We address the problem of repairing large-scale biological networks and corresponding yet often discrepant measurements in order to predict unobserved variations. To this end, we propose a range of different operations for altering experimental data and/or a biological network in order to re-establish their mutual consistency-an indispensable prerequisite for automated prediction. For accomplishing repair and prediction, we take advantage of the distinguished modeling and reasoning capacities of Answer Set Programming. We validate our framework by an empirical study on the widely investigated organism Escherichia coli.

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.

Abduction is a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining how the world behaves it aims at finding an explanation for some observed manifestation. In this paper we focus on propositional abduction, where the knowledge base and the manifestation are represented by propositional formulae. The problem of deciding whether there exists an explanation has been shown to be Σ p 2 -complete in general. We consider variants obtained by restricting the allowed connectives in the formulae to certain sets of Boolean functions. We give a complete classification of the complexity for all considerable sets of Boolean functions. In this way, we identify easier cases, namely NP-complete and polynomial cases; and we highlight sources of intractability. Further, we address the problem of counting the explanations and draw a complete picture for the counting complexity.

Abstract argumentation frameworks have received a lot of interest in recent years. Most computational problems in this area are intractable but several tractable fragments have been identified. In particular, Dunne showed that many problems can be solved in linear time for argumentation frameworks of bounded tree-width. However, these tractability results, which were obtained via Courcelle’s Theorem, do not directly lead to efficient algorithms. The goal of this paper is to turn the theoretical tractability results into efficient algorithms and to explore the potential of directed notions of tree-width for defining larger tractable fragments.

The applicability conditions of legal Norms regulating computer systems can be modelled in different rules very often refer to these institutional concepts, rather ways, see, for example, (Boella, van der Torre, and than to so called brute facts. To simplify the notation we refer Verhagen 2008). If norms are represented by hard constraints, to the former as constitutive rules, and the latter simply then computer systems are designed to avoid violations.

Measuring the inconsistency degree of a knowledge base can help us to deal with inconsistencies. Several inconsistency measures have been given under different multi-valued semantics, including 4-valued semantics, 3-valued semantics, LPm and Quasi Classical semantics. In this paper, we first carefully analyze the relationship between these inconsistency measures by showing that the inconsistency degrees under 4-valued semantics, 3-value semantics, LPm are the same, but different from the one based on Quasi Classical semantics. We then consider the computation of these inconsistency measures and show that computing inconsistency measurement under multi-valued semantics is usually intractable. To tackle this problem, we propose two novel algorithms that respectively encode the problems of computing inconsistency degrees under 4-valued semantics (3-valued semantics, LPm) and under Quasi Classical semantics into the partial Max-SAT problems. We implement these algorithms and do experiments on some benchmark data sets. The preliminary but encouraging experimental results show that our approach is efficient to handle large knowledge bases.

We present a distributed algorithm for computing equilibria of heterogeneous nonmonotonic multi-context systems (MCS). The algorithm can be parametrized to compute only partial equilibria, which can be used for reasoning tasks like query answering or satisfiability checking that need only partial information and not whole belief states. Furthermore, caching is employed to cut redundant solver calls. As a showcase, we instantiate the MCS framework with answer set program contexts. To characterize equilibria of such MCS, we develop notions of loop formulas that enable reductions to the classical satisfiability problem (SAT). Notably, loop formulas for bridge rules between contexts and for the local contexts can be combined to a uniform encoding of an MCS into a (distributed) SAT instance. As a consequence, we can use SAT solvers for belief set building. We demonstrate this approach by an experimental prototype implementation, which uses an off-the-shelf SAT solver.

We study the problem of reasoning from incoherent answer set programs, i.e., from logic programs that do not have an answer set due to cyclic dependencies of an atom from its default negation. As a starting point we consider so-called semi-stable models which have been developed for this purpose building on a program transformation, called epistemic transformation. We give a model-theoretic characterization of this semantics, considering pairs of two-valued interpretations of the original program, rather than resorting to its epistemic transformation. Moreover, we show some anomalies of semi-stable semantics with respect to basic epistemic properties and propose an alternative semantics satisfying these properties. In addition to a model-theoretic and a transformational characterization of the alternative semantics, we prove precise complexity results for main reasoning tasks under both semantics.

Horn fragments of Description Logics (DLs) have gained popularity because they provide a beneficial trade-off between expressive power and computational complexity and, more specifically, are usually tractable w.r.t. data complexity. Despite their potential, and partly due to the intricate interaction of nominals (O), inverses (I) and counting (Q), such fragments had not been studied so far for the DLs SHOIQ and SROIQ that underly OWL 1 and 2. In this paper, we present a polynomial and modular translation from Horn-SHOIQ knowledge bases into DATALOG, which shows that standard reasoning tasks are feasible in deterministic single exponential time. This improves over the previously known upper bounds, and contrasts the known NEXPTIME completeness of full SHOIQ. Thereby, Horn-SHOIQ stands out as the first EXPTIME complete DL that allows simultaneously for O, I, and Q. In addition, we show that standard reasoning in Horn-SROIQ is 2-EXPTIME complete. Despite their high expressiveness, both Horn-SHOIQ and Horn-SROIQ have polynomial data complexity. This makes them particularly attractive for reasoning in semantically enriched systems with large data sets. A promising first step in this direction could be achieved exploiting existing DATALOG engines, along the lines of our translation.

Recent years have seen the advent of large and complex ontologies, most notably in the medical domain. As a consequence, structuring mechanisms for ontologies are nowadays viewed as an indispensible tool. A basic such mechanism is the automatic decomposition of the vocabulary of an ontology into independent parts. In this paper, we study decompositions that are syntax independent in the sense that the resulting partitioning depends only on the meaning of the vocabulary items, but not on the concrete syntactic form of the axioms in the ontology. We present the first systematic investigation of decompositions of this type in the context of ontologies. Specifically, we focus on ontologies formulated in description logics and provide a variety of results that range from theorems stating the existence of unique finest decompositions to complexity results and algorithms computing decompositions. We also investigate the relationship between the existence of unique finite decompositions and a variant of the Craig interpolation property called parallel interpolation.