Topo-Logic as a Dynamic-Epistemic Logic

Baltag, Alexandru; Özgün, Aybüke; Sandoval, Ana Lucia Vargas

doi:10.1007/978-3-662-55665-8_23

Cited by 21 publications

(47 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The arbitrary announcement modality ϕ capturing "stability of the truth of ϕ after any announcement" comes close to the intuition behind the effort modality ϕ as "stability of the truth of ϕ after any effort". In Baltag et al (2017), these two modalities are even proven to be equivalent in the single-agent setting. However, the appropriate interpretation of effort in the multi-agent setting and its connection to the arbitrary announcement modality still remain elusive.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Announcement as effort on topological spaces

2017

Self Cite

View full text Add to dashboard Cite

We propose a multi-agent logic of knowledge, public announcements and arbitrary announcements, 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, with S5 knowledge modality, and demonstrate their completeness. We moreover consider the weaker axiomatizations of three logics with S4 type of knowledge and prove soundness and completeness results for these systems.

show abstract

Section: Discussionmentioning

confidence: 99%

“…Baltag et al (2017) later showed that, in spite of their different readings, the arbitrary announcement modality and the effort modality are equivalent in the single-agent case on topological spaces.…”

Section: Introductionmentioning

confidence: 99%

Announcement as effort on topological spaces

2017

Self Cite

View full text Add to dashboard Cite

show abstract

“…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%

Uncertainty About Evidence

Bjorndahl

Özgün

2019

Electron. Proc. Theor. Comput. Sci.

Self Cite

View full text Add to dashboard Cite

We develop a logical framework for reasoning about knowledge and evidence in which the agent may be uncertain about how to interpret their evidence. Rather than representing an evidential state as a fixed subset of the state space, our models allow the set of possible worlds that a piece of evidence corresponds to to vary from one possible world to another, and therefore itself be the subject of uncertainty. Such structures can be viewed as (epistemically motivated) generalizations of topological spaces. In this context, there arises a natural distinction between what is actually entailed by the evidence and what the agent knows is entailed by the evidence-with the latter, in general, being much weaker. We provide a sound and complete axiomatization of the corresponding bi-modal logic of knowledge and evidence entailment, and investigate some natural extensions of this core system, including the addition of a belief modality and its interaction with evidence interpretation and entailment, and the addition of a "knowability" modality interpreted via a (generalized) interior operator.

show abstract

“…In spite of the intuitive connections between SSL and the informational attitudes studied in DEL, connecting SSL to DEL is not entirely straightforward, even in the relatively simple case of public announcements. Connections between single-agent public announcement logic and SSL were made in [1,7,[10][11][12]36]. To the best of our knowledge, Wáng andÅgotnes [36] were the first to propose semantics for public announcements on subset spaces in terms of open set refinement rather than model restriction.…”

Section: Introductionmentioning

confidence: 99%

“…In previous work [30], we further extended the proposal in [12] with the arbitrary public announcement modality capturing information change caused by any announcement (rather than any effort) and studied a particular type of 'effort' that is in the shape of public announcements. Baltag et al [7] further investigated the relationship between the dynamic notions effort, public announcements, and arbitrary announcements, building on the settings presented in [12,30]. While the standard requirement for a truthful public announcement in DEL literature is only that it be true, the precondition int(ϕ) is stronger than ϕ simply being true (see also [12]) and it states that "ϕ is supported by truthful observation".…”

Section: Introductionmentioning

confidence: 99%

Private Announcements on Topological Spaces

2017

Self Cite

View full text Add to dashboard Cite

Abstract.In this work, we present a multi-agent logic of knowledge and change of knowledge interpreted on topological structures. Our dynamics are of the so-called semi-private character where a group G of agents is informed of some piece of information ϕ, while all the other agents observe that group G is informed, but are uncertain whether the information provided is ϕ or ¬ϕ. This article follows up on our prior work (van Ditmarsch et al. in Proceedings of the 15th TARK. pp [95][96][97][98][99][100][101][102] 2015) where the dynamics were public events. We provide a complete axiomatization of our logic, and give two detailed examples of situations with agents learning information through semi-private announcements.

show abstract

Topo-Logic as a Dynamic-Epistemic Logic

Abstract: You will be contacted as soon as possible.

Cited by 21 publications

References 10 publications

Announcement as effort on topological spaces

Announcement as effort on topological spaces

Uncertainty About Evidence

Private Announcements on Topological Spaces

Contact Info

Product

Resources

About