In epistemic logic, some axioms dealing with the notion of knowledge are rather convoluted and it is difficult to give them an intuitive interpretation, even if some of them, like .2 and .4, are considered by some epistemic logicians to be key axioms. We show that they can be characterized in terms of understandable interaction axioms relating knowledge and belief. In order to show it, we first present a theory dealing with the characterization of axioms in terms of interaction axioms in modal logic. We then apply the main results and methods of this theory to obtain our results related to epistemic logic.

We propose the Probabilistic Sentential Decision Diagram (PSDD): A complete and canonical representation of probability distributions defined over the models of a given propositional theory. Each parameter of a PSDD can be viewed as the (conditional) probability of making a decision in a corresponding Sentential Decision Diagram (SDD). The SDD itself is a recently proposed complete and canonical representation of propositional theories. We explore a number of interesting properties of PSDDs, including the independencies that underlie them. We show that the PSDD is a tractable representation. We further show how the parameters of a PSDD can be efficiently estimated, in closed form, from complete data. We empirically evaluate the quality of PSDDs learned from data, when we have knowledge, a priori, of the domain logical constraints.

This paper presents Tweety, an open source project for scientific experimentation on logical aspects of artificial intelligence and particularly knowledge representation. Tweety provides a general framework for implementing and testing knowledge representation formalisms in a way that is familiar to researchers used to logical formalizations. This framework is very general, widely applicable, and can be used to implement a variety of knowledge representation formalisms from classical logics, over logic programming and computational models for argumentation, to probabilistic modeling approaches. Tweety already contains over 15 different knowledge representation formalisms and allows easy computation of examples, comparison of algorithms and approaches, and benchmark tests. This paper gives an overview on the technical architecture of Tweety and a description of its different libraries. We also provide two case studies that show how Tweety can be used for empirical evaluation of different problems in artificial intelligence.

The invited talks presented at the Fourteenth International Conference on Principles of Knowledge Representation and Reasoning included Ontology-Based Monitoring of Dynamic Systems by Franz Baader, Knowledge Representation Meets Computer Vision: From Pixels to Symbolic Activity Descriptions by Tony Cohn, Datalog+/–: Questions and Answers by Georg Gottlob, and Situation Calculus: The Last 15 Years by Sheila McIlraith.

In this paper we present a tableau-based method to decide the satisfiability of formulas in ATEL, an extension of the alternating-time temporal logic ATL including epistemic modalities for individual knowledge. Specifically, we analyse satisfiability of ATEL formulas under a number of conditions. We evaluate the assumptions of synchronicity and of a unique initial state, which have been proposed in the context of Interpreted Systems. Also, we consider satisfiability at an initial state as opposed to any state in the system. We introduce a tableau-based decision procedure for each of these combinations. Moreover, we adopt an agent-based approach to satisfiability, namely, the decision procedure returns a set of agents inducing a concurrent game structure that satisfies the relevant specification.

Belief revision is an operation that aims at modifying old beliefs so that they become consistent with new ones. The issue of belief revision has been studied in various formalisms, in particular, in qualitative algebras (QAs) in which the result is a disjunction of belief bases that is not necessarily representable in a QA. This motivates the study of belief revision in formalisms extending QAs, namely, their propositional closures: in such a closure, the result of belief revision belongs to the formalism. Moreover, this makes it possible to define a contraction operator thanks to the Harper identity. Belief revision in the propositional closure of QAs is studied, an algorithm for a family of revision operators is designed, and an open-source implementation is made freely available on the web.

We study learning of description logic TBoxes in Angluin et al.’s framework of exact learning via queries. We admit entailment queries (“is a given subsumption entailed by the target TBox?”) and equivalence queries (“is a given TBox equivalent to the target TBox?”), assuming that the signature and logic of the target TBox are known. We present three main results: (1) TBoxes formulated in DL-Lite with role inclusions and composite concepts on the right-hand side of concept inclusions can be learned in polynomial time; (2) EL TBoxes with only concept names on the right-hand side of concept inclusions can be learned in polynomial time; and (3) EL TBoxes cannot be learned in polynomial time. It follows that non-polynomial time learnability of EL TBoxes is caused by the interaction between existential restrictions on the right and left-hand sides of concept inclusions. We also show that neither entailment nor equivalence queries alone are sufficient in cases (1) and (2) above.

Golog and ConGolog are languages defined in the situation calculus for cognitive robotics. Given a Golog program \delta, its semantics is defined by a macro Do(\delta,s,s') that expands to a logical sentence that captures the conditions under which performing \delta in s can terminate in s'. A similarmacro is defined for ConGolog programs. In general, the logical sentences that these macros expand to are second-order, and in the case of ConGolog, may involve quantification over programs. In this paper, we show that by making use of the foundational axioms in the situation calculus, in particular, the second-order closure axiom about the space of situations, these macro expressions can actually be defined using first-order sentences.

Given a set of conflicting arguments, there can exist multiple plausible opinions about which arguments should be accepted, rejected, or deemed undecided. Recent work explored some operators for deciding how multiple such judgments should be aggregated. Here, we generalize this line of study by introducing a family of operators called interval aggregation methods , which contain existing operators as instances. While these methods fail to output a complete labelling in general, we show that it is possible to transform a given aggregation method into one that does always yield collectively rational labellings. This employs the down-admissible and up-complete constructions of Caminada and Pigozzi. For interval methods, collective rationality is attained at the expense of a strong Independence postulate, but we show that an interesting weakening of the Independence postulate is retained.

We propose a model of belief and intention change over the course of a dialogue, in the case where the decisions taken during the dialogue affect the possibly conflicting goals of the agents involved. We use Situation Calculus to model the evolution of the world and an observation model to analyze the evolution of intentions and beliefs. In our formalization, utterances, that only change the beliefs and intentions, are observations. We illustrate our formalization with the game of Werewolf.