We characterize the expressive power of description logic (DL) TBoxes, both for expressive DLs such as ALC and ALCQIO and lightweight DLs such as DL-Lite and EL. Our characterizations are relative to first-order logic, based on a wide range of semantic notions such as bisimulation, equisimulation, disjoint union, and direct product. We exemplify the use of the characterizations by a first study of the following novel family of decision problems: given a TBox T formulated in one DL, decide whether T can be equivalently rewritten as a TBox in der fragment L' of L.

In a seminal paper, Lin and Reiter introduced the notion of progression for basic action theories in the situation calculus. Earlier works by Moore, Scherl and Levesque extended the situation calculus to account for knowledge. In this paper, we study progression of knowledge in the situation calculus. We first adapt the concept of bisimulation from modal logic and extend Lin and Reiter's notion of progression to accommodate knowledge. We show that for physical actions, progression of knowledge reduces to forgetting predicates in first-order modal logic. We identify a class of first-order modal formulas for which forgetting an atom is definable in first-order modal logic. This class of formulas goes beyond formulas without quantifying-in. We also identify a simple case where forgetting a predicate reduces to forgetting a finite number of atoms. Thus we are able to show that for local-effect physical actions, when the initial KB is a formula in this class, progression of knowledge is definable in first-order modal logic. Finally, we extend our results to the multi-agent case.

The ability to predict, or at least recognize, the state of the world that an action brings about, is a central feature of autonomous agents. We propose, herein, a formal framework within which we investigate whether this ability can be autonomously learned. The framework makes explicit certain premises that we contend are central in such a learning task: (i) slow sensors may prevent the sensing of an action's direct effects during learning; (ii) predictions need to be made reliably in future and novel situations. We initiate in this work a thorough investigation of the conditions under which learning is or is not feasible. Despite the very strong negative learnability results that we obtain, we also identify interesting special cases where learning is feasible and useful.

As a doxastic counterpart to epistemic logic based on S5 we study the modal logic KSD that can be viewed as an approach to modelling a kind of objective and fair belief. We apply KSD to the problem of minimal belief and develop an alterna- tive approach to nonmonotonic modal logic using a weaker concept of expansion. This corresponds to a certain minimal kind of KSD model and yields a new type of nonmonotonic doxastic reasonin

We solve constraint satisfaction problems through translation to answer set programming (ASP). Our reformulations have the property that unit-propagation in the ASP solver achieves well defined local consistency properties like arc, bound and range consistency. Experiments demonstrate the computational value of this approach.

This paper presents an algorithm of adaptation for a case-based reasoning system with cases and domain knowledge represented in the expressive description logic ALC. The principle is to first pretend that the source case to be adapted solves the current target case. This may raise some contradictions with the specification of the target case and with the domain knowledge. The adaptation consists then in repairing these contradictions. This adaptation algorithm is based on an extension of the classical tableau method used for deductive inferences in ALC.

Binary aggregation studies problems in which individuals express yes/no choices over a number of possibly correlated issues, and these individual choices need to be aggregated into a collective choice. We show how several classical frameworks of Social Choice Theory, particularly preference and judgment aggregation, can be viewed as binary aggregation problems by designing an appropriate set of integrity constraints for each specific setting. We explore the generality of this framework, showing that it makes available useful techniques both to prove theoretical results, such as a new impossibility theorem in preference aggregation, and to analyse practical problems, such as the characterisation of safe agendas in judgment aggregation in a syntactic way. The framework also allows us to formulate a general definition of paradox that is independent of the domain under consideration, which gives rise to the study of the class of aggregation procedures of generalised dictatorships.

Machine learning is traditionally formalized and researched as the study of learning concepts and decision functions from labeled examples, requiring a representation that encodes information about the domain of the decision function to be learned. We are interested in providing a way for a human teacher to interact with an automated learner using natural instructions, thus allowing the teacher to communicate the relevant domain expertise to the learner without necessarily knowing anything about the internal representations used in the learning process. In this paper we suggest to view the process of learning a decision function as a natural language lesson interpretation problem instead of learning from labeled examples. This interpretation of machine learning is motivated by human learning processes, in which the learner is given a lesson describing the target concept directly, and a few instances exemplifying it. We introduce a learning algorithm for the lesson interpretation problem that gets feedback from its performance on the final task, while learning jointly (1) how to interpret the lesson and (2) how to use this interpretation to do well on the final task. his approach alleviates the supervision burden of traditional machine learning by focusing on supplying the learner with only human-level task expertise for learning. We evaluate our approach by applying it to the rules of the Freecell solitaire card game. We show that our learning approach can eventually use natural language instructions to learn the target concept and play the game legally. Furthermore, we show that the learned semantic interpreter also generalizes to previously unseen instructions.

Research in AI has built upon the tools and techniques of many different disciplines, including formal logic, probability theory, decision theory, management science, linguistics and philosophy. However, the application of these disciplines in AI has necessitated the development of many enhancements and extensions. Among the most powerful of these are the methods of computational logic. I will argue that computational logic, embedded in an agent cycle, combines and improves upon both traditional logic and classical decision theory. I will also argue that many of its methods can be used, not only in AI, but also in ordinary life, to help people improve their own human intelligence without the assistance of computers.

We show how Finite Model Computation (FMC) of first-order theories can efficiently and transparentlybe solved by taking advantage of an extension of Answer Set Programming, called incremental Answer Set Programming (iASP). The idea is to use the incremental parameter in iASP programs to account for the domain size of a model. The FMC problem is then successively addressed for increasing domain sizes until an answer set, representing a finite model of the original first-order theory, is found. We developed a system based on the iASP solver iClingo and demonstrate its competitiveness.