2,560 research outputs found
Comparing the Update Expressivity of Communication Patterns and Action Models
Any kind of dynamics in dynamic epistemic logic can be represented as an
action model. Right? Wrong! In this contribution we prove that the update
expressivity of communication patterns is incomparable to that of action
models. Action models, as update mechanisms, were proposed by Baltag, Moss, and
Solecki in 1998 and have remained the nearly universally accepted update
mechanism in dynamic epistemic logics since then. Alternatives, such as arrow
updates that were proposed by Kooi and Renne in 2011, have update equivalent
action models. More recently, the picture is shifting. Communication patterns
are update mechanisms originally proposed in some form or other by Agotnes and
Wang in 2017 (as resolving distributed knowledge), by Baltag and Smets in 2020
(as reading events), and by Velazquez, Castaneda, and Rosenblueth in 2021 (as
communication patterns). All these logics have the same expressivity as the
base logic of distributed knowledge. However, their update expressivity, the
relation between pointed epistemic models induced by such an update, was
conjectured to be different from that of action model logic. Indeed, we show
that action model logic and communication pattern logic are incomparable in
update expressivity. We also show that, given a history-based semantics and
when restricted to (static) interpreted systems, action model logic is
(strictly) more update expressive than communication pattern logic. Our results
are relevant for distributed computing wherein oblivious models involve
arbitrary iteration of communication patterns.Comment: In Proceedings TARK 2023, arXiv:2307.0400
Arrow update synthesis
In this contribution we present arbitrary arrow update model logic (AAUML). This is a dynamic epistemic logic or update logic. In update logics, static/basic modalities are interpreted on a given relational model whereas dynamic/update modalities induce transformations (updates) of relational models. In AAUML the update modalities formalize the execution of arrow update models, and there is also a modality for quantification over arrow update models. Arrow update models are an alternative to the well-known action models. We provide an axiomatization of AAUML. The axiomatization is a rewrite system allowing to eliminate arrow update modalities from any given formula, while preserving truth. Thus, AAUML is decidable and equally expressive as the base multi-agent modal logic. Our main result is to establish arrow update synthesis: if there is an arrow update model after which φ, we can construct (synthesize) that model from φ. We also point out some pregnant differences in update expressivity between arrow update logics, action model logics, and refinement modal logic
Relation-changing modal operators
We study dynamic modal operators that can change the accessibility relation of a model during the evaluation of a formula. In particular, we extend the basic modal language with modalities that are able to delete, add or swap an edge between pairs of elements of the domain. We define a generic framework to characterize this kind of operations. First, we investigate relation-changing modal logics as fragments of classical logics. Then, we use the new framework to get a suitable notion of bisimulation for the logics introduced, and we investigate their expressive power. Finally, we show that the complexity of the model checking problem for the particular operators introduced is PSpace-complete, and we study two subproblems of model checking: formula complexity and program complexity.Fil: Areces, Carlos Eduardo. Universidad Nacional de CĂłrdoba. Facultad de Matemática, AstronomĂa y FĂsica; Argentina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; ArgentinaFil: Fervari, Raul Alberto. Universidad Nacional de CĂłrdoba. Facultad de Matemática, AstronomĂa y FĂsica; Argentina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; ArgentinaFil: Hoffmann, Guillaume Emmanuel. Universidad Nacional de CĂłrdoba. Facultad de Matemática, AstronomĂa y FĂsica; Argentina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; Argentin
Arrow update synthesis
In this contribution we present arbitrary arrow update model logic (AAUML).
This is a dynamic epistemic logic or update logic. In update logics,
static/basic modalities are interpreted on a given relational model whereas
dynamic/update modalities induce transformations (updates) of relational
models. In AAUML the update modalities formalize the execution of arrow update
models, and there is also a modality for quantification over arrow update
models. Arrow update models are an alternative to the well-known action models.
We provide an axiomatization of AAUML. The axiomatization is a rewrite system
allowing to eliminate arrow update modalities from any given formula, while
preserving truth. Thus, AAUML is decidable and equally expressive as the base
multi-agent modal logic. Our main result is to establish arrow update
synthesis: if there is an arrow update model after which phi, we can construct
(synthesize) that model from phi. We also point out some pregnant differences
in update expressivity between arrow update logics, action model logics, and
refinement modal logic
Bisimulation and expressivity for conditional belief, degrees of belief, and safe belief
Plausibility models are Kripke models that agents use to reason about
knowledge and belief, both of themselves and of each other. Such models are
used to interpret the notions of conditional belief, degrees of belief, and
safe belief. The logic of conditional belief contains that modality and also
the knowledge modality, and similarly for the logic of degrees of belief and
the logic of safe belief. With respect to these logics, plausibility models may
contain too much information. A proper notion of bisimulation is required that
characterises them. We define that notion of bisimulation and prove the
required characterisations: on the class of image-finite and preimage-finite
models (with respect to the plausibility relation), two pointed Kripke models
are modally equivalent in either of the three logics, if and only if they are
bisimilar. As a result, the information content of such a model can be
similarly expressed in the logic of conditional belief, or the logic of degrees
of belief, or that of safe belief. This, we found a surprising result. Still,
that does not mean that the logics are equally expressive: the logics of
conditional and degrees of belief are incomparable, the logics of degrees of
belief and safe belief are incomparable, while the logic of safe belief is more
expressive than the logic of conditional belief. In view of the result on
bisimulation characterisation, this is an equally surprising result. We hope
our insights may contribute to the growing community of formal epistemology and
on the relation between qualitative and quantitative modelling
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