We present the first class of mathematically rigorous, general, fully self-referential, self-improving, optimally efficient problem solvers. Inspired by Kurt Goedel's celebrated self-referential formulas (1931), such a problem solver rewrites any part of its own code as soon as it has found a proof that the rewrite is useful, where the problem-dependent utility function and the hardware and the entire initial code are described by axioms encoded in an initial proof searcher which is also part of the initial code. The searcher systematically and efficiently tests computable proof techniques (programs whose outputs are proofs) until it finds a provably useful, computable self-rewrite. We show that such a self-rewrite is globally optimal - no local maxima! - since the code first had to prove that it is not useful to continue the proof search for alternative self-rewrites. Unlike previous non-self-referential methods based on hardwired proof searchers, ours not only boasts an optimal order of complexity but can optimally reduce any slowdowns hidden by the O()-notation, provided the utility of such speed-ups is provable at all.

If one isolated species (corporation) is supposed to evolve following the logistic mapping, then we are tempted to think that the dynamics of two species (corporations) can be expressed by a coupled system of two discrete logistic equations. As three basic relationships between two species are present in Nature, namely symbiosis, predator-prey and competition, three different models are obtained. Each model is a cubic two-dimensional discrete logistic-type equation with its own dynamical properties: stationary regime, periodicit y, quasi-periodicity and chaos. We also propose that these models could be useful for thinking in the different interactions happening in the economic world, as for instance for the competition and the collaboration between corporations. Furthermore, these models could be considered as the basic ingr edients to construct more complex interactions in the ecological and economic networks.

The axiom scheme of Extensionality states that whenever two predicates or relations are coextensive they must have the same propertie s: XY ( null x(Xnull x Ynull x) Z (ZX ZY)) (1) Historically Extensionality has always been problematic, the main problem being that in many areas of application, though not perhaps in t he foundations of mathematics, the statement is simply false. This was reco gnized by Whitehead and Russell in Principia Mathematica [32], where intensional functions such as ' A believes that p ' or'it is a strange coincidence that p ' are discussed at length. However, in the introduction to the second edition ( 1927) of the Prin-cipia Whitehead and Russell (influenced by Wittgenstein's Tractatus) already entertain the possibility that "all functions of functions are extensional". Thirteen years later, in Church's [6] canonical formulation of t he Theory of Types, it is observed that axioms of Extensionality should be adopt ed "[i]n order to obtain classical real number theory (analysis)", a wording that does not seem to rule out the option of not adopting them. Church's formula tion of type theory was completely syntactic and axioms could be adopted or d ropped at will, The Journal of Symbolic Logic, to appear.

We consider methods for aggregating preferences that are base d on the resolution of discrete optimization problems. For a review and references see Cook and Kress (1992), and Belkin and Levin (1990), and also David (1988) and Van B lokland-Vogelesang (1991). Some algorithmic aspects can be found in Barth elemy (1989) and Litvak (1982). The preferences are represented by arbitra ry binary relations (possibly weighted) or incomplete paired comparison matrices. The o utcome of an aggregation method is a set of "optimal" rankings (linear or weak ord ers) of the alternatives. Namely, a ranking is said to be optimal if it provides an ex tremum of some chosen objective function that expresses the connectio n (or proximity) between an arbitrary ranking and the original preferences.

This text analyses the papers accepted for the workshop "Reuse of designs: an interdisciplinary cognitive approach". Several dimensions and questions considered as important (by the authors and/or by us) are addressed: What about the "interdisciplinary cognitive" character of the approaches adopted by the authors? Is design indeed a domain where the use of CBR is particularly suitable? Are there important distinctions between CBR and other approaches? Which types of knowledge -other than cases- is being, or might be, used in CBR systems? With respect to cases: are there different "types" of case and different types of case use? which formats are adopted for their representation? do cases have "components"? how are cases organised in the case memory? Concerning their retrieval: which types of index are used? on which types of relation is retrieval based? how does one retrieve only a selected number of cases, i.e., how does one retrieve only the "best" cases? which processes and strategies are used, by the system and by its user? Finally, some important aspects of CBR system development are shortly discussed: should CBR systems be assistance or autonomous systems? how can case knowledge be "acquired"? what about the empirical evaluation of CBR systems? The conclusion points out some lacking points: not much attention is paid to the user, and few papers have indeed adopted an interdisciplinary cognitive approach.

This paper addresses the issue of policy evaluation in Markov Decision Processes, using linear function approximation. It provides a unified view of algorithms such as TD(lambda), LSTD(lambda), iLSTD, residual-gradient TD. It is asserted that they all consist in minimizing a gradient function and differ by the form of this function and their means of minimizing it. Two new schemes are introduced in that framework: Full-gradient TD which uses a generalization of the principle introduced in iLSTD, and EGD TD, which reduces the gradient by successive equi-gradient descents. These three algorithms form a new intermediate family with the interesting property of making much better use of the samples than TD while keeping a gradient descent scheme, which is useful for complexity issues and optimistic policy iteration.

Outsourcing of complex IT infrastructure to IT service providers has increased substantially during the past years. IT service providers must be able to fulfil their service-quality commitments based upon predefined Service Level Agreements (SLAs) with the service customer. They need to manage, execute and maintain thousands of SLAs for different customers and different types of services, which needs new levels of flexibility and automation not available with the current technology. The complexity of contractual logic in SLAs requires new forms of knowledge representation to automatically draw inferences and execute contractual agreements. A logic-based approach provides several advantages including automated rule chaining allowing for compact knowledge representation as well as flexibility to adapt to rapidly changing business requirements. We suggest adequate logical formalisms for representation and enforcement of SLA rules and describe a proof-of-concept implementation. The article describes selected formalisms of the ContractLog KR and their adequacy for automated SLA management and presents results of experiments to demonstrate flexibility and scalability of the approach.

We present tableau calculi for some logics of nonmonotonic reasoning, as defined by Kraus, Lehmann and Magidor. We give a tableau proof procedure for all KLM logics, namely preferential, loop-cumulative, cumulative and rational logics. Our calculi are obtained by introducing suitable modalities to interpret conditional assertions. We provide a decision procedure for the logics considered, and we study their complexity.

It is suggested that a new area of CSCR (Computer Supported Collaborative Research) is distinguished from CSCW and CSCL and that the demarcation between the three areas could do with greater clarification and prescription. Keywords: HCI, CSCW, CSCL, CSCR 1. Introduction The twin fields of Computer Supported Collaborative Work (CSCW) and Computer supported Collaborative Learning (CSCL) have been the subject of intense interest in the HCI research community during the past seven years. The split between CSCW and CSCL has grown wider in response to the recognition that the learning process is more distinct from the working pattern and is more intensively understood through new theories of pedagogy and education. It has become apparent that CSCL requires all of the facets of CSCW but in addition is constraint by these pedagogical theories and as such it is argued here that CSCL is a subset of CSCW (see figure1) The process of research is also a learning process but one which is more highly refined and involves learning in a particular way using special techniques and tools. As such it is argued further that research which is supported by computer collaboration is a subset of CSCL (fig.1) Figure 1 2. Differences between CSCW and CSCL Diaper (2005) maintains that the History of HCI shows a lack of coherent development.

The few available French resources for evaluating linguistic models or algorithms on other linguistic levels than morpho-syntax are either insufficient from quantitative as well as qualitative point of view or not freely accessible. Based on this fact, the FREEBANK project intends to create French corpora constructed using manually revised output from a hybrid Constraint Grammar parser and annotated on several linguistic levels (structure, morpho-syntax, syntax, coreference), with the objective to make them available on-line for research purposes. Therefore, we will focus on using standard annotation schemes, integration of existing resources and maintenance allowing for continuous enrichment of the annotations. Prior to the actual presentation of the prototype that has been implemented, this paper describes a generic model for the organization and deployment of a linguistic resource archive, in compliance with the various works currently conducted within international standardization initiatives (TEI and ISO/TC 37/SC 4).