Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-18T02:31:54.065Z Has data issue: false hasContentIssue false
  • English
  • Français

PRIORITY MERGE AND INTERSECTION MODALITIES

Part of: Mathematical economics Philosophical aspects of logic and foundations General logic

Published online by Cambridge University Press:  22 February 2021

ZOÉ CHRISTOFF ,
NORBERT GRATZL  and
OLIVIER ROY
ZOÉ CHRISTOFF
Affiliation:
DEPARTMENT OF ARTIFICIAL INTELLIGENCE UNIVERSITY OF GRONINGEN GRONINGEN, NETHERLANDSE-mail: z.l.christoff@rug.nl
NORBERT GRATZL
Affiliation:
MUNICH CENTER FOR MATHEMATICAL PHILOSOPHY LUDWIG-MAXIMILIANS-UNIVERSITÄT MÜNCHENMÜNCHEN, GERMANYE-mail: norbert.gratzl@lrz.uni-muenchen.de
OLIVIER ROY
Affiliation:
DEPARTMENT OF PHILOSOPHY UNIVERSITY OF BAYREUTH BAYREUTH, GERMANYE-mail: olivier.roy@uni-bayreuth.de
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the logic of so-called lexicographic or priority merge for multi-agent plausibility models. We start with a systematic comparison between the logical behavior of priority merge and the more standard notion of pooling through intersection, used to define, for instance, distributed knowledge. We then provide a sound and complete axiomatization of the logic of priority merge, as well as a proof theory in labeled sequents that admits cut. We finally study Moorean phenomena and define a dynamic resolution operator for priority merge for which we also provide a complete set of reduction axioms.

Keywords

epistemic logicgroup knowledgepriority mergelogic of beliefsdynamic epistemic logic

MSC classification

Primary: 03A05: Philosophical and critical
Secondary: 03B42: Logics of knowledge and belief (including belief change) 03B45: Modal logic (including the logic of norms) 03B70: Logic in computer science 91B14: Social choice
Type
Research Article
Information
The Review of Symbolic Logic , Volume 15 , Issue 1 , March 2022 , pp. 165 - 196
Check for updates
Copyright
© Association for Symbolic Logic, 2021

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BIBLIOGRAPHY

Ågotnes, T. & Wáng, Y. (2017). Resolving distributed knowledge. Artificial Intelligence, 252, 1–21.10.1016/j.artint.2017.07.002CrossRefGoogle Scholar
Andréka, H., Ryan, M., & Schobbens, P. Y. (2002). Operators and laws for combining preference relations. Journal of Logic and Computation, 12(1), 13–53.10.1093/logcom/12.1.13CrossRefGoogle Scholar
Baltag, A., Bezhanishvili, N., Özgün, A., & Smets, S. (2013). The topology of belief, belief revision and defeasible knowledge. In International Workshop on Logic, Rationality and Interaction. Berlin: Springer, pp. 27–40.CrossRefGoogle Scholar
Baltag, A. & Renne, B. (2016). Dynamic epistemic logic. In Zalta, E. N., editor. The Stanford Encyclopedia of Philosophy, Winter 2016 edition. Stanford, CA: Metaphysics Research Lab, Stanford University.Google Scholar
Baltag, A. & Smets, S. (2008). A qualitative theory of dynamic interactive belief revision. In Bonanno, G., van der Hoek, W., and Wooldridge, M., editors. Logic and the Foundations of Game and Decision Theory, Texts in Logic and Games, Vol. 3. Amsterdam: Amsterdam University Press, pp. 9–58.Google Scholar
Baltag, A. & Smets, S. (2013). Protocols for belief merge: Reaching agreement via communication. Logic Journal of IGPL, 21(3), 468–487.10.1093/jigpal/jzs049CrossRefGoogle Scholar
Benthem, J., Girard, P., & Roy, O. (2009). Everything else being equal: A modal logic for ceteris paribus preferences. Journal of Philosophical Logic, 38(1), 83–125.10.1007/s10992-008-9085-3CrossRefGoogle Scholar
Benthem, J., Grossi, D., & Liu, F. (2014). Priority structures in deontic logic. Theoria, 80(2), 116–152.10.1111/theo.12028CrossRefGoogle Scholar
Benthem, J., van Otterloo, S., & Roy, O. (2005). Preference logic, conditionals and solution concepts in games. In Lagerlund, L. and Sliwinski, editors, Modality Matters: Twenty-Five Essays in Honour of Krister Segerberg. Uppsala: Department of Philosophy, Uppsala Philosophical Studies.Google Scholar
Blackburn, P., de Rijke, M., & Venema, Y. (2001). Modal logic . In Cambridge Tracts in Theoretical Computer Science, Vol. 53. United Kingdom: Cambridge University Press.Google Scholar
Boutilier, C. (1994). Conditional logics of normality: A modal approach. Artificial Intelligence, 68(1), 87–154.CrossRefGoogle Scholar
Bradley, R. (2017). Decision Theory With a Human Face. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Fagin, R., Halpern, J. Y., Moses, Y., & Vardi, M. (2004). Reasoning About Knowledge. Cambridge, MA: MIT Press.10.7551/mitpress/5803.001.0001CrossRefGoogle Scholar
Fishburn, P. C. (1974). Exceptional paper—Lexicographic orders, utilities and decision rules: A survey. Management Science, 20(11), 1442–1471.CrossRefGoogle Scholar
Gerbrandy, J. (1998). Distributed knowledge. In Proceedings of the Second Workshop on the Semantics and Pragmatics of Dialogue. Twente: University of Twente, pp. 111–124.Google Scholar
Girard, P. (2011). Modal logic for lexicographic preference aggregation. In Games, Norms and Reasons. Netherlands: Springer, pp. 97–117.10.1007/978-94-007-0714-6_6CrossRefGoogle Scholar
Girard, P. & Seligman, J. (2009). An analytic logic of aggregation. In Proceedings of the 3rd Indian Conference on Logic and Its Applications. Berlin, Heidelberg: Springer-Verlag, pp. 146–161.Google Scholar
Grove, A. (1988). Two modellings for theory change. Journal of Philosophical Logic, 17(2), 157–170.CrossRefGoogle Scholar
Kazmer, M. M., Lustria, M. L. A., Cortese, J., Burnett, G., Kim, J.-H., Ma, J., & Frost, J. (2014). Distributed knowledge in an online patient support community: Authority and discovery. Journal of the Association for Information Science and Technology, 65(7), 1319–1334.10.1002/asi.23064CrossRefGoogle Scholar
Negri, S. (2005). Proof analysis in modal logic. Journal of Philosophical Logic, 34(5–6), 507.10.1007/s10992-005-2267-3CrossRefGoogle Scholar
Negri, S. & Von Plato, J. (1998). Cut elimination in the presence of axioms. Bulletin of Symbolic Logic, 4(4), 418–435.CrossRefGoogle Scholar
Negri, S., von Plato, J., & Ranta, A. (2008). Structural Proof Theory. Cambridge: Cambridge University Press.Google Scholar
Özgün, A. (2017). Evidence in Epistemic Logic: A Topological Perspective. Ph. D. thesis.Google Scholar
Parikh, R. & Ramanujam, R. (1985). Distributed processes and the logic of knowledge. In Workshop on Logic of Programs. Berlin: Springer, pp. 256–268.CrossRefGoogle Scholar
Punčochář, V. & Sedlár, I. (2017). Substructural logics for pooling information. In International Workshop on Logic, Rationality and Interaction. Berlin: Springer, pp. 407–421.CrossRefGoogle Scholar
Roelofsen, F. (2007). Distributed knowledge. Journal of Applied Non-Classical Logics, 17(2), 255–273.CrossRefGoogle Scholar
Ryan, M. (1993). Defaults in specifications. In [1993] Proceedings of the IEEE International Symposium on Requirements Engineering. IEEE, pp. 142–149.Google Scholar
Segerberg, K. (1971). An Essay in Classical Modal Logic. Uppsala: Filosofiska Föreningen Och Filosofiska Institutionen Vid Uppsala Universitet.Google Scholar
Swanson, D. R. (1986). Undiscovered public knowledge. The Library Quarterly, 56(2), 103–118.CrossRefGoogle Scholar
van der Hoek, W., van Linder, B., & Meyer, J.-J. (1999). Group knowledge is not always distributed (neither is it always implicit). Mathematical Social Sciences, 38(2), 215–240.10.1016/S0165-4896(99)00013-XCrossRefGoogle Scholar
van Ditmarsch, H., van der Hoek, W., & Kooi, B. (2007). Dynamic Epistemic Logic, Vol. 337. Berlin: Springer Science & Business Media.Google Scholar