379 research outputs found
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
The Doxastic Interpretation of Team Semantics
We advance a doxastic interpretation for many of the logical connectives
considered in Dependence Logic and in its extensions, and we argue that Team
Semantics is a natural framework for reasoning about beliefs and belief
updates
Some Remarks on the Model Theory of Epistemic Plausibility Models
Classical logics of knowledge and belief are usually interpreted on Kripke
models, for which a mathematically well-developed model theory is available.
However, such models are inadequate to capture dynamic phenomena. Therefore,
epistemic plausibility models have been introduced. Because these are much
richer structures than Kripke models, they do not straightforwardly inherit the
model-theoretical results of modal logic. Therefore, while epistemic
plausibility structures are well-suited for modeling purposes, an extensive
investigation of their model theory has been lacking so far. The aim of the
present paper is to fill exactly this gap, by initiating a systematic
exploration of the model theory of epistemic plausibility models. Like in
'ordinary' modal logic, the focus will be on the notion of bisimulation. We
define various notions of bisimulations (parametrized by a language L) and show
that L-bisimilarity implies L-equivalence. We prove a Hennesy-Milner type
result, and also two undefinability results. However, our main point is a
negative one, viz. that bisimulations cannot straightforwardly be generalized
to epistemic plausibility models if conditional belief is taken into account.
We present two ways of coping with this issue: (i) adding a modality to the
language, and (ii) putting extra constraints on the models. Finally, we make
some remarks about the interaction between bisimulation and dynamic model
changes.Comment: 19 pages, 3 figure
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
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
Argument-based Belief in Topological Structures
This paper combines two studies: a topological semantics for epistemic
notions and abstract argumentation theory. In our combined setting, we use a
topological semantics to represent the structure of an agent's collection of
evidence, and we use argumentation theory to single out the relevant sets of
evidence through which a notion of beliefs grounded on arguments is defined. We
discuss the formal properties of this newly defined notion, providing also a
formal language with a matching modality together with a sound and complete
axiom system for it. Despite the fact that our agent can combine her evidence
in a 'rational' way (captured via the topological structure), argument-based
beliefs are not closed under conjunction. This illustrates the difference
between an agent's reasoning abilities (i.e. the way she is able to combine her
available evidence) and the closure properties of her beliefs. We use this
point to argue for why the failure of closure under conjunction of belief
should not bear the burden of the failure of rationality.Comment: In Proceedings TARK 2017, arXiv:1707.0825
Yet More Modal Logics of Preference Change and Belief Revision
We contrast Bonanno's `Belief Revision in a Temporal Framework'
\cite{Bonanno07:briatfTV} with preference change and belief revision
from the perspective of dynamic epistemic logic (DEL).
For that, we extend the
logic of communic
Dynamic-Epistemic reasoning on distributed systems
We propose a new logic designed for modelling and reasoning about information flow and information exchange between spatially located (but potentially mobile), interconnected agents witnessing a distributed computation. This is a major problem in the field of distributed systems, covering many different issues, with potential applications from Computer Science and Economy to Chemistry and Systems Biology. Underpinning on the dual algebraical-coalgebraical characteristics of process calculi, we design a decidable and completely axiomatizad logic that combines the processalgebraical/ equational and the modal/coequational features and is developed for process-algebraical semantics. The construction is done by mixing operators from dynamic and epistemic logics with operators from spatial logics for distributed and mobile systems. This is the preliminary version of a paper that will appear in Proceedings of the second Conference on Algebra and Coalgebra in Computer Science (CALCO2007), LNCS 4624, Springer, 2007. The original publication is available at www.springerlink.co
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