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Aybuke Ozgun

University of Amsterdam, Institute for Logic, Language and Computation, Post-Doc

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I am a postdoctoral research in the Logic of Conceivability project at the ILLC, University of Amsterdam. I defended my Ph.D in October 2017, a joint degree from the ILLC, University of Amsterdam and LORIA, Université de Lorraine under the supervision of Hans van Ditmarsch, Nick Bezhanishvili, and Sonja Smets.My Ph.D dissertation, Evidence in Epistemic Logic: A Topological Perspective, studies formal representations of the notion of evidence and its link to justication, justied belief, knowledge, and evidence-based information dynamics, by using tools from topology and (dynamic) epistemic logic.

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University of Nottingham

Ole T Hjortland

University of Bergen

Villanova University

Cristina Bicchieri

University of Pennsylvania

Ucla

Massachusetts Institute of Technology (MIT)

University of Genova

Serge Rosmorduc

Conservatoire National des Arts et Métiers

The Australian National University

Ludwig-Maximilians-Universität München

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Papers by Aybuke Ozgun

Justified belief, knowledge, and the topology of evidence

Synthese

We propose a new topological semantics for evidence, evidence-based justifications, belief, and k... more We propose a new topological semantics for evidence, evidence-based justifications, belief, and knowledge. Resting on the assumption that an agent’s rational belief is based on the available evidence, we try to unveil the concrete relationship between an agent’s evidence, belief, and knowledge via a rich formal framework afforded by topologically interpreted modal logics. We prove soundness, completeness, decidability, and the finite model property for the associated logics, and apply this setting to analyze key epistemological issues such as “no false lemma” Gettier examples, misleading defeaters, undefeated justification versus undefeated belief, as well as the defeasibility theories of knowledge.

Arbitrary Public Announcement Logic with Memory

Journal of Philosophical Logic

We introduce Arbitrary Public Announcement Logic with Memory (APALM), obtained by adding to the m... more We introduce Arbitrary Public Announcement Logic with Memory (APALM), obtained by adding to the models a ‘memory’ of the initial states, representing the information before any communication took place (“the prior”), and adding to the syntax operators that can access this memory. We show that APALM is recursively axiomatizable (in contrast to the original Arbitrary Public Announcement Logic, for which the corresponding question is still open). We present a complete recursive axiomatization, that includes a natural finitary rule, and study this logic’s expressivity and the appropriate notion of bisimulation. We then examine Group Announcement Logic with Memory (GALM), the extension of APALM obtained by adding to its syntax group announcement operators, and provide a complete finitary axiomatization (again in contrast to the original Group Announcement Logic, for which the only known axiomatization is infinitary). We also show that, in the memory-enhanced context, there is a natural r...

APAL with Memory Is Better

Logic, Language, Information, and Computation, 2018

We introduce Arbitrary Public Announcement Logic with Memory (APALM), obtained by adding to the m... more We introduce Arbitrary Public Announcement Logic with Memory (APALM), obtained by adding to the models a ‘memory’ of the initial states, representing the information before any communication took place (“the prior”), and adding to the syntax operators that can access this memory. We show that APALM is recursively axiomatizable (in contrast to the original Arbitrary Public Announcement Logic, for which the corresponding question is still open). We present a complete recursive axiomatization, that uses a natural finitary rule, we study this logic’s expressivity and the appropriate notion of bisimulation.

The Topological Theory of Belief

Stalnaker introduced a combined epistemic-doxastic logic that can formally express a strong conce... more 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 first provide the most general extensional semantics for this concept of ‘strong belief’, which validates the principles of Stalnaker’s epistemic-doxastic logic. We show that this general extensional semantics is a topological semantics, based on so-called extremally disconnected topological spaces. It extends the standard topological interpretation of knowledge (as the interior operator) with a new topological semantics for belief. Formally, our belief modality is interpreted as the ‘closure of the interior’. We further prove that in this semantics the logic KD45 is sound and complete with respect to the class of extremally disconnected spaces and we compare our approach to a different topological setting in which belief is interpreted in terms of the derived set operator. In the second par...

The Logic of AGM Learning from Partial Observations

We present a dynamic logic for inductive learning from partial observations by a “rational” learn... more We present a dynamic logic for inductive learning from partial observations by a “rational” learner, that obeys AGM postulates for belief revision. We apply our logic to an example, showing how various concrete properties can be learnt with certainty or inductively by such an AGM learner. We present a sound and complete axiomatization, based on a combination of relational and neighbourhood version of the canonical model method.

Topological Models for Belief and Belief Revision Msc in Logic

We introduce a new topological semantics for belief logics in which the belief modality is interp... more We introduce a new topological semantics for belief logics in which the belief modality is interpreted as the closure of the interior operator. We show that our semantics validates the axioms of Stalnaker's combined system of knowledge and belief, in fact, that it constitutes the most general extensional (and compositional) semantics validating these axioms. We further prove that in this semantics the logic KD45 is sound and complete with respect to the class of extremally disconnected spaces. We have a critical look at the topological interpretation of belief in terms of the derived set operator [45] and compare it with our proposal. We also provide two topological semantics for conditional beliefs of which especially the latter is quite successful in capturing the rationality postulates of AGM theory. We further investigate a topological analogue of dynamic belief change, namely, update. In addition, we provide a completeness result of the system wKD45, a weakened version of K...

A Topological Approach to Full Belief

Journal of Philosophical Logic, 2018

Stalnaker (Philosophical Studies, 128(1), 169–199 2006) introduced a combined epistemic-doxastic ... more Stalnaker (Philosophical Studies, 128(1), 169–199 2006) introduced a combined epistemic-doxastic logic that can formally express a strong concept of belief, a concept of belief as ‘subjective certainty’. In this paper, we provide 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. This semantics extends the standard topological interpretation of knowledge (as the interior operator) with a new topological semantics for belief. We prove that the belief logic KD45 is sound and complete with respect to the class of extremally disconnected spaces and we compare our approach to a different topological setting in which belief is interpreted in terms of the derived set operator. We also study (static) belief revision as well as belief dynamics by providing a topological semantics for conditional belief and belief update modaliti...

Dynamic Hyperintensional Belief Revision

Review of Symbolic Logic, Jul 21, 2020

We propose a dynamic hyperintensional logic of belief revision for non-omniscient agents, reducin... more We propose a dynamic hyperintensional logic of belief revision for non-omniscient agents, reducing the logical omniscience phenomena affecting standard doxastic/epistemic logic as well as AGM belief revision theory. Our agents don't know all a priori truths; their belief states are not closed under classical logical consequence; and their belief update policies are such that logically or necessarily equivalent contents can lead to different revisions. We model both plain and conditional belief, then focus on dynamic belief revision. The key idea we exploit to achieve non-omniscience focuses on topic-or subject matter-sensitivity: a feature of belief states which is gaining growing attention in the recent literature. §1. Introduction: topicality and non-omniscience. We can have different attitudes toward necessarily equivalent contents: 1. Bachelors are unmarried. 2. Barium has atomic number 56. 3. 2 + 2 = 4. 4. No three positive integers x, y, and z satisfy x n + y n = z n for integer value of n greater than 2.

The Method of Thought Experiments -- The Journal of Philosophy

by Francesco Berto and Aybuke Ozgun

The Journal of Philosophy, 2024

We find a simple counterfactual acceptable, it is argued, to the extent that (i) our probability ... more We find a simple counterfactual acceptable, it is argued, to the extent that (i) our probability of the consequent under the thought experiment of counterfactually supposing the antecedent is high, (ii) provided the latter is on-topic with respect to the former. Counterfactual supposition is represented by Lewisian imaging. Topicality, by an algebra of subject matters. A topic-sensitive probabilistic logic is then provided, to reason about the acceptability of simple counterfactuals.

Quotient Dynamics: The Logic of Abstraction

We propose a Logic of Abstraction, meant to formalize the act of “abstracting away” the irrelevan... more

Topo-Logic as a Dynamic-Epistemic Logic

We extend the ‘topologic’ framework [13] with dynamic modalities for ‘topological public announce... more We extend the ‘topologic’ framework [13] with dynamic modalities for ‘topological public announcements’ in the style of Bjorndahl [5]. We give a complete axiomatization for this “Dynamic Topo-Logic”, which is in a sense simpler than the standard axioms of topologic. Our completeness proof is also more direct (making use of a standard canonical model construction). Moreover, we study the relations between this extension and other known logical formalisms, showing in particular that it is co-expressive with the simpler (and older) logic of interior and global modality [1, 4, 10, 14]. This immediately provides an easy decidability proof (both for topologic and for our extension).

A dynamic logic for learning theory

Journal of Logical and Algebraic Methods in Programming, 2019

Building on previous work [4, 5] that bridged Formal Learning Theory and Dynamic Epistemic Logic ... more Building on previous work [4, 5] that bridged Formal Learning Theory and Dynamic Epistemic Logic in a topological setting, we introduce a Dynamic Logic for Learning Theory (DLLT), extending Subset Space Logics [17, 9] with dynamic observation modalities [o]ϕ, as well as with a learning operator L(#» o), which encodes the learner's conjecture after observing a finite sequence of data #» o. We completely axiomatise DLLT, study its expressivity and use it to characterise various notions of knowledge, belief, and learning.

Uncertainty About Evidence

Electronic Proceedings in Theoretical Computer Science, 2019

We develop a logical framework for reasoning about knowledge and evidence in which the agent may ... more We develop a logical framework for reasoning about knowledge and evidence in which the agent may be uncertain about how to interpret their evidence. Rather than representing an evidential state as a fixed subset of the state space, our models allow the set of possible worlds that a piece of evidence corresponds to to vary from one possible world to another, and therefore itself be the subject of uncertainty. Such structures can be viewed as (epistemically motivated) generalizations of topological spaces. In this context, there arises a natural distinction between what is actually entailed by the evidence and what the agent knows is entailed by the evidence-with the latter, in general, being much weaker. We provide a sound and complete axiomatization of the corresponding bi-modal logic of knowledge and evidence entailment, and investigate some natural extensions of this core system, including the addition of a belief modality and its interaction with evidence interpretation and entailment, and the addition of a "knowability" modality interpreted via a (generalized) interior operator.

Logic and Topology for Knowledge, Knowability, and Belief - Extended Abstract

Electronic Proceedings in Theoretical Computer Science, 2017

Bjorndahl, A.; Özgün, A.

Private Announcements on Topological Spaces

Studia Logica, 2017

In this work, we present a multi-agent logic of knowledge and change of knowledge interpreted on ... more In this work, we present a multi-agent logic of knowledge and change of knowledge interpreted on topological structures. Our dynamics are of the so-called semi-private character where a group G of agents is informed of some piece of information ϕ, while all the other agents observe that group G is informed, but are uncertain whether the information provided is ϕ or ¬ϕ. This article follows up on our prior work (van Ditmarsch et al. in Proceedings of the 15th TARK. pp 95-102, 2015) where the dynamics were public events. We provide a complete axiomatization of our logic, and give two detailed examples of situations with agents learning information through semi-private announcements.

The Topology of Full and Weak Belief

Lecture Notes in Computer Science, 2017

We introduce a new topological semantics for belief logics in which the belief modality is interp... more 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 weakened version of KD45, is sound and complete w.r.t. the class of all topological spaces. Moreover, we point out a problem regarding updates on extremally disconnected spaces that appears in the setting of [1] and show that our proposal for topological belief semantics on all topological spaces constitutes a solution for it. While generalizing the topological belief semantics proposed in [1] to all spaces, we model conditional beliefs and updates and give complete axiomatizations of the corresponding logics.

Announcement as effort on topological spaces

Electronic Proceedings in Theoretical Computer Science, 2016

We propose a multi-agent logic of knowledge, public announcements and arbitrary announcements, in... more We propose a multi-agent logic of knowledge, public announcements and arbitrary announcements, interpreted on topological spaces in the style of subset space semantics. The arbitrary announcement modality functions similarly to the effort modality in subset space logics, however, it comes with intuitive and semantic differences. We provide axiomatizations for three logics based on this setting, with S5 knowledge modality, and demonstrate their completeness. We moreover consider the weaker axiomatizations of three logics with S4 type of knowledge and prove soundness and completeness results for these systems.

Justified Belief and the Topology of Evidence

Logic, Language, Information, and Computation, 2016

We introduce a new topological semantics for evidence, evidencebased justifications, belief and k... more We introduce a new topological semantics for evidence, evidencebased 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, and undefeated justification versus undefeated belief. 9 A preorder on X is a reflexive-transitive relation on X. 10 A subset A ⊆ X is said to be upward-closed wrt ≤ if ∀x, y ∈ X (x ∈ A ∧ x ≤ y ⇒ y ∈ A). 11 These families generate the same topology. We denote it by τ E only because the family E of combined evidence forms a basis of this topology.

Arbitrary Announcements on Topological Subset Spaces

Lecture Notes in Computer Science, 2015

Subset space semantics for public announcement logic in the spirit of the effort modality have be... more Subset space semantics for public announcement logic in the spirit of the effort modality have been proposed by Wang and Ågotnes [17] and by Bjorndahl [6]. They propose to model the public announcement modality by shrinking the epistemic range with respect to which a postcondition of the announcement is evaluated, instead of by restricting the model to the set of worlds satisfying the announcement. Thus we get an "elegant, model-internal mechanism for interpreting public announcements" [6, p.12]. In this work, we extend Bjorndahl's logic PAL int of public announcement, which is modelled on topological spaces using subset space semantics and adding the interior operator, with an arbitrary announcement modality, and we provide topological subset space semantics for the corresponding arbitrary announcement logic APAL int , and demonstrate completeness of the logic by proving that it is equal in expressivity to the logic without arbitrary announcements, employing techniques from [2, 13]. Hans van Ditmarsch is also affiliated to IMSc, Chennai.

The Topology of Belief, Belief Revision and Defeasible Knowledge

Lecture Notes in Computer Science, 2013

We present a new topological semantics for doxastic logic, in which the belief modality is interp... more 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 validates Stalnaker's epistemicdoxastic axioms [23], and indeed it is the most general (extensional) semantics validating them. We prove, among other things, that in this semantics the doxastic logic KD45 is sound and complete with respect to the class of all extremally disconnected topological spaces. We also give a topological semantics for conditional belief and show its connection to the operation of updating with "hard information" (modeled by restricting the topology to a subspace). We show that our topological notions fit well with the defeasibility analysis of knowledge: topological knowledge coincides with undefeated true belief. We compare our semantics to the older topological interpretation of belief in terms of Cantor derivative (Steinsvold 2006), arguing in favor of our new semantics. S. Smets contribution to this paper has received funding from the ERC under the European Community's 7th Framework Programme/ERC Grant agreement no. 283963.

Justified belief, knowledge, and the topology of evidence

Synthese

We propose a new topological semantics for evidence, evidence-based justifications, belief, and k... more We propose a new topological semantics for evidence, evidence-based justifications, belief, and knowledge. Resting on the assumption that an agent’s rational belief is based on the available evidence, we try to unveil the concrete relationship between an agent’s evidence, belief, and knowledge via a rich formal framework afforded by topologically interpreted modal logics. We prove soundness, completeness, decidability, and the finite model property for the associated logics, and apply this setting to analyze key epistemological issues such as “no false lemma” Gettier examples, misleading defeaters, undefeated justification versus undefeated belief, as well as the defeasibility theories of knowledge.

Arbitrary Public Announcement Logic with Memory

Journal of Philosophical Logic

We introduce Arbitrary Public Announcement Logic with Memory (APALM), obtained by adding to the m... more We introduce Arbitrary Public Announcement Logic with Memory (APALM), obtained by adding to the models a ‘memory’ of the initial states, representing the information before any communication took place (“the prior”), and adding to the syntax operators that can access this memory. We show that APALM is recursively axiomatizable (in contrast to the original Arbitrary Public Announcement Logic, for which the corresponding question is still open). We present a complete recursive axiomatization, that includes a natural finitary rule, and study this logic’s expressivity and the appropriate notion of bisimulation. We then examine Group Announcement Logic with Memory (GALM), the extension of APALM obtained by adding to its syntax group announcement operators, and provide a complete finitary axiomatization (again in contrast to the original Group Announcement Logic, for which the only known axiomatization is infinitary). We also show that, in the memory-enhanced context, there is a natural r...

APAL with Memory Is Better

Logic, Language, Information, and Computation, 2018

We introduce Arbitrary Public Announcement Logic with Memory (APALM), obtained by adding to the m... more We introduce Arbitrary Public Announcement Logic with Memory (APALM), obtained by adding to the models a ‘memory’ of the initial states, representing the information before any communication took place (“the prior”), and adding to the syntax operators that can access this memory. We show that APALM is recursively axiomatizable (in contrast to the original Arbitrary Public Announcement Logic, for which the corresponding question is still open). We present a complete recursive axiomatization, that uses a natural finitary rule, we study this logic’s expressivity and the appropriate notion of bisimulation.

The Topological Theory of Belief

Stalnaker introduced a combined epistemic-doxastic logic that can formally express a strong conce... more 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 first provide the most general extensional semantics for this concept of ‘strong belief’, which validates the principles of Stalnaker’s epistemic-doxastic logic. We show that this general extensional semantics is a topological semantics, based on so-called extremally disconnected topological spaces. It extends the standard topological interpretation of knowledge (as the interior operator) with a new topological semantics for belief. Formally, our belief modality is interpreted as the ‘closure of the interior’. We further prove that in this semantics the logic KD45 is sound and complete with respect to the class of extremally disconnected spaces and we compare our approach to a different topological setting in which belief is interpreted in terms of the derived set operator. In the second par...

The Logic of AGM Learning from Partial Observations

We present a dynamic logic for inductive learning from partial observations by a “rational” learn... more We present a dynamic logic for inductive learning from partial observations by a “rational” learner, that obeys AGM postulates for belief revision. We apply our logic to an example, showing how various concrete properties can be learnt with certainty or inductively by such an AGM learner. We present a sound and complete axiomatization, based on a combination of relational and neighbourhood version of the canonical model method.

Topological Models for Belief and Belief Revision Msc in Logic

We introduce a new topological semantics for belief logics in which the belief modality is interp... more We introduce a new topological semantics for belief logics in which the belief modality is interpreted as the closure of the interior operator. We show that our semantics validates the axioms of Stalnaker's combined system of knowledge and belief, in fact, that it constitutes the most general extensional (and compositional) semantics validating these axioms. We further prove that in this semantics the logic KD45 is sound and complete with respect to the class of extremally disconnected spaces. We have a critical look at the topological interpretation of belief in terms of the derived set operator [45] and compare it with our proposal. We also provide two topological semantics for conditional beliefs of which especially the latter is quite successful in capturing the rationality postulates of AGM theory. We further investigate a topological analogue of dynamic belief change, namely, update. In addition, we provide a completeness result of the system wKD45, a weakened version of K...

A Topological Approach to Full Belief

Journal of Philosophical Logic, 2018

Stalnaker (Philosophical Studies, 128(1), 169–199 2006) introduced a combined epistemic-doxastic ... more Stalnaker (Philosophical Studies, 128(1), 169–199 2006) introduced a combined epistemic-doxastic logic that can formally express a strong concept of belief, a concept of belief as ‘subjective certainty’. In this paper, we provide 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. This semantics extends the standard topological interpretation of knowledge (as the interior operator) with a new topological semantics for belief. We prove that the belief logic KD45 is sound and complete with respect to the class of extremally disconnected spaces and we compare our approach to a different topological setting in which belief is interpreted in terms of the derived set operator. We also study (static) belief revision as well as belief dynamics by providing a topological semantics for conditional belief and belief update modaliti...

Dynamic Hyperintensional Belief Revision

Review of Symbolic Logic, Jul 21, 2020

We propose a dynamic hyperintensional logic of belief revision for non-omniscient agents, reducin... more We propose a dynamic hyperintensional logic of belief revision for non-omniscient agents, reducing the logical omniscience phenomena affecting standard doxastic/epistemic logic as well as AGM belief revision theory. Our agents don't know all a priori truths; their belief states are not closed under classical logical consequence; and their belief update policies are such that logically or necessarily equivalent contents can lead to different revisions. We model both plain and conditional belief, then focus on dynamic belief revision. The key idea we exploit to achieve non-omniscience focuses on topic-or subject matter-sensitivity: a feature of belief states which is gaining growing attention in the recent literature. §1. Introduction: topicality and non-omniscience. We can have different attitudes toward necessarily equivalent contents: 1. Bachelors are unmarried. 2. Barium has atomic number 56. 3. 2 + 2 = 4. 4. No three positive integers x, y, and z satisfy x n + y n = z n for integer value of n greater than 2.

The Method of Thought Experiments -- The Journal of Philosophy

by Francesco Berto and Aybuke Ozgun

The Journal of Philosophy, 2024

We find a simple counterfactual acceptable, it is argued, to the extent that (i) our probability ... more We find a simple counterfactual acceptable, it is argued, to the extent that (i) our probability of the consequent under the thought experiment of counterfactually supposing the antecedent is high, (ii) provided the latter is on-topic with respect to the former. Counterfactual supposition is represented by Lewisian imaging. Topicality, by an algebra of subject matters. A topic-sensitive probabilistic logic is then provided, to reason about the acceptability of simple counterfactuals.

Quotient Dynamics: The Logic of Abstraction

We propose a Logic of Abstraction, meant to formalize the act of “abstracting away” the irrelevan... more

Topo-Logic as a Dynamic-Epistemic Logic

We extend the ‘topologic’ framework [13] with dynamic modalities for ‘topological public announce... more We extend the ‘topologic’ framework [13] with dynamic modalities for ‘topological public announcements’ in the style of Bjorndahl [5]. We give a complete axiomatization for this “Dynamic Topo-Logic”, which is in a sense simpler than the standard axioms of topologic. Our completeness proof is also more direct (making use of a standard canonical model construction). Moreover, we study the relations between this extension and other known logical formalisms, showing in particular that it is co-expressive with the simpler (and older) logic of interior and global modality [1, 4, 10, 14]. This immediately provides an easy decidability proof (both for topologic and for our extension).

A dynamic logic for learning theory

Journal of Logical and Algebraic Methods in Programming, 2019

Building on previous work [4, 5] that bridged Formal Learning Theory and Dynamic Epistemic Logic ... more Building on previous work [4, 5] that bridged Formal Learning Theory and Dynamic Epistemic Logic in a topological setting, we introduce a Dynamic Logic for Learning Theory (DLLT), extending Subset Space Logics [17, 9] with dynamic observation modalities [o]ϕ, as well as with a learning operator L(#» o), which encodes the learner's conjecture after observing a finite sequence of data #» o. We completely axiomatise DLLT, study its expressivity and use it to characterise various notions of knowledge, belief, and learning.

Uncertainty About Evidence

Electronic Proceedings in Theoretical Computer Science, 2019

We develop a logical framework for reasoning about knowledge and evidence in which the agent may ... more We develop a logical framework for reasoning about knowledge and evidence in which the agent may be uncertain about how to interpret their evidence. Rather than representing an evidential state as a fixed subset of the state space, our models allow the set of possible worlds that a piece of evidence corresponds to to vary from one possible world to another, and therefore itself be the subject of uncertainty. Such structures can be viewed as (epistemically motivated) generalizations of topological spaces. In this context, there arises a natural distinction between what is actually entailed by the evidence and what the agent knows is entailed by the evidence-with the latter, in general, being much weaker. We provide a sound and complete axiomatization of the corresponding bi-modal logic of knowledge and evidence entailment, and investigate some natural extensions of this core system, including the addition of a belief modality and its interaction with evidence interpretation and entailment, and the addition of a "knowability" modality interpreted via a (generalized) interior operator.

Logic and Topology for Knowledge, Knowability, and Belief - Extended Abstract

Electronic Proceedings in Theoretical Computer Science, 2017

Bjorndahl, A.; Özgün, A.

Private Announcements on Topological Spaces

Studia Logica, 2017

In this work, we present a multi-agent logic of knowledge and change of knowledge interpreted on ... more In this work, we present a multi-agent logic of knowledge and change of knowledge interpreted on topological structures. Our dynamics are of the so-called semi-private character where a group G of agents is informed of some piece of information ϕ, while all the other agents observe that group G is informed, but are uncertain whether the information provided is ϕ or ¬ϕ. This article follows up on our prior work (van Ditmarsch et al. in Proceedings of the 15th TARK. pp 95-102, 2015) where the dynamics were public events. We provide a complete axiomatization of our logic, and give two detailed examples of situations with agents learning information through semi-private announcements.

The Topology of Full and Weak Belief

Lecture Notes in Computer Science, 2017

We introduce a new topological semantics for belief logics in which the belief modality is interp... more 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 weakened version of KD45, is sound and complete w.r.t. the class of all topological spaces. Moreover, we point out a problem regarding updates on extremally disconnected spaces that appears in the setting of [1] and show that our proposal for topological belief semantics on all topological spaces constitutes a solution for it. While generalizing the topological belief semantics proposed in [1] to all spaces, we model conditional beliefs and updates and give complete axiomatizations of the corresponding logics.

Announcement as effort on topological spaces

Electronic Proceedings in Theoretical Computer Science, 2016

We propose a multi-agent logic of knowledge, public announcements and arbitrary announcements, in... more We propose a multi-agent logic of knowledge, public announcements and arbitrary announcements, interpreted on topological spaces in the style of subset space semantics. The arbitrary announcement modality functions similarly to the effort modality in subset space logics, however, it comes with intuitive and semantic differences. We provide axiomatizations for three logics based on this setting, with S5 knowledge modality, and demonstrate their completeness. We moreover consider the weaker axiomatizations of three logics with S4 type of knowledge and prove soundness and completeness results for these systems.

Justified Belief and the Topology of Evidence

Logic, Language, Information, and Computation, 2016

We introduce a new topological semantics for evidence, evidencebased justifications, belief and k... more We introduce a new topological semantics for evidence, evidencebased 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, and undefeated justification versus undefeated belief. 9 A preorder on X is a reflexive-transitive relation on X. 10 A subset A ⊆ X is said to be upward-closed wrt ≤ if ∀x, y ∈ X (x ∈ A ∧ x ≤ y ⇒ y ∈ A). 11 These families generate the same topology. We denote it by τ E only because the family E of combined evidence forms a basis of this topology.

Arbitrary Announcements on Topological Subset Spaces

Lecture Notes in Computer Science, 2015

Subset space semantics for public announcement logic in the spirit of the effort modality have be... more Subset space semantics for public announcement logic in the spirit of the effort modality have been proposed by Wang and Ågotnes [17] and by Bjorndahl [6]. They propose to model the public announcement modality by shrinking the epistemic range with respect to which a postcondition of the announcement is evaluated, instead of by restricting the model to the set of worlds satisfying the announcement. Thus we get an "elegant, model-internal mechanism for interpreting public announcements" [6, p.12]. In this work, we extend Bjorndahl's logic PAL int of public announcement, which is modelled on topological spaces using subset space semantics and adding the interior operator, with an arbitrary announcement modality, and we provide topological subset space semantics for the corresponding arbitrary announcement logic APAL int , and demonstrate completeness of the logic by proving that it is equal in expressivity to the logic without arbitrary announcements, employing techniques from [2, 13]. Hans van Ditmarsch is also affiliated to IMSc, Chennai.

The Topology of Belief, Belief Revision and Defeasible Knowledge

Lecture Notes in Computer Science, 2013

We present a new topological semantics for doxastic logic, in which the belief modality is interp... more 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 validates Stalnaker's epistemicdoxastic axioms [23], and indeed it is the most general (extensional) semantics validating them. We prove, among other things, that in this semantics the doxastic logic KD45 is sound and complete with respect to the class of all extremally disconnected topological spaces. We also give a topological semantics for conditional belief and show its connection to the operation of updating with "hard information" (modeled by restricting the topology to a subspace). We show that our topological notions fit well with the defeasibility analysis of knowledge: topological knowledge coincides with undefeated true belief. We compare our semantics to the older topological interpretation of belief in terms of Cantor derivative (Steinsvold 2006), arguing in favor of our new semantics. S. Smets contribution to this paper has received funding from the ERC under the European Community's 7th Framework Programme/ERC Grant agreement no. 283963.

Topics of Thought - OUP

by Francesco Berto, Aybuke Ozgun, and Peter Hawke

Topics of Thought. The Logic of Knowledge, Belief, Imagination, 2022

When one thinks—knows, believes, imagines—that something is the case, one’s thought has a topic: ... more When one thinks—knows, believes, imagines—that something is the case, one’s thought has a topic: it is about something, towards which one’s mind is directed. What is the logic of thought, so understood?
This book begins to explore the idea that, to answer the question, we should take topics seriously. It proposes a hyperintensional account of the propositional contents of thought, arguing that these are individuated not only by the set of possible worlds at which they are true, but also by their topic: what they are about. The book then builds epistemic, doxastic, probabilistic, and conditional logics based on this view. It applies them to issues ranging from dogmatism, scepticism, and epistemic fallibilism, to imagination and suppositional reasoning, belief revision, framing effects, and the acceptability of indicative conditionals.