Modal Logics of Negotiation and Preference

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.

[1]  Tuomas Sandholm.  Contract Types for Satisficing Task Allocation:I Theoretical Results , 2002 .

[2]  Yann Chevaleyre,et al.  Negotiating over small bundles of resources , 2005, AAMAS '05.

[3]  M. de Rijke,et al.  Modal Logic , 2001, Cambridge Tracts in Theoretical Computer Science.

[4]  Ryszard Danecki,et al.  Nondeterministic Propositional Dynamic Logic with intersection is decidable , 1984, Symposium on Computation Theory.

[5]  Richard E. Ladner,et al.  Propositional Dynamic Logic of Regular Programs , 1979, J. Comput. Syst. Sci..

[6]  Yde Venema,et al.  Dynamic Logic by David Harel, Dexter Kozen and Jerzy Tiuryn. The MIT Press, Cambridge, Massachusetts. Hardback: ISBN 0–262–08289–6, $50, xv + 459 pages , 2002, Theory and Practice of Logic Programming.

[7]  Jerzy Tiuryn,et al.  Dynamic logic , 2001, SIGA.

[8]  Patrick Baillot,et al.  Elementary Complexity and Geometry of Interaction , 1999, Fundam. Informaticae.

[9]  Nicolas Maudet,et al.  Negotiating Socially Optimal Allocations of Resources , 2011, J. Artif. Intell. Res..

[10]  Michael Wooldridge,et al.  The complexity of contract negotiation , 2005, Artif. Intell..

[11]  Rohit Parikh.  Social Software , 2004, Synthese.

[12]  Carsten Lutz,et al.  2-Exp Time lower bounds for propositional dynamic logics with intersection , 2005, Journal of Symbolic Logic.

[13]  Tinko Tinchev,et al.  An Essay in Combinatory Dynamic Logic , 1991, Inf. Comput..

[14]  Vaughan R. Pratt,et al.  Semantical consideration on floyo-hoare logic , 1976, 17th Annual Symposium on Foundations of Computer Science (sfcs 1976).

[15]  P. E. Dunne,et al.  Negotiation Can be as Hard as Planning: Deciding Reachability Properties of Distributed Negotiation Schemes , 2005 .

[16]  Olivier Roy,et al.  Preference logic, conditionals and solution concepts in games , 2005 .

[17]  Michael Wooldridge,et al.  Logic for Mechanism Design A Manifesto , 2003 .

[18]  Martin Lange,et al.  Model checking propositional dynamic logic with all extras , 2006, J. Appl. Log..

[19]  Dimiter Vakarelov,et al.  Iteration-free PDL with Intersection: a Complete Axiomatization , 2001, Fundam. Informaticae.

[20]  Carsten Lutz,et al.  PDL with negation of atomic programs , 2004, J. Appl. Non Class. Logics.

[21]  Rohit Parikh,et al.  Social Interaction, Knowledge, and Social Software , 2006 .

[22]  H. Moulin.  Axioms of Cooperative Decision Making , 1988 .

[23]  Vaughan R. Pratt,et al.  SEMANTICAL CONSIDERATIONS ON FLOYD-HOARE LOGIC , 1976, FOCS 1976.