Public Announcement Logic in Geometric Frameworks

Baskent, Can

doi:10.3233/fi-2012-710

Cited by 9 publications

(7 citation statements)

References 33 publications

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“…We call V the doxastic range. 9 The semantic evaluation for the primitive propositions and the Boolean connectives is defined as usual; for the modal operators, we make use of the following semantic clauses:…”

Section: Proposition 32 Let T : L K2b → L Kb Be the Map That Repmentioning

confidence: 99%

“…10 In order to distinguish these semantics from those previous, we refer to them as epistemicdoxastic (e-d) semantics for topological subset spaces. 9 If we want to insist on consistent beliefs, we should add the axiom (D B ): Bϕ →Bϕ (or, equivalently,B ) and require that V = ∅. We begin with the more general case, without these assumptions.…”

Section: Proposition 32 Let T : L K2b → L Kb Be the Map That Repmentioning

confidence: 99%

“…Subset spaces have been employed in the representation of a variety of epistemic notions, including knowledge, learning, and public announcement (see, e.g., [1,8,9,23,24,32,45,46]), but to the best of our knowledge this article contains the first formalization of belief in subset space semantics. Stalnaker's original system is an extension of the basic logic of knowledge S4; belief emerges as a standard KD45 modality, as it is often assumed to be, while knowledge turns out to satisfy the stronger but somewhat less common S4.2 axioms.…”

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confidence: 99%

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Logic and Topology for Knowledge, Knowability, and Belief

Bjorndahl

Özgün

2019

The Review of Symbolic Logic

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In recent work, Stalnaker proposes a logical framework in which belief is realized as a weakened form of knowledge [30]. Building on Stalnaker's core insights, and using frameworks developed in [11] and [4], we employ topological tools to refine and, we argue, improve on this analysis. The structure of topological subset spaces allows for a natural distinction between what is known and (roughly speaking) what is knowable; we argue that the foundational axioms of Stalnaker's system rely intuitively on both of these notions. More precisely, we argue that the plausibility of the principles Stalnaker proposes relating knowledge and belief relies on a subtle equivocation between an "evidence-in-hand" conception of knowledge and a weaker "evidence-out-there" notion of what could come to be known. Our analysis leads to a trimodal logic of knowledge, knowability, and belief interpreted in topological subset spaces in which belief is definable in terms of knowledge and knowability. We provide a sound and complete axiomatization for this logic as well as its uni-modal belief fragment. We then consider weaker logics that preserve suitable translations of Stalnaker's postulates, yet do not allow for any reduction of belief. We propose novel topological semantics for these irreducible notions of belief, generalizing our previous semantics, and provide sound and complete axiomatizations for the corresponding logics.

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Section: Proposition 32 Let T : L K2b → L Kb Be the Map That Repmentioning

confidence: 99%

Section: Proposition 32 Let T : L K2b → L Kb Be the Map That Repmentioning

confidence: 99%

mentioning

confidence: 99%

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Logic and Topology for Knowledge, Knowability, and Belief

Bjorndahl

Özgün

2019

The Review of Symbolic Logic

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“…Subset spaces have been employed in the representation of a variety of epistemic notions, including knowledge, learning, and public announcement (see, e.g., [30,22,9,8,1,35,34,23]), but to the best of our knowledge this paper contains the first formalization of belief in subset space semantics. Stalnaker's original system is an extension of the basic logic of knowledge S4; belief emerges as a standard KD45 modality, as it is often assumed to be, while knowledge turns out to satisfy the stronger but somewhat less common S4.2 axioms.…”

Section: Introductionmentioning

confidence: 99%

Logic and Topology for Knowledge, Knowability, and Belief - Extended Abstract

Bjorndahl¹,

Özgün

2017

Electron. Proc. Theor. Comput. Sci.

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In recent work, Stalnaker proposes a logical framework in which belief is realized as a weakened form of knowledge [33]. Building on Stalnaker's core insights, and using frameworks developed in [12] and [4], we employ topological tools to refine and, we argue, improve on this analysis. The structure of topological subset spaces allows for a natural distinction between what is known and (roughly speaking) what is knowable; we argue that the foundational axioms of Stalnaker's system rely intuitively on both of these notions. More precisely, we argue that the plausibility of the principles Stalnaker proposes relating knowledge and belief relies on a subtle equivocation between an "evidence-in-hand" conception of knowledge and a weaker "evidence-out-there" notion of what could come to be known. Our analysis leads to a trimodal logic of knowledge, knowability, and belief interpreted in topological subset spaces in which belief is definable in terms of knowledge and knowability. We provide a sound and complete axiomatization for this logic as well as its uni-modal belief fragment. We then consider weaker logics that preserve suitable translations of Stalnaker's postulates, yet do not allow for any reduction of belief. We propose novel topological semantics for these irreducible notions of belief, generalizing our previous semantics, and provide sound and complete axiomatizations for the corresponding logics.

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“…Therefore, while knowledge is interpreted 'locally' in a given observation set U, effort is read as open-set-shrinking where more effort corresponds to a smaller neighbourhood, thus, a possible increase in knowledge. The schema 3Kϕ states that after some effort the agent comes to know ϕ where effort can be in the form of measurement, observation, computation, approximation [15,8,16,5], or announcement [17,1,10].…”

Section: Introductionmentioning

confidence: 99%

Announcement as effort on topological spaces

Ditmarsch¹,

Knight²,

Özgün³

2016

Electron. Proc. Theor. Comput. Sci.

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We propose a multi-agent logic of knowledge, public and arbitrary announcements, that is interpreted on topological spaces in the style of subset space semantics. The arbitrary announcement modality functions similarly to the effort modality in subset space logics, however, it comes with intuitive and semantic differences. We provide axiomatizations for three logics based on this setting, and demonstrate their completeness.Comment: In Proceedings TARK 2015, arXiv:1606.0729

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Public Announcement Logic in Geometric Frameworks

Cited by 9 publications

References 33 publications

Logic and Topology for Knowledge, Knowability, and Belief

Logic and Topology for Knowledge, Knowability, and Belief

Logic and Topology for Knowledge, Knowability, and Belief - Extended Abstract

Announcement as effort on topological spaces

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