Announcement as effort on topological spaces (original) (raw)

Announcement as effort on topological spaces-Extended version

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.

Arbitrary Announcements on Topological Subset Spaces

Subset space semantics for public announcement logic in the spirit of the effort modality have been proposed by Wang and Ågotnes [18] and by Bjorn-dahl [6]. They propose to model the public announcement modality by shrinking the epistemic range with respect to which a postcondition of the announcement is evaluated, instead of by restricting the model to the set of worlds satisfying the announcement. Thus we get an " elegant, model-internal mechanism for interpreting public announcements " [6, p.12]. In this work, we extend Bjorndahl's logic PAL int of public announcement, which is modelled on topological spaces using subset space semantics and adding the interior operator, with an arbitrary announcement modality, and we provide topological subset space semantics for the corresponding arbitrary announcement logic APAL int , and demonstrate completeness of the logic by proving that it is equal in expressivity to the logic without arbitrary announcements, employing techniques from [2, 13].

Subset Space Public Announcement Logic Revisited

2013

We reformulate a key definition given by Wang and Agotnes (2013) to provide semantics for public announcements in subset spaces. More precisely, we interpret the precondition for a public announcement of {\phi} to be the "local truth" of {\phi}, semantically rendered via an interior operator. This is closely related to the notion of {\phi} being "knowable". We argue that these revised semantics improve on the original and offer several motivating examples to this effect. A key insight that emerges is the crucial role of topological structure in this setting. Finally, we provide a simple axiomatization of the resulting logic and prove completeness.

Private Announcements on Topological Spaces

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 [31] 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.

Topological Subset Space Models for Public Announcements

Outstanding Contributions to Logic, 2018

We reformulate a key definition given by Wáng andÅgotnes (2013) to provide semantics for public announcements in subset spaces. More precisely, we interpret the precondition for a public announcement of ϕ to be the "local truth" of ϕ, semantically rendered via an interior operator. This is closely related to the notion of ϕ being "knowable". We argue that these revised semantics improve on the original and offer several motivating examples to this effect. A key insight that emerges is the crucial role of topological structure in this setting. Finally, we provide a simple axiomatization of the resulting logic and prove completeness.

Subset Space Logic with Arbitrary Announcements

Lecture Notes in Computer Science, 2013

In this paper we introduce public announcements to Subset Space Logic (SSL). In order to do this we have to change the original semantics for SSL a little and consider a weaker version of SSL without the cross axiom. We present an axiomatization, prove completeness and show that this logic is PSPACE-complete. Finally, we add the arbitrary announcement modality which expresses "true after any announcement", prove several semantic results, and show completeness for a Hilbert-style axiomatization of this logic. Proposition 23. Let ϕ be a formula. For all Γ ∈ S u , we have for all finite sequences (ψ 1 ,. .. , ψ n) of formulas, F s , θ s , ([Γ ] ≡ u , f (Γ)) |= [ψ 1 ]. .. [ψ n ]ϕ iff M u , Γ |= [ψ 1 ]. .. [ψ n ]ϕ.

Public Announcement Logics with Constrained Protocols

2008

Public announcement logic (PAL) is a paradigm case of dynamic epistemic logic, which models how agents’ epistemic states change when pieces of information are communicated publicly. PAL extends epistemic logic with the operator [A], where the intended reading of [A]φ is “After a public announcement that A, φ holds.” This logic has recently received two improvements. One improvement, studied in [1], is to extend PAL with a generalized public announcement operator that allows quantification over public announcements. The other, studied in [5, 6], is a semantic setting to model “announcement protocols” to restrict the announcable sequences of formulas, while whatever is true is assumed to be announcable in PAL itself. The purpose of the present paper is to merge these two kinds of improvements. We consider the extension of public announcement logic with the generalized public announcement operator in the semantic setting of restricted announcement protocols.

Topological Evidence Logics: Multi-Agent Setting

2019

We introduce a multi-agent topological semantics for evidencebased belief and knowledge, which extends the dense interior semantics developed in [2]. We provide the complete logic of this multi-agent framework together with generic models for a fragment of the language. We also define a new notion of group knowledge which differs conceptually from previous approaches.

A Runs-and-Systems Semantics for Logics of Announcements

Lecture Notes in Computer Science, 2010

Logics of announcements are logics of knowledge to reason about agents that communicate by broadcasting interpreted messages. These logics are typically given a semantics in terms of updatable Kripke structures, which tend to be abstract. We revisit the semantics of logics of announcements and develop a concrete semantics using runs and systems. The advantage is that we can devise models that capture scenarios without having to express properties of those scenarios within the logic itself. In this concrete setting, we study honesty as well as belief in the presence of announcements that are not broadcast to all agents in a system.

A hybrid public announcement logic with distributed knowledge

Electronic Notes in Theoretical Computer Science 273(2011): 33-50. Post-Proceedings of the International Workshop on Hybrid Logic and Applications (HyLo 2010). 2011, 2011

In this paper the machinery of Hybrid Logic and the logic of public announcements are merged. In order to bring the two logics together properly the underlying hybrid logic has been changed such that nominals only partially denote states. The hybrid logic contains nominals, satisfaction operators, the downarrow binder as well as the global modality. Following this, an axiom system for the Hybrid Public Announcement Logic is presented and using reduction axioms general completeness (in the usual style of Hybrid Logic) is proved. The general completeness allows for an easy way of adding distributed knowledge. Furthermore, it turns out that distributed knowledge is definable using satisfaction operators and the downarrow binder.