5,360 research outputs found
The logic of public announcements, common knowledge, and private suspicions
This paper presents a logical system in which various group-level epistemic actions are incorporated into the object language. That is, we consider the standard modeling of knowledge among a set of agents by multi-modal Kripke structures. One might want to consider actions that take place, such as announcements to groups privately, announcements with suspicious outsiders, etc. In our system, such actions correspond to additional modalities in the object language. That is, we do not add machinery on top of models (as in Fagin et alia), but we reify aspects of the machinery in the logical language. Special cases of our logic have been considered in Plaza, Gerbrandy, and Gerbrandy and Groeneveld. The latter group of papers introduce a language in which one can faithfully represent all of the reasoning in examples such as the Muddy Children scenario. In that paper we find operators for updating worlds via announcements to groups of agents who are isolated from all others. We advance this by considering many more actions, and by using a more general semantics. Our logic contains the infinitary operators used in the standard modeling of common knowledge. We present a sound and complete logical system for the logic, and we study its expressive power
Two Reformulations of the Verificationist Thesis in Epistemic Temporal Logic that Avoid Fitch’s Paradox
1) We will begin by offering a short introduction to Epistemic Logic
and presenting Fitch’s paradox in an epistemic‑modal logic. (2) Then, we will
proceed to presenting three Epistemic Temporal logical frameworks creat‑
ed by Hoshi (2009) : TPAL (Temporal Public Announcement Logic), TAPAL
(Temporal Arbitrary Public Announcement Logic) and TPAL+P ! (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 Fitch’s
paradox and we will propose a way to formulate it in a TAPAL‑based lan‑
guage. The language we will use is a combination of TAPAL and TPAL+P ! with
an Indefinite (Unlabeled) Past Operator (TAPAL+P !+P). Using indexed satisfi‑
ability relations (as introduced in (Wang 2010 ; 2011)) we will offer a prospec ‑
tive semantics for this language. We will investigate whether the tentative re‑
formulation of Edgington’s Verificationist Thesis in TAPAL+P !+P is free from
paradox and adequate to Edgington’s ideas on how „all truths are knowable“
should be interpreted
On the Logic of Lying
We model lying as a communicative act changing the beliefs
of the agents in a multi-agent system. With Augustine, we see lying
as an utterance believed to be false by the speaker and uttered with
the intent to deceive the addressee. The deceit is successful if
the lie is believed after the utterance by the addressee. This is
our perspective. Also, as common in dynamic epistemic logics, we
model the agents addressed by the lie, but we do not (necessarily)
model the speaker as one of those agents. This further simplifies
the picture: we do not need to model the intention of the speaker,
nor do we need to distinguish between knowledge and belief of the
speaker: he is the observer of the system and his beliefs are taken
to be the truth by the listeners. We provide a sketch of what goes
on logically when a lie is communicated. We present a complete logic
of manipulative updating, to analyse the effects of lying in public
discourse.
Next, we turn to the study of lying in games. First, a
game-theoretical analysis is used to explain how the possibility of
lying makes games such as Liar's Dice interesting, and how lying is
put to use in optimal strategies for playing the game. This is the
opposite of the logical manipulative update: instead of always
believing the utterance, now, it is never believed. We also give a
matching logical analysis for the games perspective, and implement
that in the model checker DEMO. Our running example of lying in games
is the game of Liar's Dice
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
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