arXiv subjects

Mario Alviano

Publications and source records attributed to Mario Alviano.

At least 37 records · Page 2Linked to original sources

arXiv2018

Cautious reasoning in ASP via minimal models and unsatisfiable cores

Answer Set Programming (ASP) is a logic-based knowledge representation framework, supporting---among other reasoning modes---the central task of query answering. In the propositional case, query answering amounts to computing cautious consequences of the input program among the atoms in a given set of candidates, where a cautious consequence is an atom belonging to all stable models. Currently, the most efficient algorithms either iteratively verify the existence of a stable model of the input program extended with the complement of one candidate, where the candidate is heuristically selected, or introduce a clause enforcing the falsity of at least one candidate, so that the solver is free to choose which candidate to falsify at any time during the computation of a stable model. This paper introduces new algorithms for the computation of cautious consequences, with the aim of driving the solver to search for stable models discarding more candidates. Specifically, one of such algorithms enforces minimality on the set of true candidates, where different notions of minimality can be used, and another takes advantage of unsatisfiable cores computation. The algorithms are implemented in WASP, and experiments on benchmarks from the latest ASP competitions show that the new algorithms perform better than the state of the art. (Under consideration for acceptance in TPLP).

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arXiv2018

Shared aggregate sets in answer set programming

Aggregates are among the most frequently used linguistic extensions of answer set programming. The result of an aggregation may introduce new constants during the instantiation of the input program, a feature known as value invention. When the aggregation involves literals whose truth value is undefined at instantiation time, modern grounders introduce several instances of the aggregate, one for each possible interpretation of the undefined literals. This paper introduces new data structures and techniques to handle such cases, and more in general aggregations on the same aggregate set identified in the ground program in input. The proposed solution reduces the memory footprint of the solver without sacrificing efficiency. On the contrary, the performance of the solver may improve thanks to the addition of some simple entailed clauses which are not easily discovered otherwise, and since redundant computation is avoided during propagation. Empirical evidence of the potential impact of the proposed solution is given. (Under consideration for acceptance in TPLP).

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arXiv2018

A Trajectory Calculus for Qualitative Spatial Reasoning Using Answer Set Programming

Spatial information is often expressed using qualitative terms such as natural language expressions instead of coordinates; reasoning over such terms has several practical applications, such as bus routes planning. Representing and reasoning on trajectories is a specific case of qualitative spatial reasoning that focuses on moving objects and their paths. In this work, we propose two versions of a trajectory calculus based on the allowed properties over trajectories, where trajectories are defined as a sequence of non-overlapping regions of a partitioned map. More specifically, if a given trajectory is allowed to start and finish at the same region, 6 base relations are defined (TC-6). If a given trajectory should have different start and finish regions but cycles are allowed within, 10 base relations are defined (TC-10). Both versions of the calculus are implemented as ASP programs; we propose several different encodings, including a generalised program capable of encoding any qualitative calculus in ASP. All proposed encodings are experimentally evaluated using a real-world dataset. Experiment results show that the best performing implementation can scale up to an input of 250 trajectories for TC-6 and 150 trajectories for TC-10 for the problem of discovering a consistent configuration, a significant improvement compared to previous ASP implementations for similar qualitative spatial and temporal calculi. This manuscript is under consideration for acceptance in TPLP.

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arXiv2017

Model enumeration in propositional circumscription via unsatisfiable core analysis

Many practical problems are characterized by a preference relation over admissible solutions, where preferred solutions are minimal in some sense. For example, a preferred diagnosis usually comprises a minimal set of reasons that is sufficient to cause the observed anomaly. Alternatively, a minimal correction subset comprises a minimal set of reasons whose deletion is sufficient to eliminate the observed anomaly. Circumscription formalizes such preference relations by associating propositional theories with minimal models. The resulting enumeration problem is addressed here by means of a new algorithm taking advantage of unsatisfiable core analysis. Empirical evidence of the efficiency of the algorithm is given by comparing the performance of the resulting solver, CIRCUMSCRIPTINO, with HCLASP, CAMUS MCS, LBX and MCSLS on the enumeration of minimal models for problems originating from practical applications. This paper is under consideration for acceptance in TPLP.

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arXiv2016

Anytime answer set optimization via unsatisfiable core shrinking

Unsatisfiable core analysis can boost the computation of optimum stable models for logic programs with weak constraints. However, current solvers employing unsatisfiable core analysis either run to completion, or provide no suboptimal stable models but the one resulting from the preliminary disjoint cores analysis. This drawback is circumvented here by introducing a progression based shrinking of the analyzed unsatisfiable cores. In fact, suboptimal stable models are possibly found while shrinking unsatisfiable cores, hence resulting into an anytime algorithm. Moreover, as confirmed empirically, unsatisfiable core analysis also benefits from the shrinking process in terms of solved instances. This paper is under consideration for acceptance in TPLP.

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arXiv2015

Rewriting recursive aggregates in answer set programming: back to monotonicity

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.

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arXiv2015

Complexity and Compilation of GZ-Aggregates in Answer Set Programming

Gelfond and Zhang recently proposed a new stable model semantics based on Vicious Circle Principle in order to improve the interpretation of logic programs with aggregates. The paper focuses on this proposal, and analyzes the complexity of both coherence testing and cautious reasoning under the new semantics. Some surprising results highlight similarities and differences versus mainstream stable model semantics for aggregates. Moreover, the paper reports on the design of compilation techniques for implementing the new semantics on top of existing ASP solvers, which eventually lead to realize a prototype system that allows for experimenting with Gelfond-Zhang's aggregates. To appear in Theory and Practice of Logic Programming (TPLP), Proceedings of ICLP 2015.

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arXiv2015

Fuzzy Answer Set Computation via Satisfiability Modulo Theories

Fuzzy answer set programming (FASP) combines two declarative frameworks, answer set programming and fuzzy logic, in order to model reasoning by default over imprecise information. Several connectives are available to combine different expressions; in particular the \Godel and \Luka fuzzy connectives are usually considered, due to their properties. Although the \Godel conjunction can be easily eliminated from rule heads, we show through complexity arguments that such a simplification is infeasible in general for all other connectives. %, even if bodies are restricted to \Luka or \Godel conjunctions. The paper analyzes a translation of FASP programs into satisfiability modulo theories~(SMT), which in general produces quantified formulas because of the minimality of the semantics. Structural properties of many FASP programs allow to eliminate the quantification, or to sensibly reduce the number of quantified variables. Indeed, integrality constraints can replace recursive rules commonly used to force Boolean interpretations, and completion subformulas can guarantee minimality for acyclic programs with atomic heads. Moreover, head cycle free rules can be replaced by shifted subprograms, whose structure depends on the eliminated head connective, so that ordered completion may replace the minimality check if also \Luka disjunction in rule bodies is acyclic. The paper also presents and evaluates a prototype system implementing these translations. To appear in Theory and Practice of Logic Programming (TPLP), Proceedings of ICLP 2015.

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arXiv2014

Anytime Computation of Cautious Consequences in Answer Set Programming

Query answering in Answer Set Programming (ASP) is usually solved by computing (a subset of) the cautious consequences of a logic program. This task is computationally very hard, and there are programs for which computing cautious consequences is not viable in reasonable time. However, current ASP solvers produce the (whole) set of cautious consequences only at the end of their computation. This paper reports on strategies for computing cautious consequences, also introducing anytime algorithms able to produce sound answers during the computation.

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arXiv2014

Semantics and Compilation of Answer Set Programming with Generalized Atoms

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.

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arXiv2014

Preliminary Report on WASP 2.0

Answer Set Programming (ASP) is a declarative programming paradigm. The intrinsic complexity of the evaluation of ASP programs makes the development of more effective and faster systems a challenging research topic. This paper reports on the recent improvements of the ASP solver WASP. WASP is undergoing a refactoring process which will end up in the release of a new and more performant version of the software. In particular the paper focus on the improvements to the core evaluation algorithms working on normal programs. A preliminary experiment on benchmarks from the 3rd ASP competition belonging to the NP class is reported. The previous version of WASP was often not competitive with alternative solutions on this class. The new version of WASP shows a substantial increase in performance.

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arXiv2014

Unfounded Sets and Well-Founded Semantics of Answer Set Programs with Aggregates

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.

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arXiv2013

Properties of Answer Set Programming with Convex Generalized Atoms

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.

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arXiv2013

Translating NP-SPEC into ASP

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.

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arXiv2012

Complexity of super-coherence problems in ASP

Adapting techniques from database theory in order to optimize Answer Set Programming (ASP) systems, and in particular the grounding components of ASP systems, is an important topic in ASP. In recent years, the Magic Set method has received some interest in this setting, and a variant of it, called DMS, has been proposed for ASP. However, this technique has a caveat, because it is not correct (in the sense of being query-equivalent) for all ASP programs. In recent work, a large fragment of ASP programs, referred to as super-coherent programs, has been identified, for which DMS is correct. The fragment contains all programs which possess at least one answer set, no matter which set of facts is added to them. Two open question remained: How complex is it to determine whether a given program is super-coherent? Does the restriction to super-coherent programs limit the problems that can be solved? Especially the first question turned out to be quite difficult to answer precisely. In this paper, we formally prove that deciding whether a propositional program is super-coherent is Π^P_3-complete in the disjunctive case, while it is Π^P_2-complete for normal programs. The hardness proofs are the difficult part in this endeavor: We proceed by characterizing the reductions by the models and reduct models which the ASP programs should have, and then provide instantiations that meet the given specifications. Concerning the second question, we show that all relevant ASP reasoning tasks can be transformed into tasks over super-coherent programs, even though this transformation is more of theoretical than practical interest. To appear in Theory and Practice of Logic Programming (TPLP).

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arXiv2012

Disjunctive Datalog with Existential Quantifiers: Semantics, Decidability, and Complexity Issues

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.

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arXiv2012

Magic Sets for Disjunctive Datalog Programs

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.

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arXiv2011

Team-building with Answer Set Programming in the Gioia-Tauro Seaport

(To appear in Theory and Practice of Logic Programming (TPLP).) The seaport of Gioia Tauro is the largest transshipment terminal of the Mediterranean coast. A crucial management task for the companies operating in the seaport is team building: the problem of properly allocating the available personnel for serving the incoming ships. Teams have to be carefully arranged in order to meet several constraints, such as allocation of the employees with the appropriate skills, fair distribution of the working load, and turnover of the heavy/dangerous roles. This makes team building a hard and expensive task requiring several hours per day of manual preparation. In this paper we present a system based on Answer Set Programming (ASP) for the automatic generation of the teams of employees in the seaport of Gioia Tauro. The system is currently exploited in the Gioia Tauro seaport by ICO BLG, a company specialized in automobile logistics.

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