This papers develops a logical language for representing probabilistic causal laws. Our interest in such a language is twofold. First, it can be motivated as a fundamental study of the representation of causal knowledge. Causality has an inherent dynamic aspect, which has been studied at the semantical level by Shafer in his framework of probability trees. In such a dynamic context, where the evolution of a domain over time is considered, the idea of a causal law as something which guides this evolution is quite natural. In our formalization, a set of probabilistic causal laws can be used to represent a class of probability trees in a concise, flexible and modular way. In this way, our work extends Shafer's by offering a convenient logical representation for his semantical objects. Second, this language also has relevance for the area of probabilistic logic programming. In particular, we prove that the formal semantics of a theory in our language can be equivalently defined as a probability distribution over the well-founded models of certain logic programs, rendering it formally quite similar to existing languages such as ICL or PRISM. Because we can motivate and explain our language in a completely self-contained way as a representation of probabilistic causal laws, this provides a new way of explaining the intuitions behind such probabilistic logic programs: we can say precisely which knowledge such a program expresses, in terms that are equally understandable by a non-logician. Moreover, we also obtain an additional piece of knowledge representation methodology for probabilistic logic programs, by showing how they can express probabilistic causal laws.

Semantic web services (SWS) are self-contained, self-describing, semantically marked-up software resources that can be published, discovered, composed and executed across the Web in a semi-automatic way. They are a key component of the future Semantic Web, in which networked computer programs become providers and users of information at the same time. This work focuses on developing a full-life-cycle software toolset for creating and maintaining Semantic Web Services (SWSs) based on the Web Service Modelling Ontology (WSMO) framework. A main part of WSMO-based SWS is service capability - a declarative description of Web service functionality. A formal syntax and semantics for such a description is provided by Web Service Modeling Language (WSML), which is based on different logical formalisms, namely, Description Logics, First-Order Logic and Logic Programming. A WSML description of a Web service capability is represented as a set of complex logical expressions (axioms). We develop a specialized user-friendly tool for constructing and editing WSMO-based SWS capabilities. Since the users of this tool are not specialists in first-order logic, a graphical way for constricting and editing axioms is proposed. The designed process for constructing logical expressions is ontology-driven, which abstracts away as much as possible from any concrete syntax of logical language. We propose several mechanisms to guarantees the semantic consistency of the produced logical expressions. The tool is implemented in Java using Eclipse for IDE and GEF (Graphical Editing Framework) for visualization.

The theme of this article is the dynamics of evolution of agents. That theme is applied to the evolution of constraint satisfaction, of agents themselves, of our models of agents, of artificial intelligence and, finally, of the Association for the Advancement of Artificial Intelligence (AAAI). The overall thesis is that constraint satisfaction is central to proactive and responsive intelligent behavior.

Human-computer interaction (HCI) is the interdisciplinary study of interaction between people (users) and computers. Its main goal is making computers more user-friendly and easier to use. HCI is concerned with methodologies and processes for designing interfaces, with methods for implementing interfaces, with techniques for evaluating and comparing interfaces, with developing new interfaces and interaction techniques and with developing descriptive and predictive models and theories of interaction [9]. More often than not, user interfaces for theorem provers are developed as a mere add-on to the main proving engine. The result is an interaction design suitable for proof experts only.

The management and combination of uncertain, imprecise, fuzzy and even paradoxical or high conflicting sources of information has always been, and still remains today, of primal importance for the development of reliable modern information systems involving artificial reasoning. The combination (fusion) of information arises in many fields of applications nowadays (especially in defense, medicine, finance, geo-science, economy, etc). When several sensors, observers or experts have to be combined together to solve a problem, or if one wants to update our current estimation of solutions for a given problem with some new information available, we need powerful and solid mathematical tools for the fusion, specially when the information one has to deal with is imprecise and uncertain. In this paper, we present a survey of our recent theory of plausible and paradoxical reasoning, known as Dezert-Smarandache Theory (DSmT) in the literature, developed for dealing with imprecise, uncertain and conflicting sources of information. Recent publications have shown the interest and the ability of DSmT to solve problems where other approaches fail, especially when conflict between sources becomes high. We focus this presentation rather on the foundations of DSmT, and on the main important rules of combination, than on browsing specific applications of DSmT available in literature. Several simple examples are given throughout the presentation to show the efficiency and the generality of DSmT.

In this paper, we investigate the deductive inference for the interiors and exteriors of Horn knowledge bases, where the interiors and exteriors were introduced by Makino and Ibaraki to study stability properties of knowledge bases. We present a linear time algorithm for the deduction for the interiors and show that it is co-NP-complete for the deduction for the exteriors. Under model-based representation, we show that the deduction problem for interiors is NP-complete while the one for exteriors is co-NP-complete. As for Horn envelopes of the exteriors, we show that it is linearly solvable under model-based representation, while it is co-NP-complete under formula-based representation. We also discuss the polynomially solvable cases for all the intractable problems.

We investigate cut-elimination and cut-simulation in impredicative (higher-order) logics. We illustrate that adding simple axioms such as Leibniz equations to a calculus for an impredicative logic -- in our case a sequent calculus for classical type theory -- is like adding cut. The phenomenon equally applies to prominent axioms like Boolean- and functional extensionality, induction, choice, and description. This calls for the development of calculi where these principles are built-in instead of being treated axiomatically.

The paper organizes as follows: After explaining the technical terms of the title in § 1 and the remaining basic notions in § 2, we start to explicate the differences between our two versions of calculi in§ 3. The weak version is explained in § 4. The changes necessary for the strong version in order to admit liberalization of the δ-rule are explained in § 5. After concluding in § 6 we append all the proofs, references, and notes.

We study the combination of the following already known ideas for showing confluence of unconditional or conditional term rewriting systems into practically more useful confluence criteria for conditional systems: Our syntactical separation into constructor and non-constructor symbols, Huet's introduction and Toyama's generalization of parallel closedness for non-noetherian unconditional systems, the use of shallow confluence for proving confluence of noetherian and non-noetherian conditional systems, the idea that certain kinds of limited confluence can be assumed for checking the fulfilledness or infeasibility of the conditions of conditional critical pairs, and the idea that (when termination is given) only prime superpositions have to be considered and certain normalization restrictions can be applied for the substitutions fulfilling the conditions of conditional critical pairs. Besides combining and improving already known methods, we present the following new ideas and results: We strengthen the criterion for overlay joinable noetherian systems, and, by using the expressiveness of our syntactical separation into constructor and non-constructor symbols, we are able to present criteria for level confluence that are not criteria for shallow confluence actually and also able to weaken the severe requirement of normality (stiffened with left-linearity) in the criteria for shallow confluence of noetherian and non-noetherian conditional systems to the easily satisfied requirement of quasi-normality. Finally, the whole paper may also give a practically useful overview of the syntactical means for showing confluence of conditional term rewriting systems.

Using a human-oriented formal example proof of the (lim+) theorem, i.e. that the sum of limits is the limit of the sum, which is of value for reference on its own, we exhibit a non-permutability of beta-steps and delta+-steps (according to Smullyan's classification), which is not visible with non-liberalized delta-rules and not serious with further liberalized delta-rules, such as the delta++-rule. Besides a careful presentation of the search for a proof of (lim+) with several pedagogical intentions, the main subject is to explain why the order of beta-steps plays such a practically important role in some calculi.