We present in this paper a general algorithm for solving first-order formulas in particular theories called "decomposable theories". First of all, using special quantifiers, we give a formal characterization of decomposable theories and show some of their properties. Then, we present a general algorithm for solving first-order formulas in any decomposable theory "T". The algorithm is given in the form of five rewriting rules. It transforms a first-order formula "P", which can possibly contain free variables, into a conjunction "Q" of solved formulas easily transformable into a Boolean combination of existentially quantified conjunctions of atomic formulas. In particular, if "P" has no free variables then "Q" is either the formula "true" or "false". The correctness of our algorithm proves the completeness of the decomposable theories. Finally, we show that the theory "Tr" of finite or infinite trees is a decomposable theory and give some benchmarks realized by an implementation of our algorithm, solving formulas on two-partner games in "Tr" with more than 160 nested alternated quantifiers.

Questions related to the evolution of language have recently known an impressive increase of interest (Briscoe, 2002). This short paper aims at questioning the scientific status of these models and their relations to attested data. We show that one cannot directly model non-linguistic factors (exogenous factors) even if they play a crucial role in language evolution. We then examine the relation between linguistic models and attested language data, as well as their contribution to cognitive linguistics.

Diagrammatic, analogical or iconic representations are often contrasted with linguistic or logical representations, in which the shape of the symbols is arbitrary. The aim of this paper is to make a case for the usefulness of diagrams in inferential knowledge representation systems. Although commonly used, diagrams have for a long time suffered from the reputation of being only a heuristic tool or a mere support for intuition. The first part of this paper is an historical background paying tribute to the logicians, psychologists and computer scientists who put an end to this formal prejudice against diagrams. The second part is a discussion of their characteristics as opposed to those of linguistic forms. The last part is aimed at reviving the interest for heterogeneous representation systems including both linguistic and diagrammatic representations.

A standard approach in pattern classification is to estimate the distributions of the label classes, and then to apply the Bayes classifier to the estimates of the distributions in order to classify unlabeled examples. As one might expect, the better our estimates of the label class distributions, the better the resulting classifier will be. In this paper we make this observation precise by identifying risk bounds of a classifier in terms of the quality of the estimates of the label class distributions. We show how PAC learnability relates to estimates of the distributions that have a PAC guarantee on their $L_1$ distance from the true distribution, and we bound the increase in negative log likelihood risk in terms of PAC bounds on the KL-divergence. We give an inefficient but general-purpose smoothing method for converting an estimated distribution that is good under the $L_1$ metric into a distribution that is good under the KL-divergence.

We present here a formal foundation for an iterative and incremental approach to constructing and evaluating preference queries. Our main focus is on query modification: a query transformation approach which works by revising the preference relation in the query. We provide a detailed analysis of the cases where the order-theoretic properties of the preference relation are preserved by the revision. We consider a number of different revision operators: union, prioritized and Pareto composition. We also formulate algebraic laws that enable incremental evaluation of preference queries. Finally, we consider two variations of the basic framework: finite restrictions of preference relations and weak-order extensions of strict partial order preference relations.

In this paper we propose a new family of Belief Conditioning Rules (BCRs) for belief revision. These rules are not directly related with the fusion of several sources of evidence but with the revision of a belief assignment available at a given time according to the new truth (i.e. conditioning constraint) one has about the space of solutions of the problem.

We study the adaptation of Link Grammar Parser to the biomedical sublanguage with a focus on domain terms not found in a general parser lexicon. Using two biomedical corpora, we implement and evaluate three approaches to addressing unknown words: automatic lexicon expansion, the use of morphological clues, and disambiguation using a part-of-speech tagger. We evaluate each approach separately for its effect on parsing performance and consider combinations of these approaches. In addition to a 45% increase in parsing efficiency, we find that the best approach, incorporating information from a domain part-of-speech tagger, offers a statistically significant 10% relative decrease in error. The adapted parser is available under an open-source license at http://www.it.utu.fi/biolg .

Markov models have been widely used to represent and analyse user web navigation data. In previous work we have proposed a method to dynamically extend the order of a Markov chain model and a complimentary method for assessing the predictive power of such a variable length Markov chain. Herein, we review these two methods and propose a novel method for measuring the ability of a variable length Markov model to summarise user web navigation sessions up to a given length. While the summarisation ability of a model is important to enable the identification of user navigation patterns, the ability to make predictions is important in order to foresee the next link choice of a user after following a given trail so as, for example, to personalise a web site. We present an extensive experimental evaluation providing strong evidence that prediction accuracy increases linearly with summarisation ability.

This paper describes an interdisciplinary approach which brings together the fields of corpus linguistics and translation studies. It presents ongoing work on the creation of a corpus resource in which translation shifts are explicitly annotated. Translation shifts denote departures from formal correspondence between source and target text, i.e. deviations that have occurred during the translation process. A resource in which such shifts are annotated in a systematic way will make it possible to study those phenomena that need to be addressed if machine translation output is to resemble human translation. The resource described in this paper contains English source texts (parliamentary proceedings) and their German translations. The shift annotation is based on predicate-argument structures and proceeds in two steps: first, predicates and their arguments are annotated monolingually in a straightforward manner. Then, the corresponding English and German predicates and arguments are aligned with each other. Whenever a shift - mainly grammatical or semantic -has occurred, the alignment is tagged accordingly.

This paper is based on my invited talk at the 19th Annual Conference on Learning Theory (Pittsburgh, PA, June 24, 2006). In recent years COL T invited talks have tended to aim at establishing connections between the traditio nal concerns of the learning community and the work done by other communities (s uch as game theory, statistics, information theory, and optimization). F ollowing this tradition, I will argue that some ideas from the foundations of prob ability can be fruitfully applied in competitive on-line learning. In this paper I will use the following informal taxonomy of predictions (reminiscent of Shafer's [36], Figure 2, taxonomy of probabilities): D-predictions are mere Decisions. They can never be true or false but can be good or bad.