Description Logics (DLs) are knowledge representation formalisms that provide, for example, the logical underpinning of the W3C OWL standards. Conjunctive queries (CQs), the standard query language in databases, have recently gained significant attention for querying DL knowledge bases. Several different techniques are available for a wide range of DLs. Nevertheless, for OWL 1 DL and OWL 2 DL, decidability of CQ entailment is an open problem. So far, the combination of nominals, inverse roles, and number restrictions caused unsolvable problems. We tackle this problem and present a decidability result for entailment of unions of CQs in a DL with all three problematic constructors. For queries with only simple roles, our result also shows decidability in the logic that underpins OWL 1 DL and we believe that the presented results will pave the way for further progress towards CQ entailment decision procedures for OWL.

There is currently a growing interest in techniques for hiding parts of the signature of an ontology Kh that is being reused by another ontology Kv. Towards this goal, Cuenca Grau, Motik, and Kazakov (2009) recently proposed the import-by-query framework, which makes the content of Kh accessible through a limited query interface. If Kv reuses the symbols from Kh in a certain restricted way, one can reason over Kv U Kh by accessing only Kv and the query interface. In this paper, we map out the landscape of the import-by-query problem. We show that certain restrictions of our original framework are strictly necessary to make reasoning possible, we propose extensions that overcome some of the expressivity limitations, we present several novel reasoning algorithms, and we outline the limitations of the new framework.

This paper proves that validity and satisfiability of assertions in the Fuzzy Description Logic based on infinite-valued Product Logic with universal and existential quantifiers (which are non-interdefinable) is decidable when we only consider quasi-witnessed interpretations. We prove that this restriction is neither necessary for the validity problem (i.e., the validity of assertions in the Fuzzy Description Logic based on infinite-valued Product Logic is decidable) nor for the positive satisfiability problem, because quasi-witnessed interpretations are particularly adequate for the infinite-valued Product Logic. We give an algorithm that reduces the problem of validity (and satisfiability) of assertions in our Fuzzy Description Logic (restricted to quasi-witnessed interpretations) to a semantic consequence problem, with finite number of hypothesis, on infinite-valued propositional Product Logic.

Ontologies can be used to provide an enriched vocabulary for the formulation of queries over instance data. We identify query emptiness and predicate emptiness as two central reasoning services in this context. Query emptiness asks whether a given query has an empty answer over all data sets formulated in a given signature. Predicate emptiness is defined analogously, but quantifies universally over all queries that contain a given predicate. In this paper, we determine the computational complexity of query emptiness and predicate emptiness in the EL, DL-Lite, and ALC-families of description logics, investigate the connection to ontology modules, and perform a practical case study to evaluate the new reasoning services.

Computation plays a major role in decision making.  Even if an agent is willing to ascribe a probability to all states and a utility to all outcomes, and maximize expected utility, doing so might present serious computational problems.  Moreover, computing the outcome of a given act might be difficult.  In a companion paper we develop a framework for game theory  with costly computation, where the objects of choice are Turing machines.  Here we apply that framework to decision theory.  We show how well-known phenomena like first-impression-matters biases (i.e., people tend to put more weight on evidence they hear early on), belief polarization (two people with different prior beliefs, hearing the same evidence, can end up with diametrically opposed conclusions), and the status quo bias (people are much more likely to stick with what they already have) can be easily captured in that framework.  Finally, we use the framework  to define so me new notions: value of computational information (a computational variant of value of information ) and computational value of conversation .

In this paper we present a model for decision making under complete ignorance. By complete ignorance it is meant that all that is known is the set of possible consequences associated to each action. Especially there is no set of states that can be enumerated in order to compare actions. We give two natural axioms for rational decision making under complete ignorance. We show that the optimality criteria satisfying these two axioms are the ones which consider only the extremal consequences of actions. We compare our axioms with related ones from the literature.

Improvement operators is a class of belief change operators that is a generalization of the usual class of iterated belief revision operators. The idea is to relax the success property, so the new information is not necessarily believed after the improvement, but to ensure that its plausibility has increased in the epistemic state. In this paper we explore this large classby defining several different subclasses. In particular, as minimal change is a hallmark of belief change, we study what are the operators that produce the minimal change among several subclasses.

Galles and Pearl [1998] claimed that ``for recursive models, the causal model framework does not add any restrictions to counterfactuals, beyond those imposed by Lewis's [possible-worlds] framework.''  This claim is shown to be false.  Indeed, the opposite claim is true: recursive models are shown to correspond precisely to a subclass of (possible-world) counterfactual structures.  On the other hand, a slight generalization of recursive models, models where all equations have unique solutions, is shown to be incomparable in expressive power to counterfactual structures, despite the fact that the Galles and Pearl arguments should apply to them as well.  The problem with the Galles and Pearl argument is identified: an axiom that they viewed as irrelevant, because it involved disjunction (which was not in their language), is not irrelevant at all. 

Dynamic epistemic logic deals with the representation of situations in a multi-agent and dynamic setting. It allows to express in a uniform way statements about: 1. what is true about an initial situation 2. what is true about an event occurring in this situation 3. what is true about the resulting situation after the event has occurred. We axiomatize in this framework what we can infer about (3) given (1) and (2), introducing thereby new techniques to prove completeness. We also show that this axiomatization is decidable. Besides being useful for reasoning about actions, it provides a natural characterization of the product update of dynamic epistemic logic.

Since argumentation is an inherently dynamic process, it is of great importance to understand the effect of incorporating new information into given argumentation frameworks. In this work, we address this issue by analyzing equivalence between argumentation frameworks under the assumption that the frameworks in question are incomplete, i.e. further information might be added later to both frameworks simultaneously. In other words, instead of the standard notion of equivalence (which holds between two frameworks, if they possess the same extensions), we require here that frameworks F and G are also equivalent when conjoined with any further framework H. Due to the nonmonotonicity of argumentation semantics, this concept is different to (but obviously implies) the standard notion of equivalence. We thus call our new notion strong equivalence and study how strong equivalence can be decided with respect to the most important semantics for abstract argumentation frameworks. We also consider variants of strong equivalence in which we define equivalence with respect to the sets of arguments credulously (or skeptically) accepted, and restrict strong equivalence to augmentations H where no new arguments are raised.