we elaborate on logic-based automated reasoning techniques for abduction, driven by the principle of goal-oriented reasoning. In the first part we develop two variants of a computational framework for abduction in propositional logic, based on regular connection tableaux and resolution with set-of-support. The procedures are proven to be sound and complete calculi for finding consistent, minimal and relevant solutions to abductive problems. In the second part we adapt the framework to the Description Logic ALC. We obtain a procedure for solving ABox abduction problems (i.e. abductive problems whose main part of the input and every solution are specified by a set of ABox assertions), for which we prove the results of (plain) soundness and (minimality) completeness. Contents

‘Possible worlds semantics’ for modal logic is a widely used term, sometimes with ominous metaphysical connotations, but what does this style of modeling involve today? We discuss three main issues, using epistemic logic as a running example, and drawing upon both mathematical results and practices in the expertise of working researchers. Our first question is a foundational one: how does one associate a type of model with a language, and what considerations affect that choice? Our focus is on invariance and definability results, familiar from the mathematical and computational tradition, though less so in philosophy. The second question is less deep, but maybe even more challenging in practice: once we have chosen a type of models for a language, how does one select and then maintain models appropriate to concrete scenarios of application? While there is a lot of ‘art’ to this in the literature, there is very little ‘science’ of model construction for modal logics. We show how this works in dynamic epistemic logics, and identify some current challenges for a true ‘modeling theory’ as opposed to the more abstract usual ‘model theory’. Finally, we discuss the pervasive tension between ‘thin’ and ‘thick ’ worlds in modal logic, using examples from game theory, and pointing out how the contrast can be made fruitful.

In this paper we study the expressive power and definability for (extended) modal languages interpreted on topological spaces. We provide topological analogues of the van Benthem characterization theorem and the Goldblatt-Thomason definability theorem in terms of the well established first-order topological language Lt.

The present paper applies well-investigated modal logics to provide formal foundations to specific fragments of argumentation theory. This logic-driven analysis of argumentation allows: first, to systematize several results of argumentation theory reformulating them within suitable formal languages; second, to import several techniques (calculi, model-checking, evaluation games, bisimulation games); third, to import results (eminently completeness of axiomatizations, and complexity of model-checking) from modal logic to argumentation theory.

Abstract Due to the growing popularity of Description Logics-based knowledge representation systems, predominantly in the context of Semantic Web applications, there is a rising demand for tools offering non-standard reasoning services. One particularly interesting form of reasoning, both from the user as well as the ontology engineering perspective, is abduction. In this paper we introduce two novel reasoning calculi for solving ABox abduction problems in the Description Logic ALC, i.e. problems of finding minimal sets of ABox axioms, which when added to the knowledge base enforce entailment of a requested set of assertions. The algorithms are based on regular connection tableaux and resolution with set-of-support and are proven to be sound and complete. We elaborate on a number of technical issues involved and discuss some practical aspects of reasoning with the methods.

2. Games as models for modal process logics 6 3. Preference structure and more realistic games 9

In the last few years, preference logic and in particular, the dynamic logic of preference change, has suddenly become a live topic in my Amsterdam and Stanford environments. At the request of the editors, this article explains how this interest came about, and what is happening. I mainly present a story around some recent dissertations and papers, which are found in the references. There is no pretense at complete coverage of preference logic (for that, see Hansson 2001) or even of preference change (Hansson 1995). 1 Logical dynamics of agency Agency, information, and preference Human agents acquire and transform information in different ways: they observe, or infer by themselves, and often also, they ask someone else. Traditional philosophical logics describe part of this behaviour, the ‘static’ properties produced by such actions: in particular, agents ’ knowledge and belief at some given moment. But rational human activity is goal-driven, and hence we also need to describe agents ’ evaluation of different states of the world, or of outcomes of their actions. Here is where preference logic has come to describe what agents prefer, while

In description logic (DL), ABoxes are used for describing the state of affairs in an application domain. We consider the problem of updating ABoxes when the state changes, assuming that update information is described at an atomic level, i.e., in terms of possibly negated ABox assertions that involve only atomic concepts and roles. We analyze such basic ABox updates in several standard DLs, in particular addressing questions of expressibility and succinctness: can updated ABoxes always be expressed in the DL in which the original ABox was formulated and, if so, what is the size of the updated ABox? It turns out that DLs have to include nominals and the ‘@ ’ constructor of hybrid logic for updated ABoxes to be expressible, and that this still holds when updated ABoxes are approximated. Moreover, the size of updated ABoxes is exponential in the role depth of the original ABox and the size of the update. We also show that this situation improves when updated ABoxes are allowed to contain additional auxiliary symbols. Then, DLs only need to include nominals for updated ABoxes to exist, and the size of updated ABoxes is polynomial in the size of both the original ABox and the update. Keywords: Description Logics, ABoxes, Updates