@article{CabalarFandinnoSchaubetal.2019, author = {Cabalar, Pedro and Fandinno, Jorge and Schaub, Torsten H. and Schellhorn, Sebastian}, title = {Gelfond-Zhang aggregates as propositional formulas}, series = {Artificial intelligence}, volume = {274}, journal = {Artificial intelligence}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0004-3702}, doi = {10.1016/j.artint.2018.10.007}, pages = {26 -- 43}, year = {2019}, abstract = {Answer Set Programming (ASP) has become a popular and widespread paradigm for practical Knowledge Representation thanks to its expressiveness and the available enhancements of its input language. One of such enhancements is the use of aggregates, for which different semantic proposals have been made. In this paper, we show that any ASP aggregate interpreted under Gelfond and Zhang's (GZ) semantics can be replaced (under strong equivalence) by a propositional formula. Restricted to the original GZ syntax, the resulting formula is reducible to a disjunction of conjunctions of literals but the formulation is still applicable even when the syntax is extended to allow for arbitrary formulas (including nested aggregates) in the condition. Once GZ-aggregates are represented as formulas, we establish a formal comparison (in terms of the logic of Here-and-There) to Ferraris' (F) aggregates, which are defined by a different formula translation involving nested implications. In particular, we prove that if we replace an F-aggregate by a GZ-aggregate in a rule head, we do not lose answer sets (although more can be gained). This extends the previously known result that the opposite happens in rule bodies, i.e., replacing a GZ-aggregate by an F-aggregate in the body may yield more answer sets. Finally, we characterize a class of aggregates for which GZ- and F-semantics coincide.}, language = {en} } @misc{AguadoCabalarFandinnoetal.2019, author = {Aguado, Felicidad and Cabalar, Pedro and Fandinno, Jorge and Pearce, David and Perez, Gilberto and Vidal, Concepcion}, title = {Revisiting explicit negation in answer set programming}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {1104}, issn = {1866-8372}, doi = {10.25932/publishup-46969}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-469697}, pages = {908 -- 924}, year = {2019}, abstract = {A common feature in Answer Set Programming is the use of a second negation, stronger than default negation and sometimes called explicit, strong or classical negation. This explicit negation is normally used in front of atoms, rather than allowing its use as a regular operator. In this paper we consider the arbitrary combination of explicit negation with nested expressions, as those defined by Lifschitz, Tang and Turner. We extend the concept of reduct for this new syntax and then prove that it can be captured by an extension of Equilibrium Logic with this second negation. We study some properties of this variant and compare to the already known combination of Equilibrium Logic with Nelson's strong negation.}, language = {en} } @article{GebserSchaub2013, author = {Gebser, Martin and Schaub, Torsten H.}, title = {Tableau calculi for logic programs under answer set semantics}, series = {ACM transactions on computational logic}, volume = {14}, journal = {ACM transactions on computational logic}, number = {2}, publisher = {Association for Computing Machinery}, address = {New York}, issn = {1529-3785}, doi = {10.1145/2480759.2480767}, pages = {40}, year = {2013}, abstract = {We introduce formal proof systems based on tableau methods for analyzing computations in Answer Set Programming (ASP). Our approach furnishes fine-grained instruments for characterizing operations as well as strategies of ASP solvers. The granularity is detailed enough to capture a variety of propagation and choice methods of algorithms used for ASP solving, also incorporating SAT-based and conflict-driven learning approaches to some extent. This provides us with a uniform setting for identifying and comparing fundamental properties of ASP solving approaches. In particular, we investigate their proof complexities and show that the run-times of best-case computations can vary exponentially between different existing ASP solvers. Apart from providing a framework for comparing ASP solving approaches, our characterizations also contribute to their understanding by pinning down the constitutive atomic operations. Furthermore, our framework is flexible enough to integrate new inference patterns, and so to study their relation to existing ones. To this end, we generalize our approach and provide an extensible basis aiming at a modular incorporation of additional language constructs. This is exemplified by augmenting our basic tableau methods with cardinality constraints and disjunctions.}, language = {en} } @article{MileoSchaubMericoetal.2011, author = {Mileo, Alessandra and Schaub, Torsten H. and Merico, Davide and Bisiani, Roberto}, title = {Knowledge-based multi-criteria optimization to support indoor positioning}, series = {Annals of mathematics and artificial intelligence}, volume = {62}, journal = {Annals of mathematics and artificial intelligence}, number = {3-4}, publisher = {Springer}, address = {Dordrecht}, issn = {1012-2443}, doi = {10.1007/s10472-011-9241-2}, pages = {345 -- 370}, year = {2011}, abstract = {Indoor position estimation constitutes a central task in home-based assisted living environments. Such environments often rely on a heterogeneous collection of low-cost sensors whose diversity and lack of precision has to be compensated by advanced techniques for localization and tracking. Although there are well established quantitative methods in robotics and neighboring fields for addressing these problems, they lack advanced knowledge representation and reasoning capacities. Such capabilities are not only useful in dealing with heterogeneous and incomplete information but moreover they allow for a better inclusion of semantic information and more general homecare and patient-related knowledge. We address this problem and investigate how state-of-the-art localization and tracking methods can be combined with Answer Set Programming, as a popular knowledge representation and reasoning formalism. We report upon a case-study and provide a first experimental evaluation of knowledge-based position estimation both in a simulated as well as in a real setting.}, language = {en} } @article{GebserKaminskiSchaub2011, author = {Gebser, Martin and Kaminski, Roland and Schaub, Torsten H.}, title = {Complex optimization in answer set programming}, series = {Theory and practice of logic programming}, volume = {11}, journal = {Theory and practice of logic programming}, number = {3}, publisher = {Cambridge Univ. Press}, address = {New York}, issn = {1471-0684}, doi = {10.1017/S1471068411000329}, pages = {821 -- 839}, year = {2011}, abstract = {Preference handling and optimization are indispensable means for addressing nontrivial applications in Answer Set Programming (ASP). However, their implementation becomes difficult whenever they bring about a significant increase in computational complexity. As a consequence, existing ASP systems do not offer complex optimization capacities, supporting, for instance, inclusion-based minimization or Pareto efficiency. Rather, such complex criteria are typically addressed by resorting to dedicated modeling techniques, like saturation. Unlike the ease of common ASP modeling, however, these techniques are rather involved and hardly usable by ASP laymen. We address this problem by developing a general implementation technique by means of meta-prpogramming, thus reusing existing ASP systems to capture various forms of qualitative preferences among answer sets. In this way, complex preferences and optimization capacities become readily available for ASP applications.}, language = {en} } @phdthesis{Gebser2011, author = {Gebser, Martin}, title = {Proof theory and algorithms for answer set programming}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-55425}, school = {Universit{\"a}t Potsdam}, year = {2011}, abstract = {Answer Set Programming (ASP) is an emerging paradigm for declarative programming, in which a computational problem is specified by a logic program such that particular models, called answer sets, match solutions. ASP faces a growing range of applications, demanding for high-performance tools able to solve complex problems. ASP integrates ideas from a variety of neighboring fields. In particular, automated techniques to search for answer sets are inspired by Boolean Satisfiability (SAT) solving approaches. While the latter have firm proof-theoretic foundations, ASP lacks formal frameworks for characterizing and comparing solving methods. Furthermore, sophisticated search patterns of modern SAT solvers, successfully applied in areas like, e.g., model checking and verification, are not yet established in ASP solving. We address these deficiencies by, for one, providing proof-theoretic frameworks that allow for characterizing, comparing, and analyzing approaches to answer set computation. For another, we devise modern ASP solving algorithms that integrate and extend state-of-the-art techniques for Boolean constraint solving. We thus contribute to the understanding of existing ASP solving approaches and their interconnections as well as to their enhancement by incorporating sophisticated search patterns. The central idea of our approach is to identify atomic as well as composite constituents of a propositional logic program with Boolean variables. This enables us to describe fundamental inference steps, and to selectively combine them in proof-theoretic characterizations of various ASP solving methods. In particular, we show that different concepts of case analyses applied by existing ASP solvers implicate mutual exponential separations regarding their best-case complexities. We also develop a generic proof-theoretic framework amenable to language extensions, and we point out that exponential separations can likewise be obtained due to case analyses on them. We further exploit fundamental inference steps to derive Boolean constraints characterizing answer sets. They enable the conception of ASP solving algorithms including search patterns of modern SAT solvers, while also allowing for direct technology transfers between the areas of ASP and SAT solving. Beyond the search for one answer set of a logic program, we address the enumeration of answer sets and their projections to a subvocabulary, respectively. The algorithms we develop enable repetition-free enumeration in polynomial space without being intrusive, i.e., they do not necessitate any modifications of computations before an answer set is found. Our approach to ASP solving is implemented in clasp, a state-of-the-art Boolean constraint solver that has successfully participated in recent solver competitions. Although we do here not address the implementation techniques of clasp or all of its features, we present the principles of its success in the context of ASP solving.}, language = {en} } @phdthesis{Hecher2021, author = {Hecher, Markus}, title = {Advanced tools and methods for treewidth-based problem solving}, doi = {10.25932/publishup-51251}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-512519}, school = {Universit{\"a}t Potsdam}, pages = {xv, 184}, year = {2021}, abstract = {In the last decades, there was a notable progress in solving the well-known Boolean satisfiability (Sat) problem, which can be witnessed by powerful Sat solvers. One of the reasons why these solvers are so fast are structural properties of instances that are utilized by the solver's interna. This thesis deals with the well-studied structural property treewidth, which measures the closeness of an instance to being a tree. In fact, there are many problems parameterized by treewidth that are solvable in polynomial time in the instance size when parameterized by treewidth. In this work, we study advanced treewidth-based methods and tools for problems in knowledge representation and reasoning (KR). Thereby, we provide means to establish precise runtime results (upper bounds) for canonical problems relevant to KR. Then, we present a new type of problem reduction, which we call decomposition-guided (DG) that allows us to precisely monitor the treewidth when reducing from one problem to another problem. This new reduction type will be the basis for a long-open lower bound result for quantified Boolean formulas and allows us to design a new methodology for establishing runtime lower bounds for problems parameterized by treewidth. Finally, despite these lower bounds, we provide an efficient implementation of algorithms that adhere to treewidth. Our approach finds suitable abstractions of instances, which are subsequently refined in a recursive fashion, and it uses Sat solvers for solving subproblems. It turns out that our resulting solver is quite competitive for two canonical counting problems related to Sat.}, language = {en} } @article{GebserMarateaRicca2020, author = {Gebser, Martin and Maratea, Marco and Ricca, Francesco}, title = {The Seventh Answer Set Programming Competition}, series = {Theory and practice of logic programming}, volume = {20}, journal = {Theory and practice of logic programming}, number = {2}, publisher = {Cambridge Univ. Press}, address = {Cambridge [u.a.]}, issn = {1471-0684}, doi = {10.1017/S1471068419000061}, pages = {176 -- 204}, year = {2020}, abstract = {Answer Set Programming (ASP) is a prominent knowledge representation language with roots in logic programming and non-monotonic reasoning. Biennial ASP competitions are organized in order to furnish challenging benchmark collections and assess the advancement of the state of the art in ASP solving. In this paper, we report on the design and results of the Seventh ASP Competition, jointly organized by the University of Calabria (Italy), the University of Genova (Italy), and the University of Potsdam (Germany), in affiliation with the 14th International Conference on Logic Programming and Non-Monotonic Reasoning (LPNMR 2017).}, language = {en} } @phdthesis{Kaminski2023, author = {Kaminski, Roland}, title = {Complex reasoning with answer set programming}, school = {Universit{\"a}t Potsdam}, pages = {301}, year = {2023}, abstract = {Answer Set Programming (ASP) allows us to address knowledge-intensive search and optimization problems in a declarative way due to its integrated modeling, grounding, and solving workflow. A problem is modeled using a rule based language and then grounded and solved. Solving results in a set of stable models that correspond to solutions of the modeled problem. In this thesis, we present the design and implementation of the clingo system---perhaps, the most widely used ASP system. It features a rich modeling language originating from the field of knowledge representation and reasoning, efficient grounding algorithms based on database evaluation techniques, and high performance solving algorithms based on Boolean satisfiability (SAT) solving technology. The contributions of this thesis lie in the design of the modeling language, the design and implementation of the grounding algorithms, and the design and implementation of an Application Programmable Interface (API) facilitating the use of ASP in real world applications and the implementation of complex forms of reasoning beyond the traditional ASP workflow.}, language = {en} } @article{CabalarFandinnoGareaetal.2020, author = {Cabalar, Pedro and Fandinno, Jorge and Garea, Javier and Romero, Javier and Schaub, Torsten H.}, title = {Eclingo}, series = {Theory and practice of logic programming}, volume = {20}, journal = {Theory and practice of logic programming}, number = {6}, publisher = {Cambridge Univ. Press}, address = {New York}, issn = {1471-0684}, doi = {10.1017/S1471068420000228}, pages = {834 -- 847}, year = {2020}, abstract = {We describe eclingo, a solver for epistemic logic programs under Gelfond 1991 semantics built upon the Answer Set Programming system clingo. The input language of eclingo uses the syntax extension capabilities of clingo to define subjective literals that, as usual in epistemic logic programs, allow for checking the truth of a regular literal in all or in some of the answer sets of a program. The eclingo solving process follows a guess and check strategy. It first generates potential truth values for subjective literals and, in a second step, it checks the obtained result with respect to the cautious and brave consequences of the program. This process is implemented using the multi-shot functionalities of clingo. We have also implemented some optimisations, aiming at reducing the search space and, therefore, increasing eclingo 's efficiency in some scenarios. Finally, we compare the efficiency of eclingo with two state-of-the-art solvers for epistemic logic programs on a pair of benchmark scenarios and show that eclingo generally outperforms their obtained results.}, language = {en} }