In order to meet usability requirements, most logic-based applications provide explanation facilities for reasoning services. This holds also for DLs, where research has focused on the explanation of both TBox reasoning and, more recently, query answering. Besides explaining the presence of a tuple in a query answer, it is important to explain also why a given tuple is missing. We address the latter problem for (conjunctive) query answering over DL-Lite ontologies, by adopting abductive reasoning, that is, we look for additions to the ABox that force a given tuple to be in the result. As reasoning taskswe consider existence and recognition of an explanation, and relevance and necessity of a certain assertion for an explanation. We characterize the computational complexity of these problems for subset minimal and cardinality minimal explanations.

Answering conjunctive queries (CQs) over a set of facts extended with existential rules is a key problem in knowledge representation and databases. This problem can be solved using the chase (aka materialisation) algorithm; however, CQ answering is undecidable for general existential rules, so the chase is not guaranteed to terminate. Several acyclicity conditions provide sufficient conditions for chase termination. In this paper, we present two novel such conditions—model-faithful acyclicity (MFA) and model-summarising acyclicity (MSA)—that generalise many of the acyclicity conditions known so far in the literature. Materialisation provides the basis for several widely-used OWL 2 DL reasoners. In order to avoid termination problems, many of these systems handle only the OWL 2 RL profile of OWL 2 DL; furthermore, some systems go beyond OWL 2 RL, but they provide no termination guarantees. In this paper we investigate whether various acyclicity conditions can provide a principled and practical solution to these problems. On the theoretical side, we show that query answering for acyclic ontologies is of lower complexity than for general ontologies. On the practical side, we show that many of the commonly used OWL 2 DL ontologies are MSA, and that the facts obtained via materialisation are not too large. Thus, our results suggest that principled extensions to materialisationbased OWL 2 DL reasoners may be practically feasible.

Existing methods for dealing with knowledge updates differ greatly depending on the underlying knowledge representation formalism. When Classical Logic is used, update operators are typically based on manipulating the knowledge base on the model-theoretic level. On the opposite side of the spectrum stand the semantics for updating Answer-Set Programs where most approaches need to rely on rule syntax. Yet, a unifying perspective that could embrace all these approaches is of great importance as it enables a deeper understanding of all involved methods and principles and creates room for their cross-fertilisation, ripening and further development. This paper bridges these seemingly irreconcilable approaches to updates. It introduces a novel monotonic characterisation of rules, dubbed \emph{\RE-models}, and shows it to be a more suitable semantic foundation for rule updates than \SE-models. A generic framework for defining semantic rule update operators is then proposed. It is based on the idea of viewing a program as the \emph{set of sets of \RE-models} of its rules; updates are performed by introducing additional interpretations to the sets of \RE-models of rules in the original program. It is shown that particular instances of the framework are closely related to both belief update principles and traditional approaches to rule updates and enjoy a range of plausible syntactic as well as semantic properties.

Given a 4-tuple of Boolean variables (a, b, c, d), logical proportions are modeled by a pair of equivalences relating similarity indicators (a ∧ b and a ∧ b), or dissimilarity indicators (a ∧ b and a ∧ b) pertaining to the pair (a, b), to the ones associated with the pair (c, d). Logical proportions are homogeneous when they are based on equivalences between indicators of the same kind. There are only 4 such homogeneous proportions, which respectively express that i) “a differs from b as c differs from d” (and “b differs from a as d differs from c”), ii) “a differs from b as d differs from c” (and “b differs from a as c differs from d”), iii) “what a and b have in common c and d have it also”, iv) “what a and b have in common neither c nor d have it”. We prove that each of these proportions is the unique Boolean formula (up to equivalence) that satisfies groups of remarkable properties including a stability property w.r.t. a specific permutation of the terms of the proportion. The first one (i) is shown to be the only one to satisfy the standard postulates of an analogical proportion. The paper also studies how two analogical proportions can be combined into a new one. We then examine how homogeneous proportions can be used for diverse prediction tasks. We particularly focus on the completion of analogical-like series, and on missing value abduction problems. Finally, the paper compares our approach with other existing works on qualitative prediction based on ideas of betweenness, or of matrix abduction.

Fuzzy description logics (DLs) have been investigated for over two decades, due to their capacity to formalize and reason with imprecise concepts. Very recently, it has been shown that for several fuzzy DLs, reasoning becomes undecidable. Although the proofs of these results differ in the details of each specific logic considered, they are all based on the same basic idea. In this paper, we formalize this idea and provide sufficient conditions for proving undecidability of a fuzzy DL. We demonstrate the effectiveness of our approach by strengthening all previously-known undecidability results and providing new ones. In particular, we show that undecidability may arise even if only crisp axioms are considered.

Answering queries in information systems that allow for ex- pressive inferencing is currently a field of intense research. This problem is often referred to as ontology-based data ac- cess (OBDA). We focus on conjunctive query entailment un- der logical rules known as tuple-generating dependencies, existential rules or Datalog+/-. One of the most expressive decidable classes of existential rules known today is that of greedy bounded treewidth sets (gbts). We propose an algo- rithm for this class, which is worst-case optimal for data and combined complexities, with or without bound on the pred- icate arity. A beneficial feature of this algorithm is that it allows for separation between offline and online processing steps: the knowledge base can be compiled independently from queries, which are evaluated against the compiled form. Moreover, very simple adaptations of the algorithm lead to worst-case-optimal complexities for specific subclasses of gbts which have lower complexities, such as guarded rules.

Fixpoints play a key role in the mathematical set up of abstract argumentation theory but, we argue, have been relatively underexamined in the literature. The paper studies the logical structure underlying the computation via approximation sequences of the sort of fixpoints relevant in argumentation. Concretely, it presents a number of novel results on the fixed point theory underpinning the main Dung's semantics and, inspired by recent literature on the logical analysis of equilibrium computation in games, it provides a characterization of those semantics in terms of iterated model updates.

Workshop on Knowledge-Intensive Business (KR&R) has long been a vibrant and exciting Processes (KiBP 2012). It has emerged from 256 registered abstracts. It was significantly more an understanding of how to store, retrieve, and interact than the 161 submissions to KR 2002, but somewhat with knowledge, and at the development of fewer than the record set at KR 2008 of 251 submissions. John McCarthy, recognized tasks such as planning, diagnosis, argumentation, by many as the founder of AI and KR, passed away and belief revision. KR 2012 will pay tribute to John gathering for researchers working on different aspects through an invited lecture by Leora Morgenstern of KR&R, and fosters communication, crossfertilization entitled "rough the Lens of Drosophila: John Mc-of ideas, and collaboration across research Carthy's Quest for Human-Level Artificial Intelligence."

Belief change studies how to update knowledge bases used for reasoning. Traditionally belief revision has been based on full propositional logic. However, reasoning with full propositional knowledge bases is computationally hard, whereas reasoning with Horn knowledge bases is fast. In the past several years, there has been considerable work in belief revision theory on developing a theory of belief contraction for knowledge represented in Horn form. Our main focus here is the computational complexity of belief contraction, and, in particular, of various methods and approaches suggested in the literature. This is a natural and important question, especially in connection with one of the primary motivations for considering Horn representation: efficiency. The problems considered lead to questions about Horn envelopes (or Horn LUBs), introduced earlier in the context of knowledge compilation. This work gives a syntactic characterization of the remainders of a Horn belief set with respect to a consequence to be contracted, as the Horn envelopes of the belief set and an elementary conjunction corresponding to a truth assignment satisfying a certain explicitly given formula. This gives an efficient algorithm to generate all remainders, each represented by a truth assignment. On the negative side, examples are given of Horn belief sets and consequences where Horn formulas representing the result of contraction, based either on remainders or on weak remainders, must have exponential size for almost all possible choice functions (i.e., different possible choices of partial meet contraction). Therefore using the Horn framework for belief contraction does not by itself give us computational efficiency. Further work is required to explore the possibilities for efficient belief change methods.

The advance of Internet and Sensor technology has brought about new challenges evoked by the emergence of continuous data streams. While existing data-stream management systems allow for high-throughput stream processing, they lack complex reasoning capacities. We address this shortcoming and elaborate upon an approach to knowledge-intense stream reasoning based on Answer Set Programming (ASP). The emphasis thus shifts from rapid data processing to complex reasoning. To accommodate this in ASP, we develop new techniques that allow us to formulate problem encodings dealing with emerging as well as expiring data in a seamless way. We thus propose novel language constructs and modeling techniques for specifying and reasoning with time-decaying logic programs.