Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: math
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph