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Journal of Logic, Language and Information

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01-06-2014

Dynamic Epistemic Logic for Implicit and Explicit Beliefs

Author: Fernando R. Velázquez-Quesada

Published in: Journal of Logic, Language and Information | Issue 2/2014

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Abstract

Epistemic logic with its possible worlds semantic model is a powerful framework that allows us to represent an agent’s information not only about propositional facts, but also about her own information. Nevertheless, agents represented in this framework are logically omniscient: their information is closed under logical consequence. This property, useful in some applications, is an unrealistic idealisation in some others. Many proposals to solve this problem focus on weakening the properties of the agent’s information, but some authors have argued that solutions of this kind are not completely adequate because they do not look at the heart of the matter: the actions that allow the agent to reach such omniscient state. Recent works have explored how acts of observation, inference, consideration and forgetting affect an agent’s implicit and explicit knowledge; the present work focuses on acts that affect an agent’s implicit and explicit beliefs. It starts by proposing a framework in which these two notions can be represented, and then it looks into their dynamics, first by reviewing the existing notion of belief revision, and then by introducing a rich framework for representing diverse forms of inference that involve both knowledge and beliefs.

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Then, a well preorder is obtained when the existence of maximum elements is required for every subset of the whole domain instead of just every subset of each comparability class.

A binary relation \(R\) over \(W\) is locally connected iff, for every comparability class \(C_{{R}}{(w)}\), every two elements \(w_1, w_2\) in \(C_{{R}}{(w)}\) are \(R\)-comparable, that is, \(Rw_1w_2\) or \(Rw_2w_1\) or both.

A binary relation \(R\) over \(W\) is conversely well-founded iff there is no infinite \({R}^{|}\)-ascending chain in \(W\), where \({R}^{|}\), the strict version of \(R\), is given by \({R}^{|}wu\) iff \(Rwu\) and not \(Ruw\).

This action can be seen from the perspective of the truth-table of an implication: \(\eta \rightarrow \chi \) and \(\eta \) are true so \(\chi \) must be true.

From the perspective of the truth-table of an implication, this case corresponds to the situations in which the antecedent \(\eta \) is true: either the implication \(\eta \rightarrow \chi \) (and hence its consequent) are the case, or else the implication (and hence its consequent) fails.

Again, from the perspective of a truth-table for implication, this corresponds to the three cases that are left when the implication is assumed as true.

Ågotnes, T., & Alechina, N. (2007). The dynamics of syntactic knowledge. Journal of Logic and Computation, 17(1), 83–116. doi:10.1093/logcom/exl019.CrossRef

Ågotnes, T., & Alechina, N. (eds.). (2009). Special issue on logics for resource bounded agents. Journal of Logic, Language and Information, 18(1).

Alchourrón, C. E., Gärdenfors, P., & Makinson, D. (1985). On the logic of theory change: Partial meet contraction and revision functions. The Journal of Symbolic Logic, 50(2), 510–530. doi:10.2307/2274239.CrossRef

Aliseda A (2006) Abductive reasoning. Logical investigations into discovery and explanation, synthese library series (vol. 330). Berlin: Springer.

Baltag, A., Moss, L. S., & Solecki, S. (1999). The logic of public announcements, common knowledge and private suspicions. Tech. Rep. SEN-R9922, CWI, Amsterdam.

Baltag, A., & Smets, S. (2008). A qualitative theory of dynamic interactive belief revision. In G. Bonanno, W. van der Hoek, & M. Wooldridge (Eds.), Logic and the foundations of game and decision theory (LOFT7), texts in logic and games (Vol. 3, pp. 13–60). The Netherlands: Amsterdam University Press Amsterdam.

Blackburn, P., de Rijke, M., & Venema, Y. (2001) Modal logic. No. 53 in Cambridge tracts in theoretical computer science. New York, USA: Cambridge University Press.

Board, O. (2004). Dynamic interactive epistemology. Games and Economic Behavior, 49(1), 49–80. doi:10.1016/j.geb.2003.10.006.CrossRef

Boutilier, C. (1994). Conditional logics of normality: A modal approach. Artificial Intelligence, 68(1), 87–154.CrossRef

Drapkin, J. J., & Perlis, D. (1986). Step-logics: An alternative approach to limited reasoning. In Proceedings of the European conference on artificial intelligence (pp. 160–163), Brighton, England.

Duc, H. N. (1995). Logical omniscience vs. logical ignorance. on a dilemma of epistemic logic. In C. A. Pinto-Ferreira, N. J. Mamede (Eds.), EPIA 1995, Lecture Notes in Computer Science (vol. 990, pp 237–248). Heilderberg: Springer.

Duc, H. N. (2001). Resource-bounded reasoning about knowledge. PhD thesis, Institut für Informatik, Universität Leipzig, Leipzig, Germany.

Fagin, R., & Halpern, J. Y. (1988). Belief, awareness, and limited reasoning. Artificial Intelligence, 34(1), 39–76. doi:10.1016/0004-3702(87)90003-8.

Gärdenfors, P. (Ed.). (1992). Belief revision. No. 29 in Cambridge tracts in theoretical computer science. Cambridge: Cambridge University Press.

Gärdenfors, P., & Makinson, D. (1988). Revisions of knowledge systems using epistemic entrenchment. In M. Y. Vardi (Ed.), TARK II (pp. 83–95), Morgan Kaufmann.

Gärdenfors, P., & Rott, H. (1994). Belief revision. Handbook of logic in artificial intelligence and logic programming, vol Volume 4: Epistemic and temporal logics (pp. 35–132). Oxford & New York: Oxford University Press.

Gerbrandy, J, (1999), Bisimulations on planet kripke. PhD thesis, Institute for Logic, Language and Computation (ILLC), Universiteit van Amsterdam (UvA), Amsterdam, The Netherlands, ILLC Dissertation Series DS-1999-01.

Grossi, D., & Velázquez-Quesada, F. R. (2009). Twelve angry men: A study on the fine-grain of announcements. In He et al. pp 147–160. doi:10.1007/978-3-642-04893-7_12.

Grove, A. (1988). Two modellings for theory change. Journal of Philosophical Logic, 17(2), 157–170. doi:10.1007/BF00247909.CrossRef

Halpern, J. Y. (ed.). (1986). Proceedings of the 1st conference on theoretical aspects of reasoning about knowledge, Monterey, CA/ San Francisco, CA: Morgan Kaufmann.

Harel, D., Kozen, D., & Tiuryn, J. (2000). Dynamic logic. Cambridge, MA: MIT Press.

He, X., Horty, J. F., & Pacuit, E. (eds.). (2009). Proceedings of the logic, rationality, and interaction, second international workshop (LORI 2009), Chongqing, China, October 8–11, 2009. Lecture Notes in Computer Science (vol. 5834). Berlin: Springer. doi:10.1007/978-3-642-04893-7.

Hintikka, J. (1962). Knowledge and belief: An introduction to the logic of the two notions. Ithaca, NY: Cornell University Press.

Holliday, W. H., & Icard, T. F. (2010). Moorean phenomena in epistemic logic. In L. Beklemishev, V. Goranko, & V. Shehtman (Eds.), Advances in modal logic (pp. 178–199), College Publications.

Jago, M. (2009). Epistemic logic for rule-based agents. Journal of Logic, Language and Information, 18(1), 131–158. doi:10.1007/s10849-008-9071-8.CrossRef

Konolige, K. (1984). Belief and incompleteness. Tech. Rep. 319, SRI International.

Lakemeyer, G. (1986). Steps towards a first-order logic of explicit and implicit belief. In Halpern (1986) (pp. 325–340).

Lamarre, P. (1991). S4 as the conditional logic of nonmonotonicity. In J. F. Allen, R. Fikes, & E. Sandewall (Eds.), KR 91 (pp. 357–367). Cambridge, MA: Morgan Kaufmann.

Levesque, H. J. (1984). A logic of implicit and explicit belief. In Proceedings of the AAAI-84 (pp. 198–202), Austin, TX.

Lewis, D. (1973). Counterfactuals. Cambridge, MA: Blackwell.

Plaza, J. A. (1989). Logics of public communications. In M. L. Emrich, M. S. Pfeifer, M. Hadzikadic, & Z. W. Ras (Eds.), Proceedings of the 4th international symposium on methodologies for intelligent systems, Oak Ridge National Laboratory (ORNL/DSRD-24) (pp. 201–216), Tennessee, USA.

Rott, H. (2001). Change, choice and inference: A study of belief revision and nonmonotonic reasoning. No. 42 in Oxford Logic Guides, Oxford Science Publications.

Segerberg, K. (2001). The basic dynamic doxastic logic of AGM. In Williams and Rott (2001) (pp. 57–84).

Stalnaker, R. (2006). On logics of knowledge and belief. Philosophical Studies, 128(1), 169–199. doi:10.1007/s11098-005-4062-y.CrossRef

van Benthem, J. (2007). Dynamic logic for belief revision. Journal of Applied Non-classical Logics, 17(2), 129–155. doi:10.3166/jancl.17.129-155.CrossRef

van Benthem, J. (2008). Merging observation and access in dynamic logic. Journal of Logic Studies, 1(1), 1–17.

van Benthem, J. (2011). Logical dynamics of information and interaction. Cambridge: Cambridge University Press.CrossRef

van Benthem, J., & Liu, F. (2007). Dynamic logic of preference upgrade. Journal of Applied Non-classical Logics, 17(2), 157–182. doi:10.3166/jancl.17.157-182.CrossRef

van Benthem, J., van Eijck, J., & Kooi, B. (2006). Logics of communication and change. Information and Computation, 204(11), 1620–1662. doi:10.1016/j.ic.2006.04.006.CrossRef

van Benthem, J., & Velázquez-Quesada, F. R. (2010). The dynamics of awareness. Synthese (Knowledge, Rationality and Action), 177(Supplement 1), 5–27. doi:10.1007/s11229-010-9764-9.

van Ditmarsch, H. (2005). Prolegomena to dynamic logic for belief revision. Synthese, 147(2), 229–275. doi:10.1007/s11229-005-1349-7.

van Ditmarsch, H., Herzig, A., Lang, J., & Marquis, P. (2009). Introspective forgetting. Synthese (Knowledge, Rationality and Action), 169(2), 405–423. doi:10.1007/s11229-009-9554-4.

van Ditmarsch, H., van der Hoek, W., & Kooi, B. (2007). Dynamic epistemic logic, synthese library series (vol. 337). Berlin: Springer.

van Ditmarsch, H. P., & French, T. (2009). Awareness and forgetting of facts and agents. In Web intelligence/IAT workshops (pp. 478–483), IEEE. doi:10.1109/WI-IAT.2009.330.

van Eijck, J., & Wang, Y. (2008). Propositional dynamic logic as a logic of belief revision. In W. Hodges, R. J. G. B. de Queiroz (Eds.), WoLLIC, Lecture Notes in Computer Science (vol. 5110, pp. 136–148). Berlin: Springer. doi:10.1007/978-3-540-69937-8_13.

Vardi, M. Y. (1986). On epistemic logic and logical omniscience. In Halpern (1986) (pp. 293–305).

Velázquez-Quesada, F. R. (2009a). Dynamic logics for explicit and implicit information. In He et al. (2009) (pp 325–326). doi:10.1007/978-3-642-04893-7_31.

Velázquez-Quesada, F. R. (2009b). Inference and update. Synthese (Knowledge, Rationality and Action), 169(2), 283–300. doi:10.1007/s11229-009-9556-2.

Velázquez-Quesada, F. R. (2011). Small steps in dynamics of information. PhD thesis, Institute for Logic, Language and Computation (ILLC), Universiteit van Amsterdam (UvA), Amsterdam, The Netherlands, ILLC Dissertation series DS-2011-02.

Veltman, F. (1985). Logics for conditionals. PhD thesis, Universiteit van Amsterdam.

Williams, M. A., & Rott, H. (eds.). (2001). Frontiers in belief revision, no. 22 in applied logic series. Dordrecht: Kluwer.

Title: Dynamic Epistemic Logic for Implicit and Explicit Beliefs
Author: Fernando R. Velázquez-Quesada
Publication date: 01-06-2014
Publisher: Springer Netherlands
Published in: Journal of Logic, Language and Information / Issue 2/2014
Print ISSN: 0925-8531
Electronic ISSN: 1572-9583
DOI: https://doi.org/10.1007/s10849-014-9193-0

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Other articles of this Issue 2/2014

Formal Models of Awareness

Semantics for Knowledge and Change of Awareness

A Logic for Reasoning About Knowledge of Unawareness

A Formal Model of Communication and Context Awareness in Multiagent Systems

Generation and Selection of Abductive Explanations for Non-Omniscient Agents

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