59,689 research outputs found
On the relation between plausibility logic and the maximum-entropy principle: a numerical study
What is the relationship between plausibility logic and the principle of
maximum entropy? When does the principle give unreasonable or wrong results?
When is it appropriate to use the rule `expectation = average'? Can
plausibility logic give the same answers as the principle, and better answers
if those of the principle are unreasonable? To try to answer these questions,
this study offers a numerical collection of plausibility distributions given by
the maximum-entropy principle and by plausibility logic for a set of fifteen
simple problems: throwing dice.Comment: 24 pages of main text and references, 8 pages of tables, 7 pages of
additional reference
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 Silliness of Magical Realism
Relative plausibility, even after countless explanatory articles, remains an underdeveloped model bereft of underlying theory. Multivalent logic, a fully developed and accepted system of logic, comes to the same endpoint as relative plausibility. Multivalent logic would thus provide the missing theory, while it would resolve all the old problems of using traditional probability theory to explain the standards of proof as well as the new problems raised by the relative plausibility model. For example, multivalent logic resolves the infamous ‘conjunction paradox’ that traditional probability creates for itself, and which relative plausibility tries to sweep under the rug.
Yet Professors Allen and Pardo dismiss multivalent logic as magical realism when applied to legal factfinding. They reject this ring buoy because they misunderstand nonclassical logic, as this response explains
The Silliness of Magical Realism
Relative plausibility, even after countless explanatory articles, remains an underdeveloped model bereft of underlying theory. Multivalent logic, a fully developed and accepted system of logic, comes to the same endpoint as relative plausibility. Multivalent logic would thus provide the missing theory, while it would resolve all the old problems of using traditional probability theory to explain the standards of proof as well as the new problems raised by the relative plausibility model. For example, multivalent logic resolves the infamous ‘conjunction paradox’ that traditional probability creates for itself, and which relative plausibility tries to sweep under the rug.
Yet Professors Allen and Pardo dismiss multivalent logic as magical realism when applied to legal factfinding. They reject this ring buoy because they misunderstand nonclassical logic, as this response explains
The Silliness of Magical Realism
Relative plausibility, even after countless explanatory articles, remains an underdeveloped model bereft of underlying theory. Multivalent logic, a fully developed and accepted system of logic, comes to the same endpoint as relative plausibility. Multivalent logic would thus provide the missing theory, while it would resolve all the old problems of using traditional probability theory to explain the standards of proof as well as the new problems raised by the relative plausibility model. For example, multivalent logic resolves the infamous ‘conjunction paradox’ that traditional probability creates for itself, and which relative plausibility tries to sweep under the rug.
Yet Professors Allen and Pardo dismiss multivalent logic as magical realism when applied to legal factfinding. They reject this ring buoy because they misunderstand nonclassical logic, as this response explains
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
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
Non‐Classical Knowledge
The Knower paradox purports to place surprising a priori limitations on what we can know. According to orthodoxy, it shows that we need to abandon one of three plausible and widely-held ideas: that knowledge is factive, that we can know that knowledge is factive, and that we can use logical/mathematical reasoning to extend our knowledge via very weak single-premise closure principles. I argue that classical logic, not any of these epistemic principles, is the culprit. I develop a consistent theory validating all these principles by combining Hartry Field's theory of truth with a modal enrichment developed for a different purpose by Michael Caie. The only casualty is classical logic: the theory avoids paradox by using a weaker-than-classical K3 logic.
I then assess the philosophical merits of this approach. I argue that, unlike the traditional semantic paradoxes involving extensional notions like truth, its plausibility depends on the way in which sentences are referred to--whether in natural languages via direct sentential reference, or in mathematical theories via indirect sentential reference by Gödel coding. In particular, I argue that from the perspective of natural language, my non-classical treatment of knowledge as a predicate is plausible, while from the perspective of mathematical theories, its plausibility depends on unresolved questions about the limits of our idealized deductive capacities
Four Logics for Minimal Belief Revision
It is natural to think of belief revision as the interaction of belief and information over time. Thus branching-time temporal logic seems a natural setting for a theory of belief revision. We propose a logic based on three modal operators: a belief operator, an information operator and a next-time operator. Four logics of increasing strength are proposed. The first is a logic that captures the most basic notion of minimal belief revision. The second characterizes the qualitative content of Bayes' rule. The third provides an axiomatization of the AGM theory of belief revision and the fourth provides a characterization of the notion of plausibility ordering of the set of possible worlds.
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