To appear in Theory and Practice of Logic Programming (TPLP), 2008. We are researching the interaction between the rule and the ontology layers of the Semantic Web, by comparing two options: 1) using OWL and its rule extension SWRL to develop an integrated ontology/rule language, and 2) layering rules on top of an ontology with RuleML and OWL. Toward this end, we are developing the SWORIER system, which enables efficient automated reasoning on ontologies and rules, by translating all of them into Prolog and adding a set of general rules that properly capture the semantics of OWL. We have also enabled the user to make dynamic changes on the fly, at run time. This work addresses several of the concerns expressed in previous work, such as negation, complementary classes, disjunctive heads, and cardinality, and it discusses alternative approaches for dealing with inconsistencies in the knowledge base. In addition, for efficiency, we implemented techniques called extensionalization, avoiding reanalysis, and code minimization.

We consider how an agent should update her uncertainty when it is represented by a set $\P$ of probability distributions and the agent observes that a random variable $X$ takes on value $x$, given that the agent makes decisions using the minimax criterion, perhaps the best-studied and most commonly-used criterion in the literature. We adopt a game-theoretic framework, where the agent plays against a bookie, who chooses some distribution from $\P$. We consider two reasonable games that differ in what the bookie knows when he makes his choice. Anomalies that have been observed before, like time inconsistency, can be understood as arising important because different games are being played, against bookies with different information. We characterize the important special cases in which the optimal decision rules according to the minimax criterion amount to either conditioning or simply ignoring the information. Finally, we consider the relationship between conditioning and calibration when uncertainty is described by sets of probabilities.

Computer model of a "sense of humour" suggested previously [arXiv:0711.2058, 0711.2061, 0711.2270] is raised to the level of a realistic algorithm.

Support Vector Machines (SVMs) are a relatively new supervised classification technique to the land cover mapping community. They have their roots in Statistical Learning Theory and have gained prominence because they are robust, accurate and are effective even when using a small training sample. By their nature SVMs are essentially binary classifiers, however, they can be adopted to handle the multiple classification tasks common in remote sensing studies. The two approaches commonly used are the One-Against-One (1A1) and One-Against-All (1AA) techniques. In this paper, these approaches are evaluated in as far as their impact and implication for land cover mapping. The main finding from this research is that whereas the 1AA technique is more predisposed to yielding unclassified and mixed pixels, the resulting classification accuracy is not significantly different from 1A1 approach. It is the authors conclusion therefore that ultimately the choice of technique adopted boils down to personal preference and the uniqueness of the dataset at hand.

A computer model of "a sense of humour" suggested previously [arXiv:0711.2058,0711.2061], relating the humorous effect with a specific malfunction in information processing, is given in somewhat different exposition. Psychological aspects of humour are elaborated more thoroughly. The mechanism of laughter is formulated on the more general level. Detailed discussion is presented for the higher levels of information processing, which are responsible for a perception of complex samples of humour. Development of a sense of humour in the process of evolution is discussed.

The computer realization of a "sense of humour" requires the creation of an algorithm for solving the "linguistic problem", i.e. the problem of recognizing a continuous sequence of polysemantic images. Such algorithm may be realized in the Hopfield model of a neural network after its proper modification.

A computer model of a "sense of humour" is proposed. The humorous effect is interpreted as a specific malfunction in the course of information processing due to the need for the rapid deletion of the false version transmitted into consciousness. The biological function of a sense of humour consists in speeding up the bringing of information into consciousness and in fuller use of the resources of the brain.

Building rules on top of ontologies is the ultimate goal of the logical layer of the Semantic Web. To this aim an ad-hoc mark-up language for this layer is currently under discussion. It is intended to follow the tradition of hybrid knowledge representation and reasoning systems such as $\mathcal{AL}$-log that integrates the description logic $\mathcal{ALC}$ and the function-free Horn clausal language \textsc{Datalog}. In this paper we consider the problem of automating the acquisition of these rules for the Semantic Web. We propose a general framework for rule induction that adopts the methodological apparatus of Inductive Logic Programming and relies on the expressive and deductive power of $\mathcal{AL}$-log. The framework is valid whatever the scope of induction (description vs. prediction) is. Yet, for illustrative purposes, we also discuss an instantiation of the framework which aims at description and turns out to be useful in Ontology Refinement. Keywords: Inductive Logic Programming, Hybrid Knowledge Representation and Reasoning Systems, Ontologies, Semantic Web. Note: To appear in Theory and Practice of Logic Programming (TPLP)

Probabilistic graphical models (PGMs) have become a popular tool for computational analysis of biological data in a variety of domains. But, what exactly are they and how do they work? How can we use PGMs to discover patterns that are biologically relevant? And to what extent can PGMs help us formulate new hypotheses that are testable at the bench? This note sketches out some answers and illustrates the main ideas behind the statistical approach to biological pattern discovery.

Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse principal component analysis and has a wide array of applications in machine learning and engineering. We formulate a new semidefinite relaxation to this problem and derive a greedy algorithm that computes a full set of good solutions for all target numbers of non zero coefficients, with total complexity O(n^3), where n is the number of variables. We then use the same relaxation to derive sufficient conditions for global optimality of a solution, which can be tested in O(n^3) per pattern. We discuss applications in subset selection and sparse recovery and show on artificial examples and biological data that our algorithm does provide globally optimal solutions in many cases.