12,382 research outputs found
Logic and Topology for Knowledge, Knowability, and Belief - Extended Abstract
In recent work, Stalnaker proposes a logical framework in which belief is
realized as a weakened form of knowledge. Building on Stalnaker's core
insights, and using frameworks developed by Bjorndahl and Baltag et al., we
employ topological tools to refine and, we argue, improve on this analysis. The
structure of topological subset spaces allows for a natural distinction between
what is known and (roughly speaking) what is knowable; we argue that the
foundational axioms of Stalnaker's system rely intuitively on both of these
notions. More precisely, we argue that the plausibility of the principles
Stalnaker proposes relating knowledge and belief relies on a subtle
equivocation between an "evidence-in-hand" conception of knowledge and a weaker
"evidence-out-there" notion of what could come to be known. Our analysis leads
to a trimodal logic of knowledge, knowability, and belief interpreted in
topological subset spaces in which belief is definable in terms of knowledge
and knowability. We provide a sound and complete axiomatization for this logic
as well as its uni-modal belief fragment. We then consider weaker logics that
preserve suitable translations of Stalnaker's postulates, yet do not allow for
any reduction of belief. We propose novel topological semantics for these
irreducible notions of belief, generalizing our previous semantics, and provide
sound and complete axiomatizations for the corresponding logics.Comment: In Proceedings TARK 2017, arXiv:1707.08250. The full version of this
paper, including the longer proofs, is at arXiv:1612.0205
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
Does the third law of black hole thermodynamics really have a serious failure?
The almost perfect correspondence between certain laws of classical black
hole mechanics and the ordinary laws of thermodynamics is spoiled by the
failure of the conventional back hole analogue of the third law. Our aim here
is to contribute to the associated discussion by flashing light on some simple
facts of black hole physics. However, no attempt is made to lay to rest the
corresponding long lasting debate. Instead, merely some evidence is provided to
make it clear that although the borderline between extremal and non-extremal
black holes is very thin they are essentially different. Hopefully, a careful
investigation of the related issues will end up with an appropriate form of the
third law and hence with an unblemished setting of black hole thermodynamics.Comment: 6 pages, Latex. accepted for publication in Class. Quant. Gra
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Formalising Engineering Judgement on Software Dependability via Belief Networks
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Examination of Bayesian belief network for safety assessment of nuclear computer-based systems
We report here on a continuation of work on the Bayesian Belief Network (BBN)model described in [Fenton, Littlewood et al. 1998]. As explained in the previous deliverable, our model concerns one part of the safety assessment task for computer and software based nuclear systems. We have produced a first complete, functioning version of our BBN model by eliciting a large numerical node probability table (NPT) required for our ‘Design Process Performance’ variable. The requirement for such large numerical NPTs poses some difficult questions about how, in general, large NPTs should be elicited from domain experts. We report about the methods we have devised to support the expert in building and validating a BBN. On the one hand, we have proceeded by eliciting approximate descriptions of the expert’s probabilistic beliefs, in terms of properties like stochastic orderings among distributions; on the other hand, we have explored ways of presenting to the expert visual and algebraic descriptions of relations among variables in the BBN, to assist the expert in an ongoing assessment of the validity of the BBN
On Many-Minds Interpretations of Quantum Theory
This paper is a response to some recent discussions of many-minds
interpretations in the philosophical literature. After an introduction to the
many-minds idea, the complexity of quantum states for macroscopic objects is
stressed. Then it is proposed that a characterization of the physical structure
of observers is a proper goal for physical theory. It is argued that an
observer cannot be defined merely by the instantaneous structure of a brain,
but that the history of the brain's functioning must also be taken into
account. Next the nature of probability in many-minds interpretations is
discussed and it is suggested that only discrete probability models are needed.
The paper concludes with brief comments on issues of actuality and identity
over time.Comment: 16 pages, plain TeX, no macros required. Revised following comments
November 199
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