Logic and Topology for Knowledge, Knowability, and Belief - Extended Abstract
@inproceedings{Bjorndahl2017LogicAT, title={Logic and Topology for Knowledge, Knowability, and Belief - Extended Abstract}, author={Adam Bjorndahl and Ayb{\"u}ke {\"O}zg{\"u}n}, booktitle={TARK}, year={2017} }
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…
5 Citations
Uncertainty About Evidence
- PhilosophyTARK
- 2019
A sound and complete axiomatization of the corresponding bi-modal logic of knowledge and evidence entailment is provided, and some natural extensions of this core system are investigated, including the addition of a belief modality and its interaction with evidence interpretation and entailment, and the added of a "knowability" modality interpreted via a (generalized) interior operator.
A multi-labelled sequent calculus for Topo-Logic
- Computer Science, MathematicsJ. Log. Comput.
- 2020
A labelled sequent calculus for a trimodal epistemic logic exhibitied in Baltag et al. (2017), an extension of the so called ‘Topo-Logic’, is presented, which is the first proof-calculus for this logic and proves that this calculus enjoys many structural properties such as admissibility of cut, ad admission of contraction and invertibility of its rules.
The Epistemology of Nondeterminism
- Computer Science, PhilosophyWoLLIC
- 2018
This paper proposes new semantics for nondeterministic program execution, replacing the standard relational semantics for propositional dynamic logic (PDL), and formalizes these notions using topology and the framework of dynamic topological logic (DTL).
A Simplicial Model for KB4n: Epistemic Logic with Agents that May Die
- PhilosophySTACS
- 2022
The standard semantics of multi-agent epistemic logic S5n is based on Kripke models whose accessibility relations are reflexive, symmetric and transitive, but this theory is extended to encompass all simplicial models — including the ones that are not pure.
APAL with Memory Is Better
- Computer ScienceWoLLIC
- 2018
A complete recursive axiomatization of Arbitrary Public Announcement Logic with Memory is presented, that uses a natural finitary rule, and study this logic’s expressivity and the appropriate notion of bisimulation.
References
SHOWING 1-10 OF 43 REFERENCES
The Topological Theory of Belief
- Philosophy
- 2015
Stalnaker introduced a combined epistemic-doxastic logic that can formally express a strong concept of belief, a concept which captures the ‘epistemic possibility of knowledge’. In this paper we…
The Topology of Belief, Belief Revision and Defeasible Knowledge
- PhilosophyLORI
- 2013
We present a new topological semantics for doxastic logic, in which the belief modality is interpreted as the closure of the interior operator. We show that this semantics is the most general…
Structures for Epistemic Logic
- Philosophy, Computer ScienceJohan van Benthem on Logic and Information Dynamics
- 2014
This chapter overviews the main structures of epistemic and doxastic logic, and pays special attention to ‘non-standard semantics’ for knowledge and belief, i.e., semantics that are not based on an underlying relation on the sets of states.
Justified Belief and the Topology of Evidence
- PhilosophyWoLLIC
- 2016
This work introduces a new topological semantics for evidence, evidence-based justifications, belief and knowledge, and applies this setting to analyze key issues in Epistemology: "no false lemma" Gettier examples, misleading defeaters, and undefeated justification versus undefeated belief.
The Topology of Full and Weak Belief
- PhilosophyTbiLLC
- 2015
We introduce a new topological semantics for belief logics in which the belief modality is interpreted as the interior of the closure of the interior operator. We show that the system wKD45, a…
Dynamic Logics of Belief Change
- Philosophy
- 2015
This chapter gives an overview of current dynamic logics that describe belief update and revision, both for single agents and in multi-agent settings. We employ a mixture of ideas from AGM belief…
On Logics of Knowledge and Belief
- Philosophy
- 2006
Formal epistemology, or at least the approach to formal epistemology that develops a logic and formal semantics of knowledge and belief in the possible worlds framework, began with Jaakko Hintikka’s…
Dynamic logic for belief revision
- PhilosophyJ. Appl. Non Class. Logics
- 2007
This work shows how belief revision can be treated systematically in the format of dynamicepistemic logic, when operators of conditional belief are added, and obtains complete logics for concrete mechanisms of belief revision based on compositional reduction axioms.
Dynamic epistemic logic
- Philosophy, Computer Science
- 1998
A semantics and a deduction system for a multi-agent modal language extended with a repertoire of programs that describe information change, designed in such a way that everything that is expressible in the object language can be known or learned by each of the agents.