) ⊆ θ(Z)(i) Or θ(Z)mentioning
confidence: 99%
“…And a variety of logical models for evidence and belief update assume that each piece of evidence corresponds to a set of possible worlds U and entails exactly those propositions ϕ such that U ⊆ [[ϕ]] [24,14,26,9,7,8]. Of special note are those models in which the collection of evidence is assumed to take the structure of a topology [6,12,11,2,25]; the framework we propose can be viewed as a generalization of this paradigm.…”
Section: Introductionmentioning
confidence: 99%
“…The concept of belief has been extensively studied in philosophy, logic and computer science. The representations range from purely qualitative structures including the relational models with serial, transitive and Euclidean relations (the KD45 representation in doxastic logic; [23,30]), plausibility models [10,13] and topological models [3,4,5] to quantitative structures including the ranking-based plausibility representation [35], Bayesian models using subjective probability functions and conditional probabilistic spaces designed to represent conditional belief [9].…”
Section: Introductionmentioning
confidence: 99%
“…In [12] and [11] a semantic approach is adopted, representing evidence as a set of possible worlds so beliefs are defined by the maximally consistent ways in which evidence can be combined (so called evidence models). The work in [5] follows the latter direction, adding a topological structure which represents the different ways in which the available pieces of evidence can be combined, and then using topological notions to single out relevant sets of combined pieces of evidence.…”
Section: Introductionmentioning
confidence: 99%
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