For graphs $G$ and $H$, a mapping $f: V(G)\dom V(H)$ is a homomorphism of $G$ to $H$ if $uv\in E(G)$ implies $f(u)f(v)\in E(H).$ If, moreover, each vertex $u \in V(G)$ is associated with costs $c_i(u), i \in V(H)$, then the cost of the homomorphism $f$ is $\sum_{u\in V(G)}c_{f(u)}(u)$. For each fixed graph $H$, we have the {\em minimum cost homomorphism problem}, written as MinHOM($H)$. The problem is to decide, for an input graph $G$ with costs $c_i(u),$ $u \in V(G), i\in V(H)$, whether there exists a homomorphism of $G$ to $H$ and, if one exists, to find one of minimum cost. Minimum cost homomorphism problems encompass (or are related to) many well studied optimization problems. We describe a dichotomy of the minimum cost homomorphism problems for graphs $H$, with loops allowed. When each connected component of $H$ is either a reflexive proper interval graph or an irreflexive proper interval bigraph, the problem MinHOM($H)$ is polynomial time solvable. In all other cases the problem MinHOM($H)$ is NP-hard. This solves an open problem from an earlier paper. Along the way, we prove a new characterization of the class of proper interval bigraphs.

Introduction In the last years, many useful NLP tools have been developed and many of them are now even available commercially. Most of these tools are monolingual or multi-monolingual, meaning that the software can deal with more than one language, but that the re sults will al ways be displayed in the same language as the text. We therefore distinguish these applications from cross-lingual software, which is software that helps to transgress the language bound ary. Examples for such applications are machine translation and cross-lingual document retrieval, i.e. retrieval using search engines which allow to en ter a search term in one language and which also yield results in other languages, usually because the query is translated in one way or another. In our eyes, cross-lingual applications are currently the bottleneck of available NLP tools. To our knowledge, there are no applications that allow comparing documents written in dif ferent languages with each other and there are very few which give users a quick overview of the ap proximate contents of documents written in different languages.

Automatic annotation of documents with controlled vocabulary terms (descriptors) from a conceptual thesaurus is not only useful for document indexing and retrieval. The mapping of texts onto the same thesaurus furthermore allows to establish links between similar documents. This is also a substantial requirement of the Semantic Web. This paper presents an almost language-independent system that maps documents written in different languages onto the same multilingual conceptual thesaurus, EUROVOC. Conceptual thesauri differ from Natural Language Thesauri in that they consist of relatively small controlled lists of words or phrases with a rather abstract meaning. To automatically identify which thesaurus descriptors describe the contents of a document best, we developed a statistical, associative system that is trained on texts that have previously been indexed manually. In addition to describing the large number of empirically optimised parameters of the fully functional application, we present the performance of the software according to a human evaluation by professional indexers.

We present a new method for clustering based on compression. The method doesn't use subject-specific features or background knowledge, and works as follows: First, we determine a universal similarity distance, the normalized compression distance or NCD, computed from the lengths of compressed data files (singly and in pairwise concatenation). Second, we apply a hierarchical clustering method. The NCD is universal in that it is not restricted to a specific application area, and works across application area boundaries. A theoretical precursor, the normalized information distance, co-developed by one of the authors, is provably optimal but uses the non-computable notion of Kolmogorov complexity. We propose precise notions of similarity metric, normal compressor, and show that the NCD based on a normal compressor is a similarity metric that approximates universality. To extract a hierarchy of clusters from the distance matrix, we determine a dendrogram (binary tree) by a new quartet method and a fast heuristic to implement it. The method is implemented and available as public software, and is robust under choice of different compressors. To substantiate our claims of universality and robustness, we report evidence of successful application in areas as diverse as genomics, virology, languages, literature, music, handwritten digits, astronomy, and combinations of objects from completely different domains, using statistical, dictionary, and block sorting compressors. In genomics we presented new evidence for major questions in Mammalian evolution, based on whole-mitochondrial genomic analysis: the Eutherian orders and the Marsupionta hypothesis against the Theria hypothesis.

Relational representation of knowledge makes it possible to perform all the computations and decision making in a uniform relational way by means of special relational compositions called triangle and square products. In this paper some applications in manufacturing related to cost analysis are described. Testing fuzzy relational structures for various relational properties allows us to discover dependencies, hierarchies, similarities, and equivalences of the attributes characterizing technological processes and manufactured artifacts in their relationship to costs and performance. A brief overview of mathematical aspects of BK-relational products is given in Appendix 1 together with further references in the literature.

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.