Abstract
We develop a dynamic modal logic that can be used to model scenarios where agents negotiate over the allocation of a finite number of indivisible resources. The logic includes operators to speak about both preferences of individual agents and deals regarding the reallocation of certain resources. We reconstruct a known result regarding the convergence of sequences of mutually beneficial deals to a Pareto optimal allocation of resources, and discuss the relationship between reasoning tasks in our logic and problems in negotiation. For instance, checking whether a given restricted class of deals is sufficient to guarantee convergence to a Pareto optimal allocation for a specific negotiation scenario amounts to a model checking problem; and the problem of identifying conditions on preference relations that would guarantee convergence for a restricted class of deals under all circumstances can be cast as a question in modal logic correspondence theory.
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References
Sandholm, T.W.: Contract types for satisficing task allocation: I Theoretical results. In: Proc. AAAI Spring Symposium: Satisficing Models (1998)
Endriss, U., Maudet, N., Sadri, F., Toni, F.: Negotiating socially optimal allocations of resources. Journal of Artificial Intelligence Research 25, 315–348 (2006)
Dunne, P.E., Wooldridge, M., Laurence, M.: The complexity of contract negotiation. Artificial Intelligence 164(1-2), 23–46 (2005)
Parikh, R.: Social software. Synthese 132, 187–211 (2002)
Pacuit, E., Parikh, R.: Social interaction, knowledge, and social software. In: Interactive Computation: The New Paradigm. Springer, Heidelberg (forthcoming)
Pauly, M., Wooldridge, M.: Logic for mechanism design: A manifesto. In: Proc. 5th Workshop on Game-theoretic and Decision-theoretic Agents (2003)
Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2002)
Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. MIT Press, Boston (2000)
Moulin, H.: Axioms of Cooperative Decision Making. Cambridge University Press, Cambridge (1988)
van Benthem, J., van Otterloo, S., Roy, O.: Preference logic, conditionals and solution concepts in games. In: Modality Matters: Twenty-Five Essays in Honour of Krister Segerberg, University of Uppsala (2006)
Hansson, S.O.: Preference logic. In: Handbook of Philosophical Logic, 2nd edn. Kluwer Academic Publishers, Dordrecht (2001)
Dunne, P.E., Chevaleyre, Y.: Negotiation can be as hard as planning: Deciding reachability properties of distributed negotiation schemes. Technical Report ULCS-05-009, Department of Computer Science, University of Liverpool (2005)
Lange, M.: Model checking propositional dynamic logic with all extras. Journal of Applied Logic 4(1), 39–49 (2005)
Chevaleyre, Y., Endriss, U., Lang, J., Maudet, N.: Negotiating over small bundles of resources. In: Proc. 4th International Joint Conference on Autonomous Agents and Multiagent Systems. ACM Press, New York (2005)
Passy, S., Tinchev, T.: An essay in combinatory dynamic logic. Information and Computation 93(2), 263–332 (1991)
Balbiani, P., Vakarelov, D.: Iteration-free PDL with intersection: A complete axiomatization. Fundamenta Informaticae 45, 1–22 (2001)
Fischer, M.J., Ladner, R.E.: Propositional dynamic logic of regular programs. Journal of Computer and System Sciences 18(2), 194–211 (1979)
Pratt, V.R.: Semantical considerations on Floyd-Hoare logic. In: Proc. 17th Annual Symposium on Foundations of Computer Science, pp. 109–121. IEEE, Los Alamitos (1976)
Lutz, C., Walther, D.: PDL with negation of atomic programs. Journal of Applied Non-Classical Logics 15(2), 189–214 (2005)
Danecki, R.: Non-deterministic propositional dynamic logic with intersection is decidable. In: Proc. 5th Workshop on Computation Theory. Springer, Heidelberg (1985)
Lange, M., Lutz, C.: 2-EXPTIME lower bounds for propositional dynamic logics with intersection. Journal of Symbolic Logic 70(4), 1072–1086 (2005)
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Endriss, U., Pacuit, E. (2006). Modal Logics of Negotiation and Preference. In: Fisher, M., van der Hoek, W., Konev, B., Lisitsa, A. (eds) Logics in Artificial Intelligence. JELIA 2006. Lecture Notes in Computer Science(), vol 4160. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11853886_13
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DOI: https://doi.org/10.1007/11853886_13
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