9,070 research outputs found
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
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
How to do things with modals
Mind &Language, Volume 35, Issue 1, Page 115-138, February 2020
Offline and online data: on upgrading functional information to knowledge
This paper addresses the problem of upgrading functional information to knowledge. Functional information is defined as syntactically well-formed, meaningful and collectively opaque data. Its use in the formal epistemology of information theories is crucial to solve the debate on the veridical nature of information, and it represents the companion notion to standard strongly semantic information, defined as well-formed, meaningful and true data. The formal framework, on which the definitions are based, uses a contextual version of the verificationist principle of truth in order to connect functional to semantic information, avoiding Gettierization and decoupling from true informational contents. The upgrade operation from functional information uses the machinery of epistemic modalities in order to add data localization and accessibility as its main properties. We show in this way the conceptual worthiness of this notion for issues in contemporary epistemology debates, such as the explanation of knowledge process acquisition from information retrieval systems, and open data repositories
Evidence and plausibility in neighborhood structures
The intuitive notion of evidence has both semantic and syntactic features. In
this paper, we develop an {\em evidence logic} for epistemic agents faced with
possibly contradictory evidence from different sources. The logic is based on a
neighborhood semantics, where a neighborhood indicates that the agent has
reason to believe that the true state of the world lies in . Further notions
of relative plausibility between worlds and beliefs based on the latter
ordering are then defined in terms of this evidence structure, yielding our
intended models for evidence-based beliefs. In addition, we also consider a
second more general flavor, where belief and plausibility are modeled using
additional primitive relations, and we prove a representation theorem showing
that each such general model is a -morphic image of an intended one. This
semantics invites a number of natural special cases, depending on how uniform
we make the evidence sets, and how coherent their total structure. We give a
structural study of the resulting `uniform' and `flat' models. Our main result
are sound and complete axiomatizations for the logics of all four major model
classes with respect to the modal language of evidence, belief and safe belief.
We conclude with an outlook toward logics for the dynamics of changing
evidence, and the resulting language extensions and connections with logics of
plausibility change
Multiplayer belief revision
One main topic of the epistemic program of game theory deals with the value of information. To study this question in a broad context, one needs to adapt some of the tools used in multiplayer epistemic logic. A hierarchical belief structure is introduced both in a syntactical and semantical framework. In the same framework, a generalized notion of message is characterized by its content and its status. For a given message, a multiplayer belief revision rule that transforms any initial belief structure into a final belief one is designed. A representation theorem relates syntactical axioms to the belief revision rule.Belief revision, message, epistemic logic.
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