@article{GebserSchaub2013,
  author    = {Gebser, Martin and Schaub, Torsten},
  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{OstrowskiSchaub2012,
  author    = {Ostrowski, Max and Schaub, Torsten},
  title     = {ASP modulo CSP The clingcon system},
  series = {Theory and practice of logic programming},
  volume    = {12},
  journal   = {Theory and practice of logic programming},
  publisher = {Cambridge Univ. Press},
  address   = {New York},
  issn      = {1471-0684},
  doi       = {10.1017/S1471068412000142},
  pages     = {485 -- 503},
  year      = {2012},
  abstract  = {We present the hybrid ASP solver clingcon, combining the simple modeling language and the high performance Boolean solving capacities of Answer Set Programming (ASP) with techniques for using non-Boolean constraints from the area of Constraint Programming (CP). The new clingcon system features an extended syntax supporting global constraints and optimize statements for constraint variables. The major technical innovation improves the interaction between ASP and CP solver through elaborated learning techniques based on irreducible inconsistent sets. A broad empirical evaluation shows that these techniques yield a performance improvement of an order of magnitude.},
  language  = {en}
}
@article{BrewkaEllmauthalerKernIsberneretal.2018,
  author    = {Brewka, Gerhard and Ellmauthaler, Stefan and Kern-Isberner, Gabriele and Obermeier, Philipp and Ostrowski, Max and Romero, Javier and Schaub, Torsten and Schieweck, Steffen},
  title     = {Advanced solving technology for dynamic and reactive applications},
  series = {K{\"u}nstliche Intelligenz},
  volume    = {32},
  journal   = {K{\"u}nstliche Intelligenz},
  number    = {2-3},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {0933-1875},
  doi       = {10.1007/s13218-018-0538-8},
  pages     = {199 -- 200},
  year      = {2018},
  language  = {en}
}
@article{GebserSchaubThiele2007,
  author    = {Gebser, Martin and Schaub, Torsten and Thiele, Sven},
  title     = {GrinGo : a new grounder for answer set programming},
  isbn      = {978-3-540- 72199-4},
  year      = {2007},
  language  = {en}
}
@article{BesnardSchaub1995,
  author    = {Besnard, Philippe and Schaub, Torsten},
  title     = {An approach to context-based default reasoning},
  issn      = {0169-2968},
  year      = {1995},
  language  = {en}
}
@phdthesis{Lindauer2014,
  author    = {Lindauer, T. Marius},
  title     = {Algorithm selection, scheduling and configuration of Boolean constraint solvers},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-71260},
  school      = {Universit{\"a}t Potsdam},
  pages     = {ii, 130},
  year      = {2014},
  abstract  = {Boolean constraint solving technology has made tremendous progress over the last decade, leading to industrial-strength solvers, for example, in the areas of answer set programming (ASP), the constraint satisfaction problem (CSP), propositional satisfiability (SAT) and satisfiability of quantified Boolean formulas (QBF). However, in all these areas, there exist multiple solving strategies that work well on different applications; no strategy dominates all other strategies. Therefore, no individual solver shows robust state-of-the-art performance in all kinds of applications. Additionally, the question arises how to choose a well-performing solving strategy for a given application; this is a challenging question even for solver and domain experts. One way to address this issue is the use of portfolio solvers, that is, a set of different solvers or solver configurations. We present three new automatic portfolio methods: (i) automatic construction of parallel portfolio solvers (ACPP) via algorithm configuration,(ii) solving the \$NP\$-hard problem of finding effective algorithm schedules with Answer Set Programming (aspeed), and (iii) a flexible algorithm selection framework (claspfolio2) allowing for fair comparison of different selection approaches. All three methods show improved performance and robustness in comparison to individual solvers on heterogeneous instance sets from many different applications. Since parallel solvers are important to effectively solve hard problems on parallel computation systems (e.g., multi-core processors), we extend all three approaches to be effectively applicable in parallel settings. We conducted extensive experimental studies different instance sets from ASP, CSP, MAXSAT, Operation Research (OR), SAT and QBF that indicate an improvement in the state-of-the-art solving heterogeneous instance sets. Last but not least, from our experimental studies, we deduce practical advice regarding the question when to apply which of our methods.},
  language  = {en}
}
@article{DelgrandeLiuSchaubetal.2006,
  author    = {Delgrande, James Patrick and Liu, Daphne H. and Schaub, Torsten and Thiele, Sven},
  title     = {COBA 2.0 : a consistency-based belief change system},
  year      = {2006},
  language  = {en}
}
@article{NicolasSchaub1998,
  author    = {Nicolas, Pascal and Schaub, Torsten},
  title     = {Un cadre g{\´e}n{\´e}ral pour l'interrogation automatique en logiques des d{\´e}fauts},
  year      = {1998},
  language  = {fr}
}
@article{LindauerHoosHutteretal.2015,
  author    = {Lindauer, Marius and Hoos, Holger H. and Hutter, Frank and Schaub, Torsten},
  title     = {An automatically configured algorithm selector},
  series = {The journal of artificial intelligence research},
  volume    = {53},
  journal   = {The journal of artificial intelligence research},
  publisher = {AI Access Foundation},
  address   = {Marina del Rey},
  issn      = {1076-9757},
  pages     = {745 -- 778},
  year      = {2015},
  abstract  = {Algorithm selection (AS) techniques - which involve choosing from a set of algorithms the one expected to solve a given problem instance most efficiently - have substantially improved the state of the art in solving many prominent AI problems, such as SAT, CSP, ASP, MAXSAT and QBF. Although several AS procedures have been introduced, not too surprisingly, none of them dominates all others across all AS scenarios. Furthermore, these procedures have parameters whose optimal values vary across AS scenarios. This holds specifically for the machine learning techniques that form the core of current AS procedures, and for their hyperparameters. Therefore, to successfully apply AS to new problems, algorithms and benchmark sets, two questions need to be answered: (i) how to select an AS approach and (ii) how to set its parameters effectively. We address both of these problems simultaneously by using automated algorithm configuration. Specifically, we demonstrate that we can automatically configure claspfolio 2, which implements a large variety of different AS approaches and their respective parameters in a single, highly-parameterized algorithm framework. Our approach, dubbed AutoFolio, allows researchers and practitioners across a broad range of applications to exploit the combined power of many different AS methods. We demonstrate AutoFolio can significantly improve the performance of claspfolio 2 on 8 out of the 13 scenarios from the Algorithm Selection Library, leads to new state-of-the-art algorithm selectors for 7 of these scenarios, and matches state-of-the-art performance (statistically) on all other scenarios. Compared to the best single algorithm for each AS scenario, AutoFolio achieves average speedup factors between 1.3 and 15.4.},
  language  = {en}
}
@article{HoosLindauerSchaub2014,
  author    = {Hoos, Holger and Lindauer, Marius and Schaub, Torsten},
  title     = {claspfolio 2},
  series = {Theory and practice of logic programming},
  volume    = {14},
  journal   = {Theory and practice of logic programming},
  publisher = {Cambridge Univ. Press},
  address   = {New York},
  issn      = {1471-0684},
  doi       = {10.1017/S1471068414000210},
  pages     = {569 -- 585},
  year      = {2014},
  abstract  = {Building on the award-winning, portfolio-based ASP solver claspfolio, we present claspfolio 2, a modular and open solver architecture that integrates several different portfolio-based algorithm selection approaches and techniques. The claspfolio 2 solver framework supports various feature generators, solver selection approaches, solver portfolios, as well as solver-schedule-based pre-solving techniques. The default configuration of claspfolio 2 relies on a light-weight version of the ASP solver clasp to generate static and dynamic instance features. The flexible open design of claspfolio 2 is a distinguishing factor even beyond ASP. As such, it provides a unique framework for comparing and combining existing portfolio-based algorithm selection approaches and techniques in a single, unified framework. Taking advantage of this, we conducted an extensive experimental study to assess the impact of different feature sets, selection approaches and base solver portfolios. In addition to gaining substantial insights into the utility of the various approaches and techniques, we identified a default configuration of claspfolio 2 that achieves substantial performance gains not only over clasp's default configuration and the earlier version of claspfolio, but also over manually tuned configurations of clasp.},
  language  = {en}
}
@article{TranPontelliBalduccinietal.2022,
  author    = {Tran, Son Cao and Pontelli, Enrico and Balduccini, Marcello and Schaub, Torsten},
  title     = {Answer set planning},
  series = {Theory and practice of logic programming},
  journal   = {Theory and practice of logic programming},
  publisher = {Cambridge University Press},
  address   = {New York},
  issn      = {1471-0684},
  doi       = {10.1017/S1471068422000072},
  pages     = {73},
  year      = {2022},
  abstract  = {Answer Set Planning refers to the use of Answer Set Programming (ASP) to compute plans, that is, solutions to planning problems, that transform a given state of the world to another state. The development of efficient and scalable answer set solvers has provided a significant boost to the development of ASP-based planning systems. This paper surveys the progress made during the last two and a half decades in the area of answer set planning, from its foundations to its use in challenging planning domains. The survey explores the advantages and disadvantages of answer set planning. It also discusses typical applications of answer set planning and presents a set of challenges for future research.},
  language  = {en}
}
@article{BrainGebserPuehreretal.2007,
  author    = {Brain, Martin and Gebser, Martin and P{\"u}hrer, J{\"o}rg and Schaub, Torsten and Tompits, Hans and Woltran, Stefan},
  title     = {Debugging ASP programs by means of ASP},
  isbn      = {978-3-540- 72199-4},
  year      = {2007},
  language  = {en}
}
@article{SchaubWoltran2018,
  author    = {Schaub, Torsten and Woltran, Stefan},
  title     = {Answer set programming unleashed!},
  series = {K{\"u}nstliche Intelligenz},
  volume    = {32},
  journal   = {K{\"u}nstliche Intelligenz},
  number    = {2-3},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {0933-1875},
  doi       = {10.1007/s13218-018-0550-z},
  pages     = {105 -- 108},
  year      = {2018},
  abstract  = {Answer Set Programming faces an increasing popularity for problem solving in various domains. While its modeling language allows us to express many complex problems in an easy way, its solving technology enables their effective resolution. In what follows, we detail some of the key factors of its success. Answer Set Programming [ASP; Brewka et al. Commun ACM 54(12):92-103, (2011)] is seeing a rapid proliferation in academia and industry due to its easy and flexible way to model and solve knowledge-intense combinatorial (optimization) problems. To this end, ASP offers a high-level modeling language paired with high-performance solving technology. As a result, ASP systems provide out-off-the-box, general-purpose search engines that allow for enumerating (optimal) solutions. They are represented as answer sets, each being a set of atoms representing a solution. The declarative approach of ASP allows a user to concentrate on a problem's specification rather than the computational means to solve it. This makes ASP a prime candidate for rapid prototyping and an attractive tool for teaching key AI techniques since complex problems can be expressed in a succinct and elaboration tolerant way. This is eased by the tuning of ASP's modeling language to knowledge representation and reasoning (KRR). The resulting impact is nicely reflected by a growing range of successful applications of ASP [Erdem et al. AI Mag 37(3):53-68, 2016; Falkner et al. Industrial applications of answer set programming. K++nstliche Intelligenz (2018)]},
  language  = {en}
}
@misc{BrewkaSchaubWoltran2018,
  author    = {Brewka, Gerhard and Schaub, Torsten and Woltran, Stefan},
  title     = {Interview with Gerhard Brewka},
  series = {K{\"u}nstliche Intelligenz},
  volume    = {32},
  journal   = {K{\"u}nstliche Intelligenz},
  number    = {2-3},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {0933-1875},
  doi       = {10.1007/s13218-018-0549-5},
  pages     = {219 -- 221},
  year      = {2018},
  abstract  = {This interview with Gerhard Brewka was conducted by correspondance in May 2018. The question set was compiled by Torsten Schaub and Stefan Woltran.},
  language  = {en}
}
@misc{SchaubWoltran2018,
  author    = {Schaub, Torsten and Woltran, Stefan},
  title     = {Special issue on answer set programming},
  series = {K{\"u}nstliche Intelligenz},
  volume    = {32},
  journal   = {K{\"u}nstliche Intelligenz},
  number    = {2-3},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {0933-1875},
  doi       = {10.1007/s13218-018-0554-8},
  pages     = {101 -- 103},
  year      = {2018},
  language  = {en}
}
@misc{SchaepersNiemuellerLakemeyeretal.2018,
  author    = {Sch{\"a}pers, Bj{\"o}rn and Niemueller, Tim and Lakemeyer, Gerhard and Gebser, Martin and Schaub, Torsten},
  title     = {ASP-Based Time-Bounded Planning for Logistics Robots},
  series = {Twenty-Eighth International Conference on Automated Planning and Scheduling (ICAPS 2018)},
  journal   = {Twenty-Eighth International Conference on Automated Planning and Scheduling (ICAPS 2018)},
  publisher = {ASSOC Association for the Advancement of Artificial Intelligence},
  address   = {Palo Alto},
  issn      = {2334-0835},
  pages     = {509 -- 517},
  year      = {2018},
  abstract  = {Manufacturing industries are undergoing a major paradigm shift towards more autonomy. Automated planning and scheduling then becomes a necessity. The Planning and Execution Competition for Logistics Robots in Simulation held at ICAPS is based on this scenario and provides an interesting testbed. However, the posed problem is challenging as also demonstrated by the somewhat weak results in 2017. The domain requires temporal reasoning and dealing with uncertainty. We propose a novel planning system based on Answer Set Programming and the Clingo solver to tackle these problems and incentivize robot cooperation. Our results show a significant performance improvement, both, in terms of lowering computational requirements and better game metrics.},
  language  = {en}
}
@misc{BosserCabalarDieguezetal.2018,
  author    = {Bosser, Anne-Gwenn and Cabalar, Pedro and Dieguez, Martin and Schaub, Torsten},
  title     = {Introducing temporal stable models for linear dynamic logic},
  series = {16th International Conference on Principles of Knowledge Representation and Reasoning},
  journal   = {16th International Conference on Principles of Knowledge Representation and Reasoning},
  publisher = {ASSOC Association for the Advancement of Artificial Intelligence},
  address   = {Palo Alto},
  pages     = {12 -- 21},
  year      = {2018},
  abstract  = {We propose a new temporal extension of the logic of Here-and-There (HT) and its equilibria obtained by combining it with dynamic logic over (linear) traces. Unlike previous temporal extensions of HT based on linear temporal logic, the dynamic logic features allow us to reason about the composition of actions. For instance, this can be used to exercise fine grained control when planning in robotics, as exemplified by GOLOG. In this paper, we lay the foundations of our approach, and refer to it as Linear Dynamic Equilibrium Logic, or simply DEL. We start by developing the formal framework of DEL and provide relevant characteristic results. Among them, we elaborate upon the relationships to traditional linear dynamic logic and previous temporal extensions of HT.},
  language  = {en}
}
@article{CabalarFandinoGareaetal.2020,
  author    = {Cabalar, Pedro and Fandi{\~n}o, Jorge and Garea, Javier and Romero, Javier and Schaub, Torsten},
  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}
}
@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{MileoSchaubMericoetal.2011,
  author    = {Mileo, Alessandra and Schaub, Torsten 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{FandinoLifschitzLuehneetal.2020,
  author    = {Fandi{\~n}o, Jorge and Lifschitz, Vladimir and L{\"u}hne, Patrick and Schaub, Torsten},
  title     = {Verifying tight logic programs with Anthem and Vampire},
  series = {Theory and practice of logic programming},
  volume    = {20},
  journal   = {Theory and practice of logic programming},
  number    = {5},
  publisher = {Cambridge Univ. Press},
  address   = {Cambridge [u.a.]},
  issn      = {1471-0684},
  doi       = {10.1017/S1471068420000344},
  pages     = {735 -- 750},
  year      = {2020},
  abstract  = {This paper continues the line of research aimed at investigating the relationship between logic programs and first-order theories. We extend the definition of program completion to programs with input and output in a subset of the input language of the ASP grounder gringo, study the relationship between stable models and completion in this context, and describe preliminary experiments with the use of two software tools, anthem and vampire, for verifying the correctness of programs with input and output. Proofs of theorems are based on a lemma that relates the semantics of programs studied in this paper to stable models of first-order formulas.},
  language  = {en}
}
@article{DelgrandeSchaub2000,
  author    = {Delgrande, James Patrick and Schaub, Torsten},
  title     = {A consistency-based model for belief change: preliminary report},
  year      = {2000},
  language  = {en}
}
@article{DelgrandeSchaub2000,
  author    = {Delgrande, James Patrick and Schaub, Torsten},
  title     = {The role of default logic in knowledge representation},
  isbn      = {0-7923-7224-7},
  year      = {2000},
  language  = {en}
}
@article{DelgrandeSchaub2001,
  author    = {Delgrande, James Patrick and Schaub, Torsten},
  title     = {How to reason credulously and skeptically within a single extension},
  year      = {2001},
  language  = {en}
}
@article{SchaubWang2001,
  author    = {Schaub, Torsten and Wang, Kewen},
  title     = {A comparative study of logic programs with preference},
  year      = {2001},
  language  = {en}
}
@article{DelgrandeLangSchaub2007,
  author    = {Delgrande, James Patrick and Lang, J{\´e}r{\^o}me and Schaub, Torsten},
  title     = {Belief change based on global minimisation},
  year      = {2007},
  language  = {en}
}
@phdthesis{Ostrowski2018,
  author    = {Ostrowski, Max},
  title     = {Modern constraint answer set solving},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-407799},
  school      = {Universit{\"a}t Potsdam},
  pages     = {135},
  year      = {2018},
  abstract  = {Answer Set Programming (ASP) is a declarative problem solving approach, combining a rich yet simple modeling language with high-performance solving capabilities. Although this has already resulted in various applications, certain aspects of such applications are more naturally modeled using variables over finite domains, for accounting for resources, fine timings, coordinates, or functions. Our goal is thus to extend ASP with constraints over integers while preserving its declarative nature. This allows for fast prototyping and elaboration tolerant problem descriptions of resource related applications. The resulting paradigm is called Constraint Answer Set Programming (CASP). We present three different approaches for solving CASP problems. The first one, a lazy, modular approach combines an ASP solver with an external system for handling constraints. This approach has the advantage that two state of the art technologies work hand in hand to solve the problem, each concentrating on its part of the problem. The drawback is that inter-constraint dependencies cannot be communicated back to the ASP solver, impeding its learning algorithm. The second approach translates all constraints to ASP. Using the appropriate encoding techniques, this results in a very fast, monolithic system. Unfortunately, due to the large, explicit representation of constraints and variables, translation techniques are restricted to small and mid-sized domains. The third approach merges the lazy and the translational approach, combining the strength of both while removing their weaknesses. To this end, we enhance the dedicated learning techniques of an ASP solver with the inferences of the translating approach in a lazy way. That is, the important knowledge is only made explicit when needed. By using state of the art techniques from neighboring fields, we provide ways to tackle real world, industrial size problems. By extending CASP to reactive solving, we open up new application areas such as online planning with continuous domains and durations.},
  language  = {en}
}
@article{DelgrandeSchaub2005,
  author    = {Delgrande, James Patrick and Schaub, Torsten},
  title     = {Expressing default logic variants in default logic},
  issn      = {0955-792X},
  year      = {2005},
  abstract  = {Reiter's default logic is one of the best known and most studied of the approaches to nonmonotonic reasoning. Several variants of default logic have subsequently been proposed to give systems with properties differing from the original. In this paper, we examine the relationship between default logic and its major variants. We accomplish this by translating a default theory under a variant interpretation into a second default theory, under the original Reiter semantics, wherein the variant interpretation is respected. That is, in each case we show that, given an extension of a translated theory, one may extract an extension of the original variant default logic theory. We show how constrained, rational, justified, and cumulative default logic can be expressed in Reiter's default logic. As well, we show how Reiter's default logic can be expressed in rational default logic. From this, we suggest that any such variant can be similarly treated. Consequently, we provide a unification of default logics, showing how the original formulation of default logic may express its variants. Moreover, the translations clearly express the relationships between alternative approaches to default logic. The translations themselves are shown to generally have good properties. Thus, in at least a theoretical sense, we show that these variants are in a sense superfluous, in that for any of these variants of default logic, we can exactly mimic the behaviour of a variant in standard default logic. As well, the translations lend insight into means of classifying the expressive power of default logic variants; specifically we suggest that the property of semi-monotonicity represents a division with respect to expressibility, whereas regularity and cumulativity do not},
  language  = {en}
}
@article{DelgrandeSchaub2004,
  author    = {Delgrande, James Patrick and Schaub, Torsten},
  title     = {Reasoning with sets of preferences in default logic},
  issn      = {0824-7935},
  year      = {2004},
  abstract  = {We present a general approach for representing and reasoning with sets of defaults in default logic, focusing on reasoning about preferences among sets of defaults. First, we consider how to control the application of a set of defaults so that either all apply (if possible) or none do (if not). From this, an approach to dealing with preferences among sets of default rules is developed. We begin with an ordered default theory, consisting of a standard default theory, but with possible preferences on sets of rules. This theory is transformed into a second, standard default theory wherein the preferences are respected. The approach differs from other work, in that we obtain standard default theories and do not rely on prioritized versions of default logic. In practical terms this means we can immediately use existing default logic theorem provers for an implementation. Also, we directly generate just those extensions containing the most preferred applied rules; in contrast, most previous approaches generate all extensions, then select the most preferred. In a major application of the approach, we show how semimonotonic default theories can be encoded so that reasoning can be carried out at the object level. With this, we can reason about default extensions from within the framework of a standard default logic. Hence one can encode notions such as skeptical and credulous conclusions, and can reason about such conclusions within a single extension},
  language  = {en}
}
@article{DelgrandeSchaubTompitsetal.2004,
  author    = {Delgrande, James Patrick and Schaub, Torsten and Tompits, Hans and Wang, Kewen},
  title     = {A classification and survey of preference handling approchaches in nonmonotonic reasoning},
  issn      = {0824-7935},
  year      = {2004},
  abstract  = {In recent years, there has been a large amount of disparate work concerning the representation and reasoning with qualitative preferential information by means of approaches to nonmonotonic reasoning. Given the variety of underlying systems, assumptions, motivations, and intuitions, it is difficult to compare or relate one approach with another. Here, we present an overview and classification for approaches to dealing with preference. A set of criteria for classifying approaches is given, followed by a set of desiderata that an approach might be expected to satisfy. A comprehensive set of approaches is subsequently given and classified with respect to these sets of underlying principles},
  language  = {en}
}
@article{BorchertAngerSchaubetal.2004,
  author    = {Borchert, P. and Anger, Christian and Schaub, Torsten and Truszczynski, M.},
  title     = {Towards systematic benchmarking in answer set programming : the dagstuhl initiative},
  isbn      = {3-540- 20721-x},
  year      = {2004},
  language  = {en}
}
@article{DelgrandeSchaub2004,
  author    = {Delgrande, James Patrick and Schaub, Torsten},
  title     = {Consistency-based approaches to merging knowledge based : preliminary report},
  isbn      = {92-990021-0-X},
  year      = {2004},
  language  = {en}
}
@article{KonczakLinkeSchaub2004,
  author    = {Konczak, Kathrin and Linke, Thomas and Schaub, Torsten},
  title     = {Graphs and cologings for answer set programming : adridged report},
  isbn      = {3-540- 20721-x},
  year      = {2004},
  language  = {en}
}
@article{FloeterSelbigSchaub2004,
  author    = {Fl{\"o}ter, Andr{\´e} and Selbig, Joachim and Schaub, Torsten},
  title     = {Finding metabolic pathways in decision forests},
  isbn      = {3-540-23221-4},
  year      = {2004},
  language  = {en}
}
@article{BoeselLinkeSchaub2004,
  author    = {Boesel, Andreas and Linke, Thomas and Schaub, Torsten},
  title     = {Profiling answer set programming : the visualization component of the noMoRe System},
  isbn      = {3-540-23242-7},
  year      = {2004},
  language  = {en}
}
@article{DelgrandeSchaubTompits2004,
  author    = {Delgrande, James Patrick and Schaub, Torsten and Tompits, Hans},
  title     = {Domain-specific preference for causal reasoning and planning},
  isbn      = {1-577-35201-7},
  year      = {2004},
  language  = {en}
}
@article{DelgrandeSchaub2004,
  author    = {Delgrande, James Patrick and Schaub, Torsten},
  title     = {Two approaches to merging knowledge bases},
  isbn      = {3-540-23242-7},
  year      = {2004},
  language  = {en}
}
@article{DelgrandeSchaubTompitsetal.2002,
  author    = {Delgrande, James Patrick and Schaub, Torsten and Tompits, Hans and Wang, Kewen},
  title     = {Towards a classification of preference handling approaches in nonmonotonic reasoning},
  isbn      = {1-577-35166-5},
  year      = {2002},
  language  = {en}
}
@article{DelgrandeSchaubTompitsetal.2001,
  author    = {Delgrande, James Patrick and Schaub, Torsten and Tompits, Hans and Woltran, Stefan},
  title     = {On computing solutions to belief change scenarios},
  isbn      = {3-540- 42464-4},
  year      = {2001},
  language  = {en}
}
@article{DelgrandeSchaub2001,
  author    = {Delgrande, James Patrick and Schaub, Torsten},
  title     = {How to reason credulously and skeptically within a single extension.},
  isbn      = {3-540- 42464-4},
  year      = {2001},
  language  = {en}
}
@article{SchaubWang2001,
  author    = {Schaub, Torsten and Wang, Kewen},
  title     = {A comparative study of logic programs with preference},
  isbn      = {1-558-60777-3},
  issn      = {1045-0823},
  year      = {2001},
  language  = {en}
}
@article{DelgrandeSchaubTompits2001,
  author    = {Delgrande, James Patrick and Schaub, Torsten and Tompits, Hans},
  title     = {A generic compiler for ordered logic programs},
  isbn      = {3-540-42593-4},
  year      = {2001},
  language  = {en}
}
@article{PearceSarsakovSchaubetal.2002,
  author    = {Pearce, David and Sarsakov, Vladimir and Schaub, Torsten and Tompits, Hans and Woltran, Stefan},
  title     = {A polynomial translation of logic programs with nested expressions into disjunctive logic programs : preliminary report},
  year      = {2002},
  language  = {en}
}
@article{BesnardMercerSchaub2002,
  author    = {Besnard, Philippe and Mercer, Robert E. and Schaub, Torsten},
  title     = {Optimality Theory via Default Logic},
  year      = {2002},
  language  = {en}
}
@article{LinkeSchaub2000,
  author    = {Linke, Thomas and Schaub, Torsten},
  title     = {Alternative foundations for Reiter's default logic.},
  issn      = {0004-3702},
  year      = {2000},
  language  = {en}
}
@book{OPUS4-18498,
  title     = {Proceedings of the Fifth Dutch German Workshop on Nonmonotonic Reasoning Techniques and their Applications, DGNMR'2001, Potsdam, 4. - 6. April 2001},
  editor    = {Brewka, Gerhard and Witteveen, Cees and Schaub, Torsten},
  address   = {Potsdam},
  year      = {2001},
  language  = {en}
}
@article{VolkmannLinkeWaschulziketal.1998,
  author    = {Volkmann, Gerald and Linke, Thomas and Waschulzik, Thomas and Ohmes, Rick and Schaub, Torsten and Wischnewsky, M.},
  title     = {HExProSA - ein hybrides Expertensystem zur Prozeßkontrolle und St{\"o}rfallanalyse von Abwasserbehandlungsanlagen : Erfahrungen bei der Evaluierung eines Prototypen},
  year      = {1998},
  language  = {de}
}
@article{BenhammadiNicolasSchaub1998,
  author    = {Benhammadi, Farid and Nicolas, Pascal and Schaub, Torsten},
  title     = {Extension calculus and query answering in prioritized default logic},
  isbn      = {3-540- 64993-X},
  year      = {1998},
  language  = {en}
}
@article{BenhammadiNicolasSchaub1998,
  author    = {Benhammadi, Farid and Nicolas, Pascal and Schaub, Torsten},
  title     = {Extension calculus and query answering in prioritized default logic},
  isbn      = {3-540-64993-X},
  year      = {1998},
  language  = {en}
}
@article{DelgrandeSchaub1998,
  author    = {Delgrande, James Patrick and Schaub, Torsten},
  title     = {Reasoning with sets of preferences in default logic},
  isbn      = {3-540- 65271-x},
  year      = {1998},
  language  = {en}
}
@article{BibelBrueningOttenetal.1998,
  author    = {Bibel, Wolfgang and Br{\"u}ning, Stefan and Otten, Jens and Rath, Thomas and Schaub, Torsten},
  title     = {Compressions and extensions},
  year      = {1998},
  language  = {en}
}
@article{BesnardSchaub1998,
  author    = {Besnard, Philippe and Schaub, Torsten},
  title     = {Characterization of non-monotone non-constructive systems},
  issn      = {1012-2443},
  year      = {1998},
  language  = {en}
}
@article{BesnardSchaub1998,
  author    = {Besnard, Philippe and Schaub, Torsten},
  title     = {Signed systems for paraconsistent reasoning},
  issn      = {0168-7433},
  year      = {1998},
  language  = {en}
}
@article{SchaubBruening1998,
  author    = {Schaub, Torsten and Br{\"u}ning, Stefan},
  title     = {Prolog technology for default reasoning : proof theory and compilation techniques},
  year      = {1998},
  language  = {en}
}
@article{Schaub1998,
  author    = {Schaub, Torsten},
  title     = {The family of default logics},
  year      = {1998},
  language  = {en}
}
@article{DelgrandeSchaubTompitsetal.2013,
  author    = {Delgrande, James and Schaub, Torsten and Tompits, Hans and Woltran, Stefan},
  title     = {A model-theoretic approach to belief change in answer set programming},
  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       = {10.1145/2480759.2480766},
  pages     = {46},
  year      = {2013},
  abstract  = {We address the problem of belief change in (nonmonotonic) logic programming under answer set semantics. Our formal techniques are analogous to those of distance-based belief revision in propositional logic. In particular, we build upon the model theory of logic programs furnished by SE interpretations, where an SE interpretation is a model of a logic program in the same way that a classical interpretation is a model of a propositional formula. Hence we extend techniques from the area of belief revision based on distance between models to belief change in logic programs. We first consider belief revision: for logic programs P and Q, the goal is to determine a program R that corresponds to the revision of P by Q, denoted P * Q. We investigate several operators, including (logic program) expansion and two revision operators based on the distance between the SE models of logic programs. It proves to be the case that expansion is an interesting operator in its own right, unlike in classical belief revision where it is relatively uninteresting. Expansion and revision are shown to satisfy a suite of interesting properties; in particular, our revision operators satisfy all or nearly all of the AGM postulates for revision. We next consider approaches for merging a set of logic programs, P-1,...,P-n. Again, our formal techniques are based on notions of relative distance between the SE models of the logic programs. Two approaches are examined. The first informally selects for each program P-i those models of P-i that vary the least from models of the other programs. The second approach informally selects those models of a program P-0 that are closest to the models of programs P-1,...,P-n. In this case, P-0 can be thought of as a set of database integrity constraints. We examine these operators with regards to how they satisfy relevant postulate sets. Last, we present encodings for computing the revision as well as the merging of logic programs within the same logic programming framework. This gives rise to a direct implementation of our approach in terms of off-the-shelf answer set solvers. These encodings also reflect the fact that our change operators do not increase the complexity of the base formalism.},
  language  = {en}
}
@article{DelgrandeSchaubTompits2007,
  author    = {Delgrande, James Patrick and Schaub, Torsten and Tompits, Hans},
  title     = {A general framework for expressing preferences in causal reasoning and planning},
  issn      = {0955-792X},
  doi       = {10.1093/logcom/exm046},
  year      = {2007},
  abstract  = {We consider the problem of representing arbitrary preferences in causal reasoning and planning systems. In planning, a preference may be seen as a goal or constraint that is desirable, but not necessary, to satisfy. To begin, we define a very general query language for histories, or interleaved sequences of world states and actions. Based on this, we specify a second language in which preferences are defined. A single preference defines a binary relation on histories, indicating that one history is preferred to the other. From this, one can define global preference orderings on the set of histories, the maximal elements of which are the preferred histories. The approach is very general and flexible; thus it constitutes a base language in terms of which higher-level preferences may be defined. To this end, we investigate two fundamental types of preferences that we call choice and temporal preferences. We consider concrete strategies for these types of preferences and encode them in terms of our framework. We suggest how to express aggregates in the approach, allowing, e.g. the expression of a preference for histories with lowest total action costs. Last, our approach can be used to express other approaches and so serves as a common framework in which such approaches can be expressed and compared. We illustrate this by indicating how an approach due to Son and Pontelli can be encoded in our approach, as well as the language PDDL3.},
  language  = {en}
}
@article{GebserSchaubThieleetal.2011,
  author    = {Gebser, Martin and Schaub, Torsten and Thiele, Sven and Veber, Philippe},
  title     = {Detecting inconsistencies in large biological networks with answer set programming},
  series = {Theory and practice of logic programming},
  volume    = {11},
  journal   = {Theory and practice of logic programming},
  number    = {5-6},
  publisher = {Cambridge Univ. Press},
  address   = {New York},
  issn      = {1471-0684},
  doi       = {10.1017/S1471068410000554},
  pages     = {323 -- 360},
  year      = {2011},
  abstract  = {We introduce an approach to detecting inconsistencies in large biological networks by using answer set programming. To this end, we build upon a recently proposed notion of consistency between biochemical/genetic reactions and high-throughput profiles of cell activity. We then present an approach based on answer set programming to check the consistency of large-scale data sets. Moreover, we extend this methodology to provide explanations for inconsistencies by determining minimal representations of conflicts. In practice, this can be used to identify unreliable data or to indicate missing reactions.},
  language  = {en}
}
@article{GebserKaminskiSchaub2011,
  author    = {Gebser, Martin and Kaminski, Roland and Schaub, Torsten},
  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}
}
@article{GebserGharibMerceretal.2009,
  author    = {Gebser, Martin and Gharib, Mona and Mercer, Robert E. and Schaub, Torsten},
  title     = {Monotonic answer set programming},
  issn      = {0955-792X},
  doi       = {10.1093/logcom/exn040},
  year      = {2009},
  abstract  = {Answer set programming (ASP) does not allow for incrementally constructing answer sets or locally validating constructions like proofs by only looking at a part of the given program. In this article, we elaborate upon an alternative approach to ASP that allows for incremental constructions. Our approach draws its basic intuitions from the area of default logics. We investigate the feasibility of the concept of semi-monotonicity known from default logics as a basis of incrementality. On the one hand, every logic program has at least one answer set in our alternative setting, which moreover can be constructed incrementally based on generating rules. On the other hand, the approach may produce answer sets lacking characteristic properties of standard answer sets, such as being a model of the given program. We show how integrity constraints can be used to re-establish such properties, even up to correspondence with standard answer sets. Furthermore, we develop an SLD-like proof procedure for our incremental approach to ASP, which allows for query-oriented computations. Also, we provide a characterization of our definition of answer sets via a modification of Clarks completion. Based on this notion of program completion, we present an algorithm for computing the answer sets of a logic program in our approach.},
  language  = {en}
}
@article{GebserKaufmannSchaub2012,
  author    = {Gebser, Martin and Kaufmann, Benjamin and Schaub, Torsten},
  title     = {Multi-threaded ASP solving with clasp},
  series = {Theory and practice of logic programming},
  volume    = {12},
  journal   = {Theory and practice of logic programming},
  number    = {8},
  publisher = {Cambridge Univ. Press},
  address   = {New York},
  issn      = {1471-0684},
  doi       = {10.1017/S1471068412000166},
  pages     = {525 -- 545},
  year      = {2012},
  abstract  = {We present the new multi-threaded version of the state-of-the-art answer set solver clasp. We detail its component and communication architecture and illustrate how they support the principal functionalities of clasp. Also, we provide some insights into the data representation used for different constraint types handled by clasp. All this is accompanied by an extensive experimental analysis of the major features related to multi-threading in clasp.},
  language  = {en}
}
@article{HermenegildoSchaub2010,
  author    = {Hermenegildo, Manuel and Schaub, Torsten},
  title     = {Introduction to the technical communications of the 26th International Conference on Logic Programming : special issue},
  issn      = {1471-0684},
  doi       = {10.1017/S1471068410000153},
  year      = {2010},
  language  = {en}
}
@article{DelgrandeLiuSchaubetal.2007,
  author    = {Delgrande, James Patrick and Liu, Daphne H. and Schaub, Torsten and Thiele, Sven},
  title     = {COBA 2.0 : a consistency-based belief change system},
  year      = {2007},
  language  = {en}
}
@article{GharibSchaubMercer2007,
  author    = {Gharib, Mona and Schaub, Torsten and Mercer, Robert E.},
  title     = {Incremental answer set programming : a preliminary report},
  year      = {2007},
  language  = {en}
}
@article{DelgrandeSchaubTompits2006,
  author    = {Delgrande, James Patrick and Schaub, Torsten and Tompits, Hans},
  title     = {An Extended Query language for action languages (and its application to aggregates and preferences)},
  year      = {2006},
  language  = {en}
}
@article{KonczakLinkeSchaub2003,
  author    = {Konczak, Kathrin and Linke, Thomas and Schaub, Torsten},
  title     = {Graphs and colorings for answer set programming : abridged report},
  issn      = {1613-0073},
  year      = {2003},
  language  = {en}
}
@article{AngerGebserSchaub2006,
  author    = {Anger, Christian and Gebser, Martin and Schaub, Torsten},
  title     = {Approaching the core of unfounded sets},
  year      = {2006},
  language  = {en}
}
@article{MileoSchaub2006,
  author    = {Mileo, Alessandra and Schaub, Torsten},
  title     = {Extending ordered disjunctions for policy enforcement : preliminary report},
  year      = {2006},
  language  = {en}
}
@article{DelgrandeSchaubTompits2007,
  author    = {Delgrande, James Patrick and Schaub, Torsten and Tompits, Hans},
  title     = {A preference-based framework for updating logic programs},
  isbn      = {978-3-540- 72199-4},
  year      = {2007},
  language  = {en}
}
@article{GressmannJanhunenMerceretal.2006,
  author    = {Gressmann, Jean and Janhunen, Tomi and Mercer, Robert E. and Schaub, Torsten and Thiele, Sven and Tichy, Richard},
  title     = {On probing and multi-threading in platypus},
  year      = {2006},
  language  = {en}
}
@article{GrellSchaubSelbig2006,
  author    = {Grell, Susanne and Schaub, Torsten and Selbig, Joachim},
  title     = {Modelling biological networks by action languages via set programming},
  issn      = {0302-9743},
  doi       = {10.1007/11799573},
  year      = {2006},
  language  = {en}
}
@article{GerbserSchaub2006,
  author    = {Gerbser, Martin and Schaub, Torsten},
  title     = {Tableau calculi for answer set programming},
  issn      = {0302-9743},
  doi       = {10.1007/11799573},
  year      = {2006},
  language  = {en}
}
@article{GerbserSchaub2006,
  author    = {Gerbser, Martin and Schaub, Torsten},
  title     = {Characterizing (ASP) inferences by unit propagation},
  year      = {2006},
  language  = {en}
}
@phdthesis{Kaufmann2015,
  author    = {Kaufmann, Benjamin},
  title     = {High performance answer set solving},
  pages     = {182},
  year      = {2015},
  language  = {en}
}
@article{DelgrandeSchaubTompitsetal.2004,
  author    = {Delgrande, James Patrick and Schaub, Torsten and Tompits, Hans and Woltran, Stefan},
  title     = {On Computing belief change operations using quantifield boolean formulas},
  issn      = {0955-792X},
  year      = {2004},
  abstract  = {In this paper, we show how an approach to belief revision and belief contraction can be axiomatized by means of quantified Boolean formulas. Specifically, we consider the approach of belief change scenarios, a general framework that has been introduced for expressing different forms of belief change. The essential idea is that for a belief change scenario (K, R, C), the set of formulas K, representing the knowledge base, is modified so that the sets of formulas R and C are respectively true in, and consistent with the result. By restricting the form of a belief change scenario, one obtains specific belief change operators including belief revision, contraction, update, and merging. For both the general approach and for specific operators, we give a quantified Boolean formula such that satisfying truth assignments to the free variables correspond to belief change extensions in the original approach. Hence, we reduce the problem of determining the results of a belief change operation to that of satisfiability. This approach has several benefits. First, it furnishes an axiomatic specification of belief change with respect to belief change scenarios. This then leads to further insight into the belief change framework. Second, this axiomatization allows us to identify strict complexity bounds for the considered reasoning tasks. Third, we have implemented these different forms of belief change by means of existing solvers for quantified Boolean formulas. As well, it appears that this approach may be straightforwardly applied to other specific approaches to belief change},
  language  = {en}
}
@article{FloeterNicolasSchaubetal.2004,
  author    = {Fl{\"o}ter, Andr{\´e} and Nicolas, Jacques and Schaub, Torsten and Selbig, Joachim},
  title     = {Threshold extraction in metabolite concentration data},
  year      = {2004},
  abstract  = {Motivation: Continued development of analytical techniques based on gas chromatography and mass spectrometry now facilitates the generation of larger sets of metabolite concentration data. An important step towards the understanding of metabolite dynamics is the recognition of stable states where metabolite concentrations exhibit a simple behaviour. Such states can be characterized through the identification of significant thresholds in the concentrations. But general techniques for finding discretization thresholds in continuous data prove to be practically insufficient for detecting states due to the weak conditional dependences in concentration data. Results: We introduce a method of recognizing states in the framework of decision tree induction. It is based upon a global analysis of decision forests where stability and quality are evaluated. It leads to the detection of thresholds that are both comprehensible and robust. Applied to metabolite concentration data, this method has led to the discovery of hidden states in the corresponding variables. Some of these reflect known properties of the biological experiments, and others point to putative new states},
  language  = {en}
}
@article{DelgrandeGharibMerceretal.2003,
  author    = {Delgrande, James Patrick and Gharib, Mona and Mercer, Robert E. and Risch, V. and Schaub, Torsten},
  title     = {Lukaszewicz-style answer set programming : a preliminary report},
  issn      = {1613-0073},
  year      = {2003},
  language  = {en}
}
@article{DelgrandeSchaub2003,
  author    = {Delgrande, James Patrick and Schaub, Torsten},
  title     = {On the relation between Reiter{\"i}s default logic and its (major) variants},
  isbn      = {3-540- 409494-5},
  year      = {2003},
  language  = {en}
}
@article{KonczakSchaubLinke2003,
  author    = {Konczak, Kathrin and Schaub, Torsten and Linke, Thomas},
  title     = {Graphs and colorings for answer set programming with prefernces : preliminary report},
  issn      = {1613-0073},
  year      = {2003},
  language  = {en}
}
@article{BesnardMercerSchaub2003,
  author    = {Besnard, Philippe and Mercer, Robert E. and Schaub, Torsten},
  title     = {Optimality theory throught default logic},
  isbn      = {3-540-20059-2},
  year      = {2003},
  language  = {en}
}
@article{DelgrandeSchaubTompits2003,
  author    = {Delgrande, James Patrick and Schaub, Torsten and Tompits, Hans},
  title     = {A framework for compiling preferences in logic programs},
  year      = {2003},
  language  = {en}
}
@article{DelgrandeSchaub2003,
  author    = {Delgrande, James Patrick and Schaub, Torsten},
  title     = {Reasoning credulously and skeptically within a single extension},
  year      = {2003},
  language  = {en}
}
@article{SchaubWang2003,
  author    = {Schaub, Torsten and Wang, Kewen},
  title     = {A semantic framework for prefernce handling in answer set programming},
  year      = {2003},
  language  = {en}
}
@article{BenhammadiNicolasSchaub1999,
  author    = {Benhammadi, Farid and Nicolas, Pascal and Schaub, Torsten},
  title     = {Query-answering in prioritized default logic},
  isbn      = {3-540-66131-X},
  year      = {1999},
  language  = {en}
}
@article{LinkeSchaub1999,
  author    = {Linke, Thomas and Schaub, Torsten},
  title     = {On bottom-up pre-processing techniques for automated default reasoning},
  isbn      = {3-540-66131-x},
  year      = {1999},
  language  = {en}
}
@article{BenhammadiNicolasSchaub1999,
  author    = {Benhammadi, Farid and Nicolas, Pascal and Schaub, Torsten},
  title     = {Query-answering in prioritized default logic},
  isbn      = {3-540-66131-X},
  year      = {1999},
  language  = {en}
}
@article{BrueningSchaub1999,
  author    = {Br{\"u}ning, Stefan and Schaub, Torsten},
  title     = {Avoiding non-ground variables},
  isbn      = {3-540-66131-x},
  year      = {1999},
  language  = {en}
}
@article{NicolasSchaub1998,
  author    = {Nicolas, Pascal and Schaub, Torsten},
  title     = {The XRay system : an implementation platform for local query-answering in default logics},
  isbn      = {3-540-65312-0},
  year      = {1998},
  language  = {en}
}
@article{BrueningSchaub1999,
  author    = {Br{\"u}ning, Stefan and Schaub, Torsten},
  title     = {A voiding non-ground variables},
  year      = {1999},
  language  = {en}
}
@book{Schaub1999,
  author    = {Schaub, Torsten},
  title     = {The automation of reasoning with incomplete information : from semantic foundations to efficient computation},
  series = {Lecture notes in computer science},
  volume    = {1409},
  journal   = {Lecture notes in computer science},
  publisher = {Springer},
  address   = {Berlin},
  isbn      = {3-540-64515-2},
  doi       = {10.1007/BFb0054963},
  pages     = {XI, 159 S.},
  year      = {1999},
  language  = {en}
}
@article{BesnardSchaub1998,
  author    = {Besnard, Philippe and Schaub, Torsten},
  title     = {Signed systems for paraconsistent reasoning},
  year      = {1998},
  language  = {en}
}
@article{BrainGebserPuehreretal.2007,
  author    = {Brain, Martin and Gebser, Martin and P{\"u}hrer, J{\"o}rg and Schaub, Torsten and Tompits, Hans and Woltran, Stefan},
  title     = {"That is illogical, Captain!" : the debugging support tool spock for answer-set programs ; system description},
  year      = {2007},
  language  = {en}
}
@article{GebserKaufmannNeumannetal.2007,
  author    = {Gebser, Martin and Kaufmann, Benjamin and Neumann, Andr{\´e} and Schaub, Torsten},
  title     = {Conflict-driven answer set enumeration},
  isbn      = {978-3-540- 72199-4},
  year      = {2007},
  language  = {en}
}
@article{LinkeSchaub1996,
  author    = {Linke, Thomas and Schaub, Torsten},
  title     = {Putting default logics in perspective},
  isbn      = {3-540-61708-6},
  year      = {1996},
  language  = {en}
}
@article{LinkeSchaub1995,
  author    = {Linke, Thomas and Schaub, Torsten},
  title     = {Lemma handling in default logic theorem provers},
  isbn      = {3540601120},
  year      = {1995},
  language  = {en}
}
@article{GebserKaufmannNeumannetal.2007,
  author    = {Gebser, Martin and Kaufmann, Benjamin and Neumann, Andr{\´e} and Schaub, Torsten},
  title     = {Conflict-driven answer set solving},
  isbn      = {978-1-57735-323-2},
  year      = {2007},
  language  = {en}
}
@article{BesnardSchaub1993,
  author    = {Besnard, Philippe and Schaub, Torsten},
  title     = {A context-based framework for default logics},
  isbn      = {0-262-51071-5},
  year      = {1993},
  language  = {en}
}
@article{GebserGharibSchaub2007,
  author    = {Gebser, Martin and Gharib, Mona and Schaub, Torsten},
  title     = {Incremental answer sets and their computation},
  year      = {2007},
  language  = {en}
}
@article{GebserSchaub2007,
  author    = {Gebser, Martin and Schaub, Torsten},
  title     = {Generic tableaux for answer set programming},
  year      = {2007},
  language  = {en}
}
@article{DelgrandeSchaub2007,
  author    = {Delgrande, James Patrick and Schaub, Torsten},
  title     = {A consistency-based framework for merging knowledge bases},
  issn      = {1570-8683},
  year      = {2007},
  language  = {en}
}