Abstract. The effects of public announcements, private communications, deceptive messages to groups, and so on, can all be captured by a general mechanism of updating multi-agent models with update action models [3], now in widespread use (see [10] for a textbook treatment). There is a natural extension of the definition of a bisimulation to action models. Surely enough, updating with bisimilar action models gives the same result (modulo bisimulation). But the converse turns out to be false: update models may have the same update effects without being bisimilar. We propose action emulation as a notion of structural equivalence more appropriate for action models, and generalizing standard bisimulation. It is proved that action emulation provides a full characterization of update effect, provided we confine attention to ‘smooth ’ action models. We also give a recipe for turning any action model into a smooth one with the same update effect. Together, this yields a simplification procedure for action models, and it gives designers of multi-agent systems a useful tool for comparing different ways of representing a particular communicative action. 1.

We give a simple example of a variety V of modal algebras that is canonical but cannot be axiomatised by canonical equations or first-order sentences. We then show that the variety RRA of representable relation algebras, although canonical, has no canonical axiomatisation. Indeed, we show that every axiomatisation of these varieties involves infinitely many noncanonical sentences. Using probabilistic methods...

We present a generalization of Segerberg’s onion semantics for belief revision, in which the linearity of the spheres need not occur. The resulting logic is called broccoli logic. We provide a minimal relational logic, introducing a new neighborhood semantics operator. We then show that broccoli logic is a well-known conditional logic, the Burgess-Veltman minimal conditional logic. Belief revision is the study of theory change in which a set of formulas is ascribed to an agent as a belief set revisable in the face of new information. A dominant paradigm in belief revision is the so-called AGM paradigm, which describes a functional notion of revision (cf. [1]). A natural semantics in terms of sphere systems (cf. [6]) was given by Grove in [5] and a logical axiomatization was extensively studied by Segerberg (cf. [9, 10, 11, 12] and the forthcoming [13]). The resulting logic is called “dynamic doxastic logic ” (DDL). A generalization of the AGM approach in which revision is taken to be relational rather

We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion S4 S4. We axiomatize the modal logic of products of topological spaces with horizontal, vertical, and standard product topologies. We prove that both of these logics are complete for the product of rational numbers Q Q with the appropriate topologies.

Summary. In this paper we provide a foundation for a new generation of services and tools. We define new ways of capturing, sharing and reusing information and intelligence provided by single users and communities, as well as organizations by enabling the extraction, generation, interpretation and management of Collective Intelligence from user generated digital multimedia content. Different layers of intelligence are generated, which together constitute the notion of Collective Intelligence. The automatic generation of Collective Intelligence constitutes a departure from traditional methods for information sharing, since information from both the multimedia content and social aspects will be merged, while at the same time the social dynamics will be taken into account. In the context of this work, we present

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We define a multi-modal version of Computation Tree Logic (ctl) by extending the language with path quantifiers E δ and A δ where δ denotes one of finitely many dimensions, interpreted over Kripke structures with one total relation for each dimension. As expected, the logic is axiomatised by taking a copy of a ctl axiomatisation for each dimension. Completeness is proved by employing the completeness result for ctl to obtain a model along each dimension at a time. We also show that the logic is decidable and that its satisfiability problem is no harder than the corresponding problem for ctl.

Generalizing ordinary topological and pretopological spaces, we introduce the notion of peritopology where neighborhoods of a point need not contain that point, and some points might even have an empty neighborhood. We briefly describe various intrinsic aspects of this notion. Applied to modal logic, it gives rise to peritopological models, a generalization of topological models, a spacial case of neighborhood semantics. (In a last section, the relation between the latter and the former is discussed, cursorily). A new cladding for bisimulation is presented. The concept of Alexandroff peritopology is used in order to determine the logic of all peritopological spaces, and we prove that the minimal logic K is strongly complete with respect to the class of all peritopological spaces. We also show that the classes of T0, T1 and T2-peritopological spaces are not modal definable, and that D is the logic of all proper peritopological spaces.

We define a multi-modal version of Computation Tree Logic (ctl) by extending the language with path quantifiers E δ and A δ where δ denotes one of finitely many dimensions, interpreted over Kripke structures with one total relation for each dimension. As expected, the logic is axiomatised by taking a copy of a ctl axiomatisation for each dimension. Completeness is proved by employing the completeness result for ctl to obtain a model along each dimension at a time. We also show that the logic is decidable and that its satisfiability problem is no harder than the corresponding problem for ctl. Keywords: Temporal logic, computation tree logic, fusion, completeness