Promoting Modular Nonmonotonic Logic Programs

Modularity in Logic Programming has gained much attention over the past years. To date, many formalisms have been proposed that feature various aspects of modularity. In this paper, we present our current work on Modular Nonmonotonic Logic Programs (MLPs), which are logic programs under answer set semantics with modules that have contextualized input provided by other modules. Moreover, they allow for (mutually) recursive module calls. We pinpoint issues that are present in such cyclic module systems and highlight how MLPs addresses them

The Answer Set Programming (ASP) Competition

is a biannual event for evaluating declarative knowledge representation systems on hard and demanding AI problems. The competition consists of two main tracks: the ASP System Track and the Model & Solve Track. The traditional System Track compares dedicated answer set solvers on ASP benchmarks, while the Model & Solve Track invites any researcher and developer of declarative knowledge representation systems to participate in an open challenge for solving sophisticated AI problems with their tools of choice. This article provides an overview of the ASP Competition series, reviews its origins and history, giving insights on organizing and running such an elaborate event, and briefly discusses about the lessons learned so far. 1 A Brief History Answer Set Programming (ASP) is a well-established paradigm of declarative programming with roots in the stable models semantics for logic programs (Gelfond and Lifschitz, 1991; Niemelä, 1999; Marek and Truszczyński, 1999). The main goal of ASP is to provide a versatile declarative modeling framework with many attractive characteristics. These features allow to turn—with little to no effort—problem statements of computationally hard problems into executable formal specifications, also called Answer Set Programs. These programs can be used to describe and reason over problems in a large variety of domains, such as commonsense and agent reasoning, diagnosis, deductive databases, planning, bioinformatics, scheduling and timetabling. See (Brewka et al., 2012) for an overview, while for introductory material on ASP, the reader might refer to (Baral, 2003; Eiter et al., 2009). ASP has a close relationship to other declarative modeling paradigms and languages, such as SA

Exploiting Unfounded Sets for HEX-Program Evaluation

HEX programs extend logic programs with external computations through external atoms, whose answer sets are the minimal models of the Faber-Leone-Pfeifer-reduct. As already reasoning from Horn programs with nonmonotonic external atoms of polynomial complexity is on the second level of the polynomial hierarchy, answer set checking needs special attention; simply computing reducts and searching for smaller models does not scale well. We thus extend an approach based on unfounded sets to HEX and integrate it in a Conflict Driven Clause Learning framework for HEX program evaluation. It reduces the check to a search for unfounded sets, which is more efficiently implemented as a SAT problem. We give a basic encoding for HEX and show optimizations by additional clauses. Experiments show that the new approach significantly decreases runtime

Modular nonmonotonic logic programs

Modular programming is common practice in software development, and the vast majority of general-purpose programming languages use modularity concepts to aid software engineers in designing and building complex systems based on reusable software components. Answer Set Programming (ASP), in comparison, is a popular paradigm for declarative programming and knowledge representation, but methods for reusing subprograms and program elements in ASP have not arrived for common use yet. This thesis proposes Modular Nonmonotonic Logic Programs (MLPs), which are disjunctive logic programs under answer set semantics with modules that have contextualized input. Such programs incorporate a call by value mechanism and allow for unrestricted calls between modulesincluding mutual and self recursionas a new approach to extend ASP with module constructs akin to those found in conventional programming. We define a model-theoretic semantics for this extended setting, show that many desired properties of ordinary logic programming generalize to modular ASP, and determine the computational complexity of the new formalism. For the purpose of implementation, we consider rewriting techniques that make MLP semantics amenable to off-the-shelf ASP solvers. We present translations that take an MLP with module input and rewrite them in stages to a combined logic program without input that is evaluable with ASP reasoners. This operation comes at the price of inflating the program exponentially, but complexity-theoretic assumptions suggest that this is unavoidable. The alternative macro expansion technique applicable to syntactically restricted MLPs does not incur the blowup observable in the general setting, and we make use of it to develop an application by embedding hybrid Description Logic Programs into MLPs. This effectively unites MLP with established Datalog engines as backbone for the computation, which we experimentally evaluate. We characterize answers sets in terms of classical (Herbrand) models of propositional, first-, and second-order sentences, extending a line of research for conventional logic programs. To this end, we lift on one side well-known loop formulas to MLPs, and otherwise augment ordered program completion for MLPs, which avoids explicit loop formula construction by auxiliary predicates. A further result is a study on the relationship of MLPs and DLP-functions, which is a notable formalism for compositional modular ASP with well-defined input/output interface. These investigations widen our understanding of MLPs and may prove beneficial for further semantic analysis and implementation perspectives.29

Integration of conjunctive queries over description logics into HEX-programs

Zsfassung in dt. Sprachehttp://www.postsubmeta.net/pub/2007/thesis.pdfWe present cq-programs, which enhance nonmonotonic description logics (dl-) programs by conjunctive queries (CQ) and union of conjunctive queries (UCQ) over Description Logics (DL) knowledge bases, as well as disjunctive rules. dl-programs had been proposed as a powerful formalism for integrating nonmonotonic logic programming and DL reasoning on a clear semantic basis. The new cq-programs have at least 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 and present respective algorithms. Experimental results for the cq-program prototype show that this can lead to significant performance improvements. Moreover, the developed optimization methods may be of general interest in the context of hybrid knowledge bases.HEX-programs, which extend answer-set programming (ASP) with higher-order features and provide powerful interfacing to external computation sources, have been demonstrated to be a versatile formalism for extending the ASP paradigm. The cq-program prototype dl-plugin, which will be introduced in this work, has been developed as a plugin for dlvhex, an implementation for HEX-programs. The dl-plugin integrates ASP with description logics knowledge bases by means of external atoms.For this purpose, a partial equivalence between HEX-programs and cq-programs shows that HEX-programs can serve as a host language for our new formalism, provided that only monotonic dl-atoms appear in the cq-program.11

Dynamic Querying of Mass-Storage RDF Data with Rule-Based Entailment Regimes

RDF Schema (RDFS) as a lightweight ontology language is gaining popularity and, consequently, tools for scalable RDFS inference and querying are needed. SPARQL has become recently aW3C standard for querying RDF data, but it mostly provides means for querying simple RDF graphs only, whereas querying with respect to RDFS or other entailment regimes is left outside the current specification. In this paper, we show that SPARQL faces certain unwanted ramifications when querying ontologies in conjunction with RDF datasets that comprise multiple named graphs, and we provide an extension for SPARQL that remedies these effects. Moreover, since RDFS inference has a close relationship with logic rules, we generalize our approach to select a custom rule set for specifying inferences to be taken into account in a SPARQL query. We show that our extensions are technically feasible by providing benchmark results for RDFS querying in our prototype system GiaBATA, which uses Datalog coupled with a persistent Relational Database as a back-end for implementing SPARQL with dynamic rule-based inference. By employing different optimization techniques like magic set rewriting our system remains competitive with state-of-the-art RDFS querying systems.peer-reviewe