Wolfgang Faber

Haya Majid Qureshi, Wolfgang Faber

Metamodeling is a general approach to expressing knowledge about classes and properties in an ontology. It is a desirable modeling feature in multiple applications that simplifies the extension and reuse of ontologies. Nevertheless, allowing metamodeling without restrictions is problematic for several reasons, mainly due to undecidability issues. Practical languages, therefore, forbid classes to occur as instances of other classes or treat such occurrences as semantically different objects. Specifically, meta-querying in SPARQL under the Direct Semantic Entailment Regime (DSER) uses the latter approach, thereby effectively not supporting meta-queries. However, several extensions enabling different metamodeling features have been proposed over the last decade. This paper deals with the Metamodeling Semantics (MS) over OWL 2 QL and the Metamodeling Semantic Entailment Regime (MSER), as proposed in Lenzerini et al. (2015) and Lenzerini et al. (2020); Cima et al. (2017). A reduction from OWL 2 QL to Datalog for meta-querying was proposed in Cima et al. (2017). In this paper, we experiment with various logic programming tools that support Datalog querying to determine their suitability as back-ends to MSER query answering. These tools stem from different logic programming paradigms (Prolog, pure Datalog, Answer Set Programming, Hybrid Knowledge Bases). Our work shows that the Datalog approach to MSER querying is practical also for sizeable ontologies with limited resources (time and memory). This paper significantly extends Qureshi & Faber (2021) by a more detailed experimental analysis and more background. Under consideration in Theory and Practice of Logic Programming (TPLP).

Haya Majid Qureshi, Wolfgang Faber

Metamodeling refers to scenarios in ontologies in which classes and roles can be members of classes or occur in roles. This is a desirable modelling feature in several applications, but allowing it without restrictions is problematic for several reasons, mainly because it causes undecidability. Therefore, practical languages either forbid metamodeling explicitly or treat occurrences of classes as instances to be semantically different from other occurrences, thereby not allowing metamodeling semantically. Several extensions have been proposed to provide metamodeling to some extent. Building on earlier work that reduces metamodeling query answering to Datalog query answering, recently reductions to query answering over hybrid knowledge bases were proposed with the aim of using the Datalog transformation only where necessary. Preliminary work showed that the approach works, but the hoped-for performance improvements were not observed yet. In this work we expand on this body of work by improving the theoretical basis of the reductions and by using alternative tools that show competitive performance.

Wolfgang Faber, Giuseppe Mazzotta, Francesco Ricca

Answer Set Programming with Quantifiers ASP(Q) extends Answer Set Programming (ASP) to allow for declarative and modular modeling of problems from the entire polynomial hierarchy. The first implementation of ASP(Q), called qasp, was based on a translation to Quantified Boolean Formulae (QBF) with the aim of exploiting the well-developed and mature QBF-solving technology. However, the implementation of the QBF encoding employed in qasp is very general and might produce formulas that are hard to evaluate for existing QBF solvers because of the large number of symbols and sub-clauses. In this paper, we present a new implementation that builds on the ideas of qasp and features both a more efficient encoding procedure and new optimized encodings of ASP(Q) programs in QBF. The new encodings produce smaller formulas (in terms of the number of quantifiers, variables, and clauses) and result in a more efficient evaluation process. An algorithm selection strategy automatically combines several QBF-solving back-ends to further increase performance. An experimental analysis, conducted on known benchmarks, shows that the new system outperforms qasp.

Mario Alviano, Wolfgang Faber, Martin Gebser

Answer Set Programming (ASP) emerged in the late 1990ies as a paradigm for Knowledge Representation and Reasoning. The attractiveness of ASP builds on an expressive high-level modeling language along with the availability of powerful off-the-shelf solving systems. While the utility of incorporating aggregate expressions in the modeling language has been realized almost simultaneously with the inception of the first ASP solving systems, a general semantics of aggregates and its efficient implementation have been long-standing challenges. Aggregates have been proposed and widely used in database systems, and also in the deductive database language Datalog, which is one of the main precursors of ASP. The use of aggregates was, however, still restricted in Datalog (by either disallowing recursion or only allowing monotone aggregates), while several ways to integrate unrestricted aggregates evolved in the context of ASP. In this survey, we pick up at this point of development by presenting and comparing the main aggregate semantics that have been proposed for propositional ASP programs. We highlight crucial properties such as computational complexity and expressive power, and outline the capabilities and limitations of different approaches by illustrative examples.

Jorge Fandinno, Wolfgang Faber, Michael Gelfond

The language of epistemic specifications and epistemic logic programs extends disjunctive logic programs under the stable model semantics with modal constructs called subjective literals. Using subjective literals, it is possible to check whether a regular literal is true in every or some stable models of the program, those models, in this context also called \emph{belief sets}, being collected in a set called world view. This allows for representing, within the language, whether some proposition should be understood accordingly to the open or the closed world assumption. Several attempts for capturing the intuitions underlying the language by means of a formal semantics were given, resulting in a multitude of proposals that makes it difficult to understand the current state of the art. In this paper, we provide an overview of the inception of the field and the knowledge representation and reasoning tasks it is suitable for. We also provide a detailed analysis of properties of proposed semantics, and an outlook of challenges to be tackled by future research in the area. Under consideration in Theory and Practice of Logic Programming (TPLP)

Wolfgang Faber, Michael Morak, Lukáš Chrpa

In the context of planning and reasoning about actions and change, we call an action reversible when its effects can be reverted by applying other actions, returning to the original state. Renewed interest in this area has led to several results in the context of the PDDL language, widely used for describing planning tasks. In this paper, we propose several solutions to the computational problem of deciding the reversibility of an action. In particular, we leverage an existing translation from PDDL to Answer Set Programming (ASP), and then use several different encodings to tackle the problem of action reversibility for the STRIPS fragment of PDDL. For these, we use ASP, as well as Epistemic Logic Programming (ELP), an extension of ASP with epistemic operators, and compare and contrast their strengths and weaknesses. Under consideration for acceptance in TPLP.

Francesco Calimeri, Wolfgang Faber, Martin Gebser et al.

Standardization of solver input languages has been a main driver for the growth of several areas within knowledge representation and reasoning, fostering the exploitation in actual applications. In this document we present the ASP-Core-2 standard input language for Answer Set Programming, which has been adopted in ASP Competition events since 2013.

Wolfgang Faber, Michael Morak, Stefan Woltran

Epistemic Logic Programs (ELPs) extend Answer Set Programming (ASP) with epistemic negation and have received renewed interest in recent years. This led to the development of new research and efficient solving systems for ELPs. In practice, ELPs are often written in a modular way, where each module interacts with other modules by accepting sets of facts as input, and passing on sets of facts as output. An interesting question then presents itself: under which conditions can such a module be replaced by another one without changing the outcome, for any set of input facts? This problem is known as uniform equivalence, and has been studied extensively for ASP. For ELPs, however, such an investigation is, as of yet, missing. In this paper, we therefore propose a characterization of uniform equivalence that can be directly applied to the language of state-of-the-art ELP solvers. We also investigate the computational complexity of deciding uniform equivalence for two ELPs, and show that it is on the third level of the polynomial hierarchy.

Giovanni Amendola, Carmine Dodaro, Wolfgang Faber et al.

Answer Set Programming (ASP) is a well-established formalism for nonmonotonic reasoning. An ASP program can have no answer set due to cyclic default negation. In this case, it is not possible to draw any conclusion, even if this is not intended. Recently, several paracoherent semantics have been proposed that address this issue, and several potential applications for these semantics have been identified. However, paracoherent semantics have essentially been inapplicable in practice, due to the lack of efficient algorithms and implementations. In this paper, this lack is addressed, and several different algorithms to compute semi-stable and semi-equilibrium models are proposed and implemented into an answer set solving framework. An empirical performance comparison among the new algorithms on benchmarks from ASP competitions is given as well.

Wolfgang Faber, Mauro Vallati, Federico Cerutti et al.

Optimization - minimization or maximization - in the lattice of subsets is a frequent operation in Artificial Intelligence tasks. Examples are subset-minimal model-based diagnosis, nonmonotonic reasoning by means of circumscription, or preferred extensions in abstract argumentation. Finding the optimum among many admissible solutions is often harder than finding admissible solutions with respect to both computational complexity and methodology. This paper addresses the former issue by means of an effective method for finding subset-optimal solutions. It is based on the relationship between cardinality-optimal and subset-optimal solutions, and the fact that many logic-based declarative programming systems provide constructs for finding cardinality-optimal solutions, for example maximum satisfiability (MaxSAT) or weak constraints in Answer Set Programming (ASP). Clearly each cardinality-optimal solution is also a subset-optimal one, and if the language also allows for the addition of particular restricting constructs (both MaxSAT and ASP do) then all subset-optimal solutions can be found by an iterative computation of cardinality-optimal solutions. As a showcase, the computation of preferred extensions of abstract argumentation frameworks using the proposed method is studied.

Mario Alviano, Wolfgang Faber, Martin Gebser

Aggregation functions are widely used in answer set programming for representing and reasoning on knowledge involving sets of objects collectively. Current implementations simplify the structure of programs in order to optimize the overall performance. In particular, aggregates are rewritten into simpler forms known as monotone aggregates. Since the evaluation of normal programs with monotone aggregates is in general on a lower complexity level than the evaluation of normal programs with arbitrary aggregates, any faithful translation function must introduce disjunction in rule heads in some cases. However, no function of this kind is known. The paper closes this gap by introducing a polynomial, faithful, and modular translation for rewriting common aggregation functions into the simpler form accepted by current solvers. A prototype system allows for experimenting with arbitrary recursive aggregates, which are also supported in the recent version 4.5 of the grounder \textsc{gringo}, using the methods presented in this paper. To appear in Theory and Practice of Logic Programming (TPLP), Proceedings of ICLP 2015.

Ilias Tachmazidis, Grigoris Antoniou, Wolfgang Faber

Data originating from the Web, sensor readings and social media result in increasingly huge datasets. The so called Big Data comes with new scientific and technological challenges while creating new opportunities, hence the increasing interest in academia and industry. Traditionally, logic programming has focused on complex knowledge structures/programs, so the question arises whether and how it can work in the face of Big Data. In this paper, we examine how the well-founded semantics can process huge amounts of data through mass parallelization. More specifically, we propose and evaluate a parallel approach using the MapReduce framework. Our experimental results indicate that our approach is scalable and that well-founded semantics can be applied to billions of facts. To the best of our knowledge, this is the first work that addresses large scale nonmonotonic reasoning without the restriction of stratification for predicates of arbitrary arity. To appear in Theory and Practice of Logic Programming (TPLP).

Mario Alviano, Wolfgang Faber

Answer Set Programming (ASP) is logic programming under the stable model or answer set semantics. During the last decade, this paradigm has seen several extensions by generalizing the notion of atom used in these programs. Among these, there are aggregate atoms, HEX atoms, generalized quantifiers, and abstract constraints. In this paper we refer to these constructs collectively as generalized atoms. The idea common to all of these constructs is that their satisfaction depends on the truth values of a set of (non-generalized) atoms, rather than the truth value of a single (non-generalized) atom. Motivated by several examples, we argue that for some of the more intricate generalized atoms, the previously suggested semantics provide unintuitive results and provide an alternative semantics, which we call supportedly stable or SFLP answer sets. We show that it is equivalent to the major previously proposed semantics for programs with convex generalized atoms, and that it in general admits more intended models than other semantics in the presence of non-convex generalized atoms. We show that the complexity of supportedly stable models is on the second level of the polynomial hierarchy, similar to previous proposals and to stable models of disjunctive logic programs. Given these complexity results, we provide a compilation method that compactly transforms programs with generalized atoms in disjunctive normal form to programs without generalized atoms. Variants are given for the new supportedly stable and the existing FLP semantics, for which a similar compilation technique has not been known so far.

Mario Alviano, Francesco Calimeri, Wolfgang Faber et al.

Logic programs with aggregates (LPA) are one of the major linguistic extensions to Logic Programming (LP). In this work, we propose a generalization of the notions of unfounded set and well-founded semantics for programs with monotone and antimonotone aggregates (LPAma programs). In particular, we present a new notion of unfounded set for LPAma programs, which is a sound generalization of the original definition for standard (aggregate-free) LP. On this basis, we define a well-founded operator for LPAma programs, the fixpoint of which is called well-founded model (or well-founded semantics) for LPAma programs. The most important properties of unfounded sets and the well-founded semantics for standard LP are retained by this generalization, notably existence and uniqueness of the well-founded model, together with a strong relationship to the answer set semantics for LPAma programs. We show that one of the D-well-founded semantics, defined by Pelov, Denecker, and Bruynooghe for a broader class of aggregates using approximating operators, coincides with the well-founded model as defined in this work on LPAma programs. We also discuss some complexity issues, most importantly we give a formal proof of tractable computation of the well-founded model for LPA programs. Moreover, we prove that for general LPA programs, which may contain aggregates that are neither monotone nor antimonotone, deciding satisfaction of aggregate expressions with respect to partial interpretations is coNP-complete. As a consequence, a well-founded semantics for general LPA programs that allows for tractable computation is unlikely to exist, which justifies the restriction on LPAma programs. Finally, we present a prototype system extending DLV, which supports the well-founded semantics for LPAma programs, at the time of writing the only implemented system that does so. Experiments with this prototype show significant computational advantages of aggregate constructs over equivalent aggregate-free encodings.

Mario Alviano, Wolfgang Faber

In recent years, Answer Set Programming (ASP), logic programming under the stable model or answer set semantics, has seen several extensions by generalizing the notion of an atom in these programs: be it aggregate atoms, HEX atoms, generalized quantifiers, or abstract constraints, the idea is to have more complicated satisfaction patterns in the lattice of Herbrand interpretations than traditional, simple atoms. In this paper we refer to any of these constructs as generalized atoms. Several semantics with differing characteristics have been proposed for these extensions, rendering the big picture somewhat blurry. In this paper, we analyze the class of programs that have convex generalized atoms (originally proposed by Liu and Truszczynski in [10]) in rule bodies and show that for this class many of the proposed semantics coincide. This is an interesting result, since recently it has been shown that this class is the precise complexity boundary for the FLP semantics. We investigate whether similar results also hold for other semantics, and discuss the implications of our findings.

Mario Alviano, Wolfgang Faber

NP-SPEC is a language for specifying problems in NP in a declarative way. Despite the fact that the semantics of the language was given by referring to Datalog with circumscription, which is very close to ASP, so far the only existing implementations are by means of ECLiPSe Prolog and via Boolean satisfiability solvers. In this paper, we present translations from NP-SPEC into various forms of ASP and analyze them. We also argue that it might be useful to incorporate certain language constructs of NP-SPEC into mainstream ASP.

Mario Alviano, Wolfgang Faber, Nicola Leone et al.

Datalog is one of the best-known rule-based languages, and extensions of it are used in a wide context of applications. An important Datalog extension is Disjunctive Datalog, which significantly increases the expressivity of the basic language. Disjunctive Datalog is useful in a wide range of applications, ranging from Databases (e.g., Data Integration) to Artificial Intelligence (e.g., diagnosis and planning under incomplete knowledge). However, in recent years an important shortcoming of Datalog-based languages became evident, e.g. in the context of data-integration (consistent query-answering, ontology-based data access) and Semantic Web applications: The language does not permit any generation of and reasoning with unnamed individuals in an obvious way. In general, it is weak in supporting many cases of existential quantification. To overcome this problem, Datalogex has recently been proposed, which extends traditional Datalog by existential quantification in rule heads. In this work, we propose a natural extension of Disjunctive Datalog and Datalogex, called Datalogexor, which allows both disjunctions and existential quantification in rule heads and is therefore an attractive language for knowledge representation and reasoning, especially in domains where ontology-based reasoning is needed. We formally define syntax and semantics of the language Datalogexor, and provide a notion of instantiation, which we prove to be adequate for Datalogexor. A main issue of Datalogex and hence also of Datalogexor is that decidability is no longer guaranteed for typical reasoning tasks. In order to address this issue, we identify many decidable fragments of the language, which extend, in a natural way, analog classes defined in the non-disjunctive case. Moreover, we carry out an in-depth complexity analysis, deriving interesting results which range from Logarithmic Space to Exponential Time.

Mario Alviano, Wolfgang Faber, Gianluigi Greco et al.

In this paper, a new technique for the optimization of (partially) bound queries over disjunctive Datalog programs with stratified negation is presented. The technique exploits the propagation of query bindings and extends the Magic Set (MS) optimization technique. An important feature of disjunctive Datalog is nonmonotonicity, which calls for nondeterministic implementations, such as backtracking search. A distinguishing characteristic of the new method is that the optimization can be exploited also during the nondeterministic phase. In particular, after some assumptions have been made during the computation, parts of the program may become irrelevant to a query under these assumptions. This allows for dynamic pruning of the search space. In contrast, the effect of the previously defined MS methods for disjunctive Datalog is limited to the deterministic portion of the process. In this way, the potential performance gain by using the proposed method can be exponential, as could be observed empirically. The correctness of MS is established thanks to a strong relationship between MS and unfounded sets that has not been studied in the literature before. This knowledge allows for extending the method also to programs with stratified negation in a natural way. The proposed method has been implemented in DLV and various experiments have been conducted. Experimental results on synthetic data confirm the utility of MS for disjunctive Datalog, and they highlight the computational gain that may be obtained by the new method w.r.t. the previously proposed MS methods for disjunctive Datalog programs. Further experiments on real-world data show the benefits of MS within an application scenario that has received considerable attention in recent years, the problem of answering user queries over possibly inconsistent databases originating from integration of autonomous sources of information.