Justified Belief and the Topology of Evidence

@inproceedings{Baltag2016JustifiedBA,
  title={Justified Belief and the Topology of Evidence},
  author={Alexandru Baltag and Nick Bezhanishvili and Ayb{\"u}ke {\"O}zg{\"u}n and Sonja Smets},
  booktitle={WoLLIC},
  year={2016}
}
We introduce a new topological semantics for evidence, evidence-based justifications, belief and knowledge. This setting builds on the evidence model framework of van Benthem and Pacuit, as well as our own previous work on a topological semantics for Stalnaker's doxastic-epistemic axioms. We prove completeness, decidability and finite model property for the associated logics, and we apply this setting to analyze key issues in Epistemology: "no false lemma" Gettier examples, misleading defeaters… 
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53 Citations
Highly Influential Citations
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Background Citations
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53 Citations

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A new semantics for justification logic based on subset relations is introduced, which model justifications as sets of possible worlds and shows that they subsume Artemov's approach to aggregating probabilistic evidence.
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The main contribution of this paper is a counter-intuitive result about the notion of knowledge based on justification, which is related to the no false lemmas in Stalnaker’s BK system.
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The formalization shows that one of the two notions of knowledge proposed by Clark, justified belief with true grounds, satisfies Stalnaker’s axiom system of belief and knowledge except for the axiom of closure under conjunction.
Logic and Topology for Knowledge, Knowability, and Belief - Extended Abstract
TLDR
It is argued 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.
Topological Subset Space Models for Belief
TLDR
It is argued 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.
Evidence in Epistemic Logic : A Topological Perspective
TLDR
This dissertation re-interprets some existing epistemic and doxastic logics and their dynamic extensions from a topological perspective, providing an evidence-based interpretation and using topological tools to refine and extend earlier analysis, leading to novel logics of evidence and information dynamics.
A Topological Approach to Full Belief
TLDR
This paper provides a topological semantics for belief, in particular, for Stalnaker’s notion of belief defined as ‘epistemic possibility of knowledge’, in terms of the closure of the interior operator on extremally disconnected spaces, and provides a complete axiomatization of the logic of conditional belief and knowledge.
LOGIC AND TOPOLOGY FOR KNOWLEDGE, KNOWABILITY, AND BELIEF
TLDR
It is argued 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.
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References

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