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Sigma algebras in probabilistic epistemic dynamics

Authors:

Luca Aceto,

Wiebe van der Hoek,

Anna Ingolfsdottir,

Joshua SackAuthors Info & Claims

TARK XIII: Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge

Pages 191 - 199

https://doi.org/10.1145/2000378.2000401

Published: 12 July 2011 Publication History

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Abstract

This paper extends probabilistic dynamic epistemic logic from a finite setting to an infinite setting, by introducing σ-algebras to the probability spaces in the models. This may extend the applicability of the logic to a real world setting with infinitely many possible measurements. It is shown that the dynamics preserves desirable properties of measurability and that completeness of the proof system holds with the extended semantics.

References

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H. v. Ditmarsch, W. van der Hoek, and B. Kooi. Dynamic Epistemic Logic. Springer Publishing Company, Incorporated, 1st edition, 2007.

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B. Renne, J. Sack, and A. Yap. Dynamic epistemic temporal logic. In X. He, J. Horty, and E. Pacuit, editors, Logic, Rationality, and Interaction, volume 5834 of Lecture Notes in Computer Science, pages 263--277. Springer Berlin/Heidelberg, 2009. 10.1007/978-3-642-04893-7 21.

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B. Renne, J. Sack, and A. Yap. Dynamic epistemic temporal logic. Extended manuscript, 2009.

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J. Sack. Extending probabilistic dynamic epistemic logic. Synthese, 169:241--257, 2009. 10.1007/s11229-009-9555-3.

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Cited By

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Pan YGuo M(2024)Probabilistic epistemic logic based on neighborhood semanticsSynthese10.1007/s11229-024-04557-4203:5Online publication date: 20-Apr-2024
https://doi.org/10.1007/s11229-024-04557-4
Sack Jvan der Hoek W(2014)A Modal Logic for Mixed StrategiesStudia Logica10.1007/s11225-014-9548-1102:2(339-360)Online publication date: 27-Feb-2014
https://doi.org/10.1007/s11225-014-9548-1
Klein DPacuit E(2014)Changing Types: Information Dynamics for Qualitative Type SpacesStudia Logica10.1007/s11225-014-9545-4102:2(297-319)Online publication date: 27-Feb-2014
https://doi.org/10.1007/s11225-014-9545-4

Index Terms

Sigma algebras in probabilistic epistemic dynamics
1. Computing methodologies
  1. Artificial intelligence
    1. Knowledge representation and reasoning
  2. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Theorem proving algorithms
2. Theory of computation
  1. Logic
    1. Modal and temporal logics
    2. Proof theory

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Published In

TARK XIII: Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge

July 2011

270 pages

ISBN:9781450307079

DOI:10.1145/2000378

Conference Chair:
Krzysztof R. Apt
CWI and University of Amsterdam

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

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Published: 12 July 2011

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Icelandic Centre for Research

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TARK XIII

TARK XIII: Thirteenth conference on Theoretical Aspects of Rationality and Knowledge

July 12 - 14, 2011

Groningen, The Netherlands

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Overall Acceptance Rate 61 of 177 submissions, 34%

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Pan YGuo M(2024)Probabilistic epistemic logic based on neighborhood semanticsSynthese10.1007/s11229-024-04557-4203:5Online publication date: 20-Apr-2024
https://doi.org/10.1007/s11229-024-04557-4
Sack Jvan der Hoek W(2014)A Modal Logic for Mixed StrategiesStudia Logica10.1007/s11225-014-9548-1102:2(339-360)Online publication date: 27-Feb-2014
https://doi.org/10.1007/s11225-014-9548-1
Klein DPacuit E(2014)Changing Types: Information Dynamics for Qualitative Type SpacesStudia Logica10.1007/s11225-014-9545-4102:2(297-319)Online publication date: 27-Feb-2014
https://doi.org/10.1007/s11225-014-9545-4

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Probabilistic stit logic and its decomposition

Temporal Languages for Epistemic Programs

An Epistemic Separation Logic with Action Models

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