The concept of a stable model provided a declarative semantics for Prolog programs with negation as failure and became a starting point for the development of answer set programming. In this paper we propose a new definition of that concept, which covers many constructs used in answer set programming and, unlike the original definition, refers neither to grounding nor to fixpoints. It is based on a syntactic transformation similar to parallel circumscription. 1

Splitting a logic program allows us to reduce the task of computing its stable models to similar tasks for smaller programs. This idea is extended here to the general theory of stable models that replaces traditional logic programs by arbitrary firstorder sentences and distinguishes between intensional and extensional predicates. We discuss two kinds of splitting: a set of intensional predicates can be split into subsets, and a formula can be split into its conjunctive terms.

Abstract. Recently, enabling modularity aspects in Answer Set Programming (ASP) has gained increasing interest to ease the composition of program parts to an overall program. In this paper, we focus on modular nonmonotonic logic programs (MLP) under the answer set semantics, whose modules may have contextually dependent input provided by other modules. Moreover, (mutually) recursive module calls are allowed. We define a model-theoretic semantics for this extended setting, show that many desired properties of ordinary logic programming generalize to our modular ASP, and determine the computational complexity of the new formalism. We investigate the relationship of modular programs to disjunctive logic programs with well-defined input/output interface (DLP-functions) and show that they can be embedded into MLPs.

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

Abstract. The success of the Semantic Web is impossible without any form of modularity, encapsulation, and access control. In an earlier paper, we extended RDF graphs with weak and strong negation, as well as derivation rules. The ERDF #n-stable model semantics of the extended RDF framework (ERDF) is defined, extending RDF(S) semantics. In this paper, we propose a framework for modular ERDF ontologies, called modular ERDF framework, which enables collaborative reasoning over a set of ERDF ontologies, while support for hidden knowledge is also provided. In particular, the modular ERDF stable model semantics of modular ERDF ontologies is defined, extending the ERDF #n-stable model semantics. Our proposed framework supports local semantics and different points of view, local closed-world and open-world assumptions, and scoped negation-as-failure. Several complexity results are provided. 1

Abstract. Modular nonmonotonic logic programs (MLPs) under the answer-set semantics have been recently introduced as an ASP formalism in which modules can receive context-dependent input from other modules, while allowing (mutually) recursive module calls. This can be used for more succinct and natural problem representation at the price of an exponential increase of evaluation time. In this paper, we aim at an efficient top-down evaluation of MLPs, considering only calls to relevant module instances. To this end, we generalize the well-known Splitting Theorem to the MLP setting and present notions of call stratification, for which we determine sufficient conditions. Call-stratified MLPs allow to split module instantiations into two parts, one for computing input of module calls, and one for evaluating the calls themselves with subsequent computations. Based on these results, we develop a top-down evaluation procedure that expands only relevant module instantiations. Finally, we discuss syntactic conditions for its exploitation. 1

Abstract. The evaluation of logic programs with access to external knowledge sources requires to interleave external computation and model building. Deciding where and how to stop with one task and proceed with the next is a difficult problem, and existing approaches have severe scalability limitations in many real-world application scenarios. We introduce a new approach for organizing the evaluation of logic programs with external knowledge sources and describe a configurable framework for dividing the non-ground program into overlapping possiblysmaller parts called evaluation units. These units will then be processed by interleaving external evaluations and model building according to an evaluation and a model graph, and by combining intermediate results. Experiments with our prototype implementation show a significant improvement of this technique compared to existing approaches. Interestingly, even for ordinary logic programs (with no external access), our decomposition approach speeds up existing state of the art ASP solvers in some cases, showing its potential for wider usage. 1

Abstract. We present a framework which allows to combine answer-set programs in a way that consequences (rather than answer sets themselves) of programs can be used as input to other programs. Situations in which such a composition of programs is required appear in many practical application problems. So far, to deal with such problems, multiple calls to answer-set solvers were usually indispensable, as a direct ASP encoding is often much less obvious. In addition, we provide a technique for compiling such frameworks into a single ASP program which consequently can be evaluated by a single call to an answer-set solver. Our approach relies on the recently introduced concept of manifold programs which make use of weak constraints to identify consequences of programs. 1

Abstract. In answer-set programming (ASP), many notions of program equivalence have been introduced and formally analysed. A particular line of research in this direction aims at studying conditions under which certain syntactic constructs can be eliminated from programs preserving some given equivalence relation. In this paper, we continue this endeavour introducing novel conditions under which disjunction and negation can be eliminated from answer-set programs under relativised strong equivalence with projection. This notion is a generalisation of the usual strong-equivalence relation, as introduced by Lifschitz, Pearce, and Valverde, by allowing parametrisable context and output alphabets, which is an important feature in view of practical programming techniques like the use of local variables and modules. We provide model-theoretic conditions that hold for a disjunctive logic program P precisely when there is a program Q, equivalent to P under our considered notion, such that Q is either positive, normal, or Horn, respectively. Moreover, we outline how such a Q, called a casting of P, can be obtained, and consider complexity issues. 1