Extending Answer Set Programming with Rational Numbers

Answer Set Programming (ASP) is a widely used declarative programming paradigm that has shown great potential in solving complex computational problems. However, the inability to natively support non-integer arithmetic has been highlighted as a major drawback in real-world applications. This feature is crucial to accurately model and manage real-world data and information as emerged in various contexts, such as the smooth movement of video game characters, the 3D movement of mechanical arms, and data streamed by sensors. Nevertheless, extending ASP in this direction, without affecting its declarative nature and its well-defined semantics, poses non-trivial challenges; thus, no ASP system is able to reason natively with non-integer domains. Indeed, the widespread floating-point arithmetic is not applicable to the ASP case, as the reproducibility of results cannot be guaranteed and the semantics of an ASP program would not be uniquely and declaratively determined, regardless of the employed machine or solver. To overcome such limitations and in the realm of pure ASP, this paper proposes an extension of ASP in which non-integers are approximated to rational numbers, fully granting reproducibility and declarativity. We provide a well-defined semantics for the ASP-Core-2 standard extended with rational numbers and an implementation thereof. We hope this work could serve as a stepping stone towards a more expressive and versatile ASP language that can handle a broader range of real-world problems.

Rethinking Answer Set Programming Templates

In imperative programming, the Domain-Driven Design methodology helps in coping with the complexity of software development by materializing in code the invariants of a domain of interest. Code is cleaner and more secure because any implicit assumption is removed in favor of invariants, thus enabling a fail fast mindset and the immediate reporting of unexpected conditions. This article introduces a notion of template for Answer Set Programming that, in addition to the don't repeat yourself principle, enforces locality of some predicates by means of a simple naming convention. Local predicates are mapped to the usual global namespace adopted by mainstream engines, using universally unique identifiers to avoid name clashes. This way, local predicates can be used to enforce invariants on the expected outcome of a template in a possibly empty context of application, independently by other rules that can be added to such a context. Template applications transpiled this way can be processed by mainstream engines and safely shared with other knowledge designers, even when they have zero knowledge of templates.

I-DLV-sr: A Stream Reasoning System based on I-DLV

We introduce a novel logic-based system for reasoning over data streams, which relies on a framework enabling a tight, fine-tuned interaction between Apache Flink and the I^2-DLV system. The architecture allows to take advantage from both the powerful distributed stream processing capabilities of Flink and the incremental reasoning capabilities of I^2-DLV based on overgrounding techniques. Besides the system architecture, we illustrate the supported input language and its modeling capabilities, and discuss the results of an experimental activity aimed at assessing the viability of the approach. This paper is under consideration in Theory and Practice of Logic Programming (TPLP).

A Machine Learning guided Rewriting Approach for ASP Logic Programs

Answer Set Programming (ASP) is a declarative logic formalism that allows to encode computational problems via logic programs. Despite the declarative nature of the formalism, some advanced expertise is required, in general, for designing an ASP encoding that can be efficiently evaluated by an actual ASP system. A common way for trying to reduce the burden of manually tweaking an ASP program consists in automatically rewriting the input encoding according to suitable techniques, for producing alternative, yet semantically equivalent, ASP programs. However, rewriting does not always grant benefits in terms of performance; hence, proper means are needed for predicting their effects with this respect. In this paper we describe an approach based on Machine Learning (ML) to automatically decide whether to rewrite. In particular, given an ASP program and a set of input facts, our approach chooses whether and how to rewrite input rules based on a set of features measuring their structural properties and domain information. To this end, a Multilayer Perceptrons model has then been trained to guide the ASP grounder I-DLV on rewriting input rules. We report and discuss the results of an experimental evaluation over a prototypical implementation.

Incremental maintenance of overgrounded logic programs with tailored simplifications

The repeated execution of reasoning tasks is desirable in many applicative scenarios, such as stream reasoning and event processing. When using answer set programming in such contexts, one can avoid the iterative generation of ground programs thus achieving a significant payoff in terms of computing time. However, this may require some additional amount of memory and/or the manual addition of operational directives in the declarative knowledge base at hand. We introduce a new strategy for generating series of monotonically growing propositional programs. The proposed overgrounded programs with tailoring (OPTs) can be updated and reused in combination with consecutive inputs. With respect to earlier approaches, our tailored simplification technique reduces the size of instantiated programs. A maintained OPT slowly grows in size from an iteration to another while the update cost decreases, especially in later iterations. In this paper we formally introduce tailored embeddings, a family of equivalence-preserving ground programs which are at the theoretical basis of OPTs and we describe their properties. We then illustrate an OPT update algorithm and report about our implementation and its performance. This paper is under consideration in Theory and Practice of Logic Programming (TPLP).

DaRLing: A Datalog rewriter for OWL 2 RL ontological reasoning under SPARQL queries

The W3C Web Ontology Language (OWL) is a powerful knowledge representation formalism at the basis of many semantic-centric applications. Since its unrestricted usage makes reasoning undecidable already in case of very simple tasks, expressive yet decidable fragments have been identified. Among them, we focus on OWL 2 RL, which offers a rich variety of semantic constructors, apart from supporting all RDFS datatypes. Although popular Web resources - such as DBpedia - fall in OWL 2 RL, only a few systems have been designed and implemented for this fragment. None of them, however, fully satisfy all the following desiderata: (i) being freely available and regularly maintained; (ii) supporting query answering and SPARQL queries; (iii) properly applying the sameAs property without adopting the unique name assumption; (iv) dealing with concrete datatypes. To fill the gap, we present DaRLing, a freely available Datalog rewriter for OWL 2 RL ontological reasoning under SPARQL queries. In particular, we describe its architecture, the rewriting strategies it implements, and the result of an experimental evaluation that demonstrates its practical applicability. This paper is under consideration in Theory and Practice of Logic Programming (TPLP).

Precomputing Datalog evaluation plans in large-scale scenarios

With the more and more growing demand for semantic Web services over large databases, an efficient evaluation of Datalog queries is arousing a renewed interest among researchers and industry experts. In this scenario, to reduce memory consumption and possibly optimize execution times, the paper proposes novel techniques to determine an optimal indexing schema for the underlying database together with suitable body-orderings for the Datalog rules. The new approach is compared with the standard execution plans implemented in DLV over widely used ontological benchmarks. The results confirm that the memory usage can be significantly reduced without paying any cost in efficiency. This paper is under consideration in Theory and Practice of Logic Programming (TPLP).

Incremental Answer Set Programming with Overgrounding

Repeated executions of reasoning tasks for varying inputs are necessary in many applicative settings, such as stream reasoning. In this context, we propose an incremental grounding approach for the answer set semantics. We focus on the possibility of generating incrementally larger ground logic programs equivalent to a given non-ground one; so called overgrounded programs can be reused in combination with deliberately many different sets of inputs. Updating overgrounded programs requires a small effort, thus making the instantiation of logic programs considerably faster when grounding is repeated on a series of inputs similar to each other. Notably, the proposed approach works "under the hood", relieving designers of logic programs from controlling technical aspects of grounding engines and answer set systems. In this work we present the theoretical basis of the proposed incremental grounding technique, we illustrate the consequent repeated evaluation strategy and report about our experiments. This paper is under consideration in Theory and Practice of Logic Programming (TPLP).

Enhancing magic sets with an application to ontological reasoning

Magic sets are a Datalog to Datalog rewriting technique to optimize query answering. The rewritten program focuses on a portion of the stable model(s) of the input program which is sufficient to answer the given query. However, the rewriting may introduce new recursive definitions, which can involve even negation and aggregations, and may slow down program evaluation. This paper enhances the magic set technique by preventing the creation of (new) recursive definitions in the rewritten program. It turns out that the new version of magic sets is closed for Datalog programs with stratified negation and aggregations, which is very convenient to obtain efficient computation of the stable model of the rewritten program. Moreover, the rewritten program is further optimized by the elimination of subsumed rules and by the efficient handling of the cases where binding propagation is lost. The research was stimulated by a challenge on the exploitation of Datalog/\textsc{dlv} for efficient reasoning on large ontologies. All proposed techniques have been hence implemented in the \textsc{dlv} system, and tested for ontological reasoning, confirming their effectiveness. Under consideration for publication in Theory and Practice of Logic Programming.

Optimizing Answer Set Computation via Heuristic-Based Decomposition

Answer Set Programming (ASP) is a purely declarative formalism developed in the field of logic programming and nonmonotonic reasoning: computational problems are encoded by logic programs whose answer sets, corresponding to solutions, are computed by an ASP system. Different, semantically equivalent, programs can be defined for the same problem; however, performance of systems evaluating them might significantly vary. We propose an approach for automatically transforming an input logic program into an equivalent one that can be evaluated more efficiently. One can make use of existing tree-decomposition techniques for rewriting selected rules into a set of multiple ones; the idea is to guide and adaptively apply them on the basis of proper new heuristics, to obtain a smart rewriting algorithm to be integrated into an ASP system. The method is rather general: it can be adapted to any system and implement different preference policies. Furthermore, we define a set of new heuristics tailored at optimizing grounding, one of the main phases of the ASP computation; we use them in order to implement the approach into the ASP system DLV, in particular into its grounding subsystem I-DLV, and carry out an extensive experimental activity for assessing the impact of the proposal. Under consideration in Theory and Practice of Logic Programming (TPLP).