Fundamenta Informaticae XX (2011) 1–25 1 IOS Press A Nonmonotonic Soft Concurrent Constraint Language to Model the Negotiation Process ∗ Stefano Bistarelli Dipartimento di Matematica e Informatica, Universit` a di Perugia, Via Vanvitelli 1, Perugia, Italy and Instituto di Informatica e Telematica (CNR), Via Moruzzi 1, Pisa, Italy bista@dmi.unipg.it and stefano.bistarelli@iit.cnr.it Francesco Santini C Dipartimento di Matematica e Informatica, Universit` a di Perugia, Via Vanvitelli 1, Perugia, Italy francesco.santini@dmi.unipg.it Abstract. We present an extension of the Soft Concurrent Constraint language that allows the nonmonotonic evolution of the constraint store. To accomplish this, we introduce some new operations: retract(c) reduces the current store by c, update X (c) transactionally relaxes all the constraints of the store that deal with the variables in the set X, and then adds a constraint c; nask(c) tests if c is not entailed by the store. The new retraction operators also permit to reason about Belief Revision, i.e. the process of changing beliefs to take into account a new piece of information. We present this framework as a possible solution to the negotiation of resources (e.g. web services and network resource allocation) that need a given Quality of Service (QoS). For this reason we also show the the new operators of the language satisfy the Belief Revision postulates [20], which can be used in the negotiation process. The QoS requirements (expressed as semiring levels) of all the parties should converge on a formal agreement through a negotiation process, which specifies the contract that must be enforced. ∗ Research partially supported by MIUR PRIN 20089M932N project: “Innovative and multi-disciplinary approaches for constraint and preference reasoning”, by CCOS FLOSS project “Software open source per la gestione dell’epigrafia dei corpus di lingue antiche”, and by INDAM GNCS project “Fairness, Equit` a e Linguaggi”. C Corresponding author