58,478 research outputs found
Logics with Group Announcements and Distributed Knowledge: Completeness and Expressive Power
Public announcement logic (PAL) is an extension of epistemic logic with dynamic operators that model the effects of all agents simultaneously and publicly acquiring the same piece of information. One of the extensions of PAL, group announcement logic (GAL), allows quantification over (possibly joint) announcements made by agents. In GAL, it is possible to reason about what groups can achieve by making such announcements. It seems intuitive that this notion of coalitional ability should be closely related to the notion of distributed knowledge, the implicit knowledge of a group. Thus, we study the extension of GAL with distributed knowledge, and in particular possible interaction properties between GAL operators and distributed knowledge. The perhaps surprising result is that, in fact, there are no interaction properties, contrary to intuition. We make this claim precise by providing a sound and complete axiomatisation of GAL with distributed knowledge. We also consider several natural variants of GAL with distributed knowledge, as well as some other related logic, and compare their expressive power.publishedVersio
Logics with Group Announcements and Distributed Knowledge: Completeness and Expressive Power.
Public announcement logic (PAL) is an extension of epistemic logic with dynamic operators that model the effects of all agents simultaneously and publicly acquiring the same piece of information. One of the extensions of PAL, group announcement logic (GAL), allows quantification over (possibly joint) announcements made by agents. In GAL, it is possible to reason about what groups can achieve by making such announcements. It seems intuitive that this notion of coalitional ability should be closely related to the notion of distributed knowledge, the implicit knowledge of a group. Thus, we study the extension of GAL with distributed knowledge, and in particular possible interaction properties between GAL operators and distributed knowledge. The perhaps surprising result is that, in fact, there are no interaction properties, contrary to intuition. We make this claim precise by providing a sound and complete axiomatisation of GAL with distributed knowledge. We also consider several natural variants of GAL with distributed knowledge, as well as some other related logic, and compare their expressive power
The Dynamics of Group Knowledge and Belief
5th International Workshop On Philosophy and Logic of Social Reality. 15-17 November 2019.Hokkaido University, Sapporo, Japa
Resolving Distributed Knowledge
Distributed knowledge is the sum of the knowledge in a group; what someone
who is able to discern between two possible worlds whenever any member of the
group can discern between them, would know. Sometimes distributed knowledge is
referred to as the potential knowledge of a group, or the joint knowledge they
could obtain if they had unlimited means of communication. In epistemic logic,
the formula D_G{\phi} is intended to express the fact that group G has
distributed knowledge of {\phi}, that there is enough information in the group
to infer {\phi}. But this is not the same as reasoning about what happens if
the members of the group share their information. In this paper we introduce an
operator R_G, such that R_G{\phi} means that {\phi} is true after G have shared
all their information with each other - after G's distributed knowledge has
been resolved. The R_G operators are called resolution operators. Semantically,
we say that an expression R_G{\phi} is true iff {\phi} is true in what van
Benthem [11, p. 249] calls (G's) communication core; the model update obtained
by removing links to states for members of G that are not linked by all members
of G. We study logics with different combinations of resolution operators and
operators for common and distributed knowledge. Of particular interest is the
relationship between distributed and common knowledge. The main results are
sound and complete axiomatizations.Comment: In Proceedings TARK 2015, arXiv:1606.0729
Asynchronous Announcements
We propose a multi-agent epistemic logic of asynchronous announcements, where
truthful announcements are publicly sent but individually received by agents,
and in the order in which they were sent. Additional to epistemic modalities
the logic contains dynamic modalities for making announcements and for
receiving them. What an agent believes is a function of her initial uncertainty
and of the announcements she has received. Beliefs need not be truthful,
because announcements already made may not yet have been received. As
announcements are true when sent, certain message sequences can be ruled out,
just like inconsistent cuts in distributed computing.
We provide a complete axiomatization for this \emph{asynchronous announcement
logic} (AA). It is a reduction system that also demonstrates that any formula
in is equivalent to one without dynamic modalities, just as for public
announcement logic. The model checking complexity is in PSPACE. A detailed
example modelling message exchanging processes in distributed computing in
closes our investigation
Two Reformulations of the Verificationist Thesis in Epistemic Temporal Logic that Avoid Fitchâs Paradox
1) We will begin by offering a short introduction to Epistemic Logic
and presenting Fitchâs paradox in an epistemicâmodal logic. (2) Then, we will
proceed to presenting three Epistemic Temporal logical frameworks creatâ
ed by Hoshi (2009)â: TPAL (Temporal Public Announcement Logic), TAPAL
(Temporal Arbitrary Public Announcement Logic) and TPAL+Pâ! (Temporal
Public Announcement Logic with Labeled Past Operators). We will show how
Hoshi stated the Verificationist Thesis in the language of TAPAL and analyze
his argument on why this version of it is immune from paradox. (3) Edgington
(1985) offered an interpretation of the Verificationist Thesis that blocks Fitchâs
paradox and we will propose a way to formulate it in a TAPALâbased lanâ
guage. The language we will use is a combination of TAPAL and TPAL+Pâ! with
an Indefinite (Unlabeled) Past Operator (TAPAL+Pâ!+P). Using indexed satisfiâ
ability relations (as introduced in (Wang 2010â; 2011)) we will offer a prospec â
tive semantics for this language. We will investigate whether the tentative reâ
formulation of Edgingtonâs Verificationist Thesis in TAPAL+Pâ!+P is free from
paradox and adequate to Edgingtonâs ideas on how âall truths are knowableâ
should be interpreted
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