16,459 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
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
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