Modal Logics of Negotiation and Preference
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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
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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