Abstract not found

We present the class FDNC of logic programs which allows for function symbols(F), disjunction (D), non-monotonic negation under the answer set semantics (N), and constraints (C), while still retaining the decidability of the standard reasoning tasks. Thanks to these features, FDNC programs are a powerful formalism for rule-based modeling of applications with potentially infinite processes and objects, and which allows also for common-sense reasoning in this context. This is evidenced, for instance, by tasks in reasoning about actions and planning: brave and open queries over FDNC programs capture the well-known problems of plan existence and secure (conformant) plan existence, respectively, in transition-based actions domains. As for reasoning from FDNC programs, we show that consistency checking and brave/cautious reasoning tasks are ExpTimecomplete in general, but have lower complexity under syntactic restrictions that give rise to a family of program classes. Furthermore, we also determine the complexity of open queries (i.e., with answer variables), for which deciding non-empty answers is shown to be ExpSpace-complete under cautious entailment. Furthermore, we present algorithms for all reasoning tasks that are worst-case optimal. The majority of them resorts to a finite representation of the stable models of an FDNC program that employs maximal founded sets of knots, which are labeled trees of depth at most 1 from which each stable model can be reconstructed. Due to this property, reasoning over FDNC programs can in many cases be reduced to reasoning from knots. Once the knotrepresentation for a program is derived (which can be done off-line), several reasoning tasks are not more expensive than in the function-free case, and some are even feasible in polynomial time. This knowledge compilation technique paves the way to potentially more efficient online reasoning methods not only for FDNC, but also for other formalisms.

Abstract. In this paper general mechanisms and syntactic restrictions are explored in order to specify and merge rule bases in the Semantic Web. Rule bases are expressed by extended logic programs having two forms of negation, namely strong (or explicit) and weak (also known as default negation or negation-as-failure). The proposed mechanisms are defined by very simple modular program transformations, and integrate both open and closed world reasoning. These program transformations are shown to be appropriate for the two major semantics for extended logic programs: answer set semantics and well-founded semantics with explicit negation. Moreover, the results obtained by both semantics are compared. 1

Multi-Context Systems (MCS) are formalisms that enable the interlinkage of single knowledge bases, called contexts, via bridge rules. Recently, the evaluation of heterogeneous, nonmonotonic MCS was considered in Dao-Tran et al. (2010), where a fully distributed algorithm was described. In this paper, we continue this line of work and present a decomposition technique for MCS which analyzes the topology of an MCS. It applies pruning techniques to get economically small representations of context dependencies. Orthogonal to this, we characterize minimal interfaces for information exchange between contexts, such that data transmissions can be minimized. We then present a novel evaluation algorithm that operates on a query plan which is compiled with topology pruning and interface minimization. The effectiveness of the optimization techniques is demonstrated by a prototype implementation, which uses an off-the-shelf SAT solver and shows encouraging experimental results.

The purpose of this tutorial is to get the audience familiar with the Answer Set Programming (ASP) Paradigm in the perspective of its fruitful usage for Semantic Web applications. ASP is a declarative programming paradigm with its roots in Knowledge Representation and Logic Programming. Systems and languages based on ASP are ready for tackling many of the challenges the Semantic Web offers, and in particular, are good candidates for solving a variety of issues which have been delegated to the Rule/Logic Layers in the Semantic Web vision. ASP systems are scalable, allow to mix monotonic with nonmonotonic reasoning, permit to combine rules with ontologies, and can interface external reasoners. Moreover, ASP is especially tailored at solving configuration and matchmaking problems involving reasoning with preferences by featuring easy to use, fully declarative soft & hard constraint specification languages. We introduce the attendees to the ASP basics and its principal extensions tailored at Semantic Web applications. We discuss the current impact of Answer Set Programming in the Semantic Web Area and possible future directions. Applications and exercises are presented. The attendees will practice through an online interface using one of the state-of-the-art ASP solvers and some of its extensions.

Abstract. We present cq-programs, which enhance nonmonotonic description logics (dl-) programs by conjunctive queries (CQ) and union of conjunctive queries (UCQ) over Description Logics knowledge bases, as well as disjunctive rules. dl-programs had been proposed as a powerful formalism for integrating nonmonotonic logic programming and DL-engines on a clear semantic basis. The new cq-programs have two advantages: First, they offer increased expressivity by allowing general (U)CQs in the body. And second, this combination of rules and ontologies gives rise to strategies for optimizing calls to the DL-reasoner, by exploiting (U)CQ facilities of the DL-reasoner. To this end, we discuss some equivalences which can be exploited for program rewriting. Experimental results for a cq-program prototype show that this can lead to significant performance improvements. 1

Abstract. We present a principled framework for modular web rule bases, called MWeb. According to this framework, each predicate defined in a rule base is characterized by its defining reasoning mode, scope, and exporting rule base list. Each predicate used in a rule base is characterized by its requesting reasoning mode and importing rule base list. For legal MWeb modular rule bases S, the MWebAS and MWebWFS semantics of each rule base s ∈ S w.r.t. S are defined model-theoretically. These semantics extend the answer set semantics (AS) and the well-founded semantics with explicit negation (WFSX) on ELPs, respectively, keeping all of their semantical and computational characteristics. Our framework supports: (i) local semantics and different points of view, (ii) local closed-world and open-world assumptions, (iii) scoped negation-as-failure, (iv) restricted propagation of local inconsistencies, and (v) monotonicity of reasoning, for “fully shared ” predicates.

Abstract. We develop a module-based framework for constraint modeling where it is possible to combine different constraint modeling languages and exploit their strengths in a flexible way. In the framework a constraint model consists of modules with clear input/output interfaces. When combining modules, apart from the interface, a module is a black box whose internals are invisible to the outside world. Inside a module a chosen constraint language (approaches such as CP, ASP, SAT, and MIP) can be used. This leads to a clear modular semantics where the overall semantics of the whole constraint model is obtained from the semantics of individual modules. The framework supports multi-language modeling without the need to develop a complicated joint semantics and enables the use of alternative semantical underpinnings such as default negation and classical negation in the same model. Furthermore, computational aspects of the framework are considered and, in particular, possibilities of benefiting from the known module structure in solving constraint models are studied. 1

We provide two approaches for explaining inconsistency in multi-context systems, where decentralized and heterogeneous system parts interact via nonmonotonic bridge rules. Inconsistencies arise easily in such scenarios, and nonmonotonicity calls for specific methods of inconsistency analysis. Both our approaches characterize inconsistency in terms of involved bridge rules: either by pointing out rules which need to be altered for restoring consistency, or by finding combinations of rules which cause inconsistency. We show duality and modularity properties, give precise complexity characterizations, and provide algorithms for computation using HEXprograms. Our results form a basis for inconsistency management in heterogeneous knowledge integration systems.

Abstract. Recent studies showed how a seamless integration of formal concept analysis (FCA), logic of domains, and answer set programming (ASP) can be achieved. Based on these results for combining hierarchical knowledge with classical rule-based formalisms, we introduce an expressive common-sense query language for formal contexts. Although this approach is conceptually based on order-theoretic paradigms, we show how it can be implemented on top of standard ASP systems. Advanced features, such as default negation and disjunctive rules, thus become practically available for processing contextual data. 1