TY - JOUR A1 - Anger, Christian A1 - Gebser, Martin A1 - Janhunen, Tomi A1 - Schaub, Torsten H. T1 - What's a head without a body? Y1 - 2006 ER - TY - JOUR A1 - Anger, Christian A1 - Gebser, Martin A1 - Linke, Thomas A1 - Neumann, Andre A1 - Schaub, Torsten H. T1 - The nomore++ approach to answer set solving Y1 - 2005 UR - http://www.cs.uni-potsdam.de/wv/pdfformat/angelinesc05c.pdf ER - TY - JOUR A1 - Anger, Christian A1 - Gebser, Martin A1 - Linke, Thomas A1 - Neumann, Andre A1 - Schaub, Torsten H. T1 - The nomore++ approach to answer set solving Y1 - 2005 UR - http://www.cs.uni-potsdam.de/wv/pdfformat/angelinesc05c.pdf ER - TY - JOUR A1 - Anger, Christian A1 - Gebser, Martin A1 - Schaub, Torsten H. T1 - Approaching the core of unfounded sets Y1 - 2006 UR - http://www.cs.uni-potsdam.de/wv/pdfformat/angesc06a.pdf ER - TY - JOUR A1 - Anger, Christian A1 - Konczak, Kathrin A1 - Linke, Thomas A1 - Schaub, Torsten H. T1 - A Glimpse of Answer Set Programming Y1 - 2005 UR - http://www.cs.uni-potsdam.de/~konczak/Papers/ankolisc05.pdf SN - 0170-4516 ER - TY - JOUR A1 - Banbara, Mutsunori A1 - Inoue, Katsumi A1 - Kaufmann, Benjamin A1 - Okimoto, Tenda A1 - Schaub, Torsten H. A1 - Soh, Takehide A1 - Tamura, Naoyuki A1 - Wanko, Philipp T1 - teaspoon BT - solving the curriculum-based course timetabling problems with answer set programming JF - Annals of operation research N2 - Answer Set Programming (ASP) is an approach to declarative problem solving, combining a rich yet simple modeling language with high performance solving capacities. We here develop an ASP-based approach to curriculum-based course timetabling (CB-CTT), one of the most widely studied course timetabling problems. The resulting teaspoon system reads a CB-CTT instance of a standard input format and converts it into a set of ASP facts. In turn, these facts are combined with a first-order encoding for CB-CTT solving, which can subsequently be solved by any off-the-shelf ASP systems. We establish the competitiveness of our approach by empirically contrasting it to the best known bounds obtained so far via dedicated implementations. Furthermore, we extend the teaspoon system to multi-objective course timetabling and consider minimal perturbation problems. KW - Educational timetabling KW - Course timetabling KW - Answer set programming KW - Multi-objective optimization KW - Minimal perturbation problems Y1 - 2018 U6 - https://doi.org/10.1007/s10479-018-2757-7 SN - 0254-5330 SN - 1572-9338 VL - 275 IS - 1 SP - 3 EP - 37 PB - Springer CY - Dordrecht ER - TY - JOUR A1 - Banbara, Mutsunori A1 - Soh, Takehide A1 - Tamura, Naoyuki A1 - Inoue, Katsumi A1 - Schaub, Torsten H. T1 - Answer set programming as a modeling language for course timetabling JF - Theory and practice of logic programming N2 - The course timetabling problem can be generally defined as the task of assigning a number of lectures to a limited set of timeslots and rooms, subject to a given set of hard and soft constraints. The modeling language for course timetabling is required to be expressive enough to specify a wide variety of soft constraints and objective functions. Furthermore, the resulting encoding is required to be extensible for capturing new constraints and for switching them between hard and soft, and to be flexible enough to deal with different formulations. In this paper, we propose to make effective use of ASP as a modeling language for course timetabling. We show that our ASP-based approach can naturally satisfy the above requirements, through an ASP encoding of the curriculum-based course timetabling problem proposed in the third track of the second international timetabling competition (ITC-2007). Our encoding is compact and human-readable, since each constraint is individually expressed by either one or two rules. Each hard constraint is expressed by using integrity constraints and aggregates of ASP. Each soft constraint S is expressed by rules in which the head is the form of penalty (S, V, C), and a violation V and its penalty cost C are detected and calculated respectively in the body. We carried out experiments on four different benchmark sets with five different formulations. We succeeded either in improving the bounds or producing the same bounds for many combinations of problem instances and formulations, compared with the previous best known bounds. KW - answer set programming KW - educational timetabling KW - course timetabling Y1 - 2013 U6 - https://doi.org/10.1017/S1471068413000495 SN - 1471-0684 VL - 13 IS - 2 SP - 783 EP - 798 PB - Cambridge Univ. Press CY - New York ER - TY - JOUR A1 - Benhammadi, Farid A1 - Nicolas, Pascal A1 - Schaub, Torsten H. T1 - Extension calculus and query answering in prioritized default logic Y1 - 1998 SN - 3-540-64993-X ER - TY - JOUR A1 - Benhammadi, Farid A1 - Nicolas, Pascal A1 - Schaub, Torsten H. T1 - Extension calculus and query answering in prioritized default logic Y1 - 1998 SN - 3-540- 64993-X ER - TY - JOUR A1 - Benhammadi, Farid A1 - Nicolas, Pascal A1 - Schaub, Torsten H. T1 - Query-answering in prioritized default logic Y1 - 1999 SN - 3-540-66131-X ER - TY - JOUR A1 - Benhammadi, Farid A1 - Nicolas, Pascal A1 - Schaub, Torsten H. T1 - Query-answering in prioritized default logic Y1 - 1999 SN - 3-540-66131-X ER - TY - JOUR A1 - Besnard, Philippe A1 - Fanselow, Gisbert A1 - Schaub, Torsten H. T1 - Optimality theory as a family of cumulative logics Y1 - 2002 ER - TY - JOUR A1 - Besnard, Philippe A1 - Mercer, Robert E. A1 - Schaub, Torsten H. T1 - Optimality theory throught default logic Y1 - 2003 SN - 3-540-20059-2 ER - TY - JOUR A1 - Besnard, Philippe A1 - Mercer, Robert E. A1 - Schaub, Torsten H. T1 - Optimality Theory via Default Logic Y1 - 2002 ER - TY - JOUR A1 - Besnard, Philippe A1 - Schaub, Torsten H. T1 - A simple signed system for paraconsistent reasoning Y1 - 1996 SN - 3-540-61630-6 ER - TY - JOUR A1 - Besnard, Philippe A1 - Schaub, Torsten H. T1 - A context-based framework for default logics Y1 - 1993 SN - 0-262-51071-5 ER - TY - JOUR A1 - Besnard, Philippe A1 - Schaub, Torsten H. T1 - Signed systems for paraconsistent reasoning Y1 - 1998 ER - TY - JOUR A1 - Besnard, Philippe A1 - Schaub, Torsten H. T1 - Characterization of non-monotone non-constructive systems Y1 - 1998 SN - 1012-2443 ER - TY - JOUR A1 - Besnard, Philippe A1 - Schaub, Torsten H. T1 - Signed systems for paraconsistent reasoning Y1 - 1998 SN - 0168-7433 ER - TY - JOUR A1 - Besnard, Philippe A1 - Schaub, Torsten H. T1 - An approach to context-based default reasoning Y1 - 1995 SN - 0169-2968 ER - TY - JOUR A1 - Besnard, Philippe A1 - Schaub, Torsten H. T1 - Circumscribing inconsistency Y1 - 1997 SN - 1-558-60480-4 SN - 1045-0823 ER - TY - JOUR A1 - Besnard, Philippe A1 - Schaub, Torsten H. T1 - Significant inferences Y1 - 2000 SN - 1-55860-690-4 ER - TY - JOUR A1 - Besnard, Philippe A1 - Schaub, Torsten H. T1 - What is a (non-constructive) non-monotone logical system? Y1 - 2000 SN - 0304-3975 ER - TY - JOUR A1 - Besnard, Philippe A1 - Schaub, Torsten H. A1 - Tompits, Hans A1 - Woltran, Stefan T1 - Paraconsistent reasoning via quantified boolean formulas Y1 - 2002 SN - 3-540-44190-5 ER - TY - JOUR A1 - Besnard, Philippe A1 - Schaub, Torsten H. A1 - Tompits, Hans A1 - Woltran, Stefan T1 - Paraconsistent reasoning via quantified boolean formulas : Part II: Circumscribing inconsistent theories Y1 - 2003 SN - 3-540- 409494-5 ER - TY - JOUR A1 - Bibel, Wolfgang A1 - Brüning, Stefan A1 - Otten, Jens A1 - Rath, Thomas A1 - Schaub, Torsten H. T1 - Compressions and extensions Y1 - 1998 ER - TY - JOUR A1 - Boesel, Andreas A1 - Linke, Thomas A1 - Schaub, Torsten H. T1 - Profiling answer set programming : the visualization component of the noMoRe System Y1 - 2004 SN - 3-540-23242-7 ER - TY - JOUR A1 - Borchert, P. A1 - Anger, Christian A1 - Schaub, Torsten H. A1 - Truszczynski, M. T1 - Towards systematic benchmarking in answer set programming : the dagstuhl initiative Y1 - 2004 SN - 3-540- 20721-x ER - TY - JOUR A1 - Brain, Martin A1 - Faber, Wolfgang A1 - Maratea, Marco A1 - Polleres, Axel A1 - Schaub, Torsten H. A1 - Schindlauer, Roman T1 - What should an ASP solver output? : a multiple position paper Y1 - 2007 ER - TY - JOUR A1 - Brain, Martin A1 - Gebser, Martin A1 - Pührer, Jörg A1 - Schaub, Torsten H. A1 - Tompits, Hans A1 - Woltran, Stefan T1 - "That is illogical, Captain!" : the debugging support tool spock for answer-set programs ; system description Y1 - 2007 ER - TY - JOUR A1 - Brain, Martin A1 - Gebser, Martin A1 - Pührer, Jörg A1 - Schaub, Torsten H. A1 - Tompits, Hans A1 - Woltran, Stefan T1 - Debugging ASP programs by means of ASP Y1 - 2007 SN - 978-3-540- 72199-4 ER - TY - JOUR A1 - Brewka, Gerhard A1 - Ellmauthaler, Stefan A1 - Kern-Isberner, Gabriele A1 - Obermeier, Philipp A1 - Ostrowski, Max A1 - Romero, Javier A1 - Schaub, Torsten H. A1 - Schieweck, Steffen T1 - Advanced solving technology for dynamic and reactive applications JF - Künstliche Intelligenz Y1 - 2018 U6 - https://doi.org/10.1007/s13218-018-0538-8 SN - 0933-1875 SN - 1610-1987 VL - 32 IS - 2-3 SP - 199 EP - 200 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Brüning, Stefan A1 - Schaub, Torsten H. T1 - A model-based approach to consistency-checking Y1 - 1996 SN - 3-540-61286-6 ER - TY - JOUR A1 - Brüning, Stefan A1 - Schaub, Torsten H. T1 - A connection calculus for handling incomplete information Y1 - 2000 ER - TY - JOUR A1 - Brüning, Stefan A1 - Schaub, Torsten H. T1 - Avoiding non-ground variables Y1 - 1999 SN - 3-540-66131-x ER - TY - JOUR A1 - Brüning, Stefan A1 - Schaub, Torsten H. T1 - A voiding non-ground variables Y1 - 1999 ER - TY - JOUR A1 - Cabalar, Pedro A1 - Dieguez, Martin A1 - Schaub, Torsten H. A1 - Schuhmann, Anna T1 - Towards metric temporal answer set programming JF - Theory and practice of logic programming N2 - We elaborate upon the theoretical foundations of a metric temporal extension of Answer Set Programming. In analogy to previous extensions of ASP with constructs from Linear Temporal and Dynamic Logic, we accomplish this in the setting of the logic of Here-and-There and its non-monotonic extension, called Equilibrium Logic. More precisely, we develop our logic on the same semantic underpinnings as its predecessors and thus use a simple time domain of bounded time steps. This allows us to compare all variants in a uniform framework and ultimately combine them in a common implementation. Y1 - 2020 U6 - https://doi.org/10.1017/S1471068420000307 SN - 1471-0684 SN - 1475-3081 VL - 20 IS - 5 SP - 783 EP - 798 PB - Cambridge Univ. Press CY - Cambridge [u.a.] ER - TY - JOUR A1 - Cabalar, Pedro A1 - Fandinno, Jorge A1 - Garea, Javier A1 - Romero, Javier A1 - Schaub, Torsten H. T1 - Eclingo BT - a solver for epistemic logic programs JF - Theory and practice of logic programming N2 - 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. KW - Answer Set Programming KW - Epistemic Logic Programs KW - Non-Monotonic KW - Reasoning KW - Conformant Planning Y1 - 2020 U6 - https://doi.org/10.1017/S1471068420000228 SN - 1471-0684 SN - 1475-3081 VL - 20 IS - 6 SP - 834 EP - 847 PB - Cambridge Univ. Press CY - New York ER - TY - JOUR A1 - Cabalar, Pedro A1 - Fandinno, Jorge A1 - Schaub, Torsten H. A1 - Schellhorn, Sebastian T1 - Gelfond-Zhang aggregates as propositional formulas JF - Artificial intelligence N2 - 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. KW - Aggregates KW - Answer Set Programming Y1 - 2019 U6 - https://doi.org/10.1016/j.artint.2018.10.007 SN - 0004-3702 SN - 1872-7921 VL - 274 SP - 26 EP - 43 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Delgrande, James Patrick A1 - Gharib, Mona A1 - Mercer, Robert E. A1 - Risch, V. A1 - Schaub, Torsten H. T1 - Lukaszewicz-style answer set programming : a preliminary report Y1 - 2003 UR - http://sunsite.informatik.rwth-aachen.de/Publications/CEUR-WS/Vol-78/ SN - 1613-0073 ER - TY - JOUR A1 - Delgrande, James Patrick A1 - Hunter, Anthony A1 - Schaub, Torsten H. T1 - COBA: a consistency-based belief revision system Y1 - 2002 SN - 3-540-44190-5 ER - TY - JOUR A1 - Delgrande, James Patrick A1 - Lang, Jérôme A1 - Schaub, Torsten H. T1 - Belief change based on global minimisation Y1 - 2007 ER - TY - JOUR A1 - Delgrande, James Patrick A1 - Liu, Daphne H. A1 - Schaub, Torsten H. A1 - Thiele, Sven T1 - COBA 2.0 : a consistency-based belief change system Y1 - 2006 UR - http://www2.in.tu-clausthal.de/~tmbehrens/NMR_Proc_TR4.pdf ER - TY - JOUR A1 - Delgrande, James Patrick A1 - Liu, Daphne H. A1 - Schaub, Torsten H. A1 - Thiele, Sven T1 - COBA 2.0 : a consistency-based belief change system Y1 - 2007 ER - TY - JOUR A1 - Delgrande, James Patrick A1 - Schaub, Torsten H. T1 - Expressing default logic variants in default logic N2 - 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 Y1 - 2005 SN - 0955-792X ER - TY - JOUR A1 - Delgrande, James Patrick A1 - Schaub, Torsten H. T1 - Two approaches to merging knowledge bases Y1 - 2004 SN - 3-540-23242-7 ER - TY - JOUR A1 - Delgrande, James Patrick A1 - Schaub, Torsten H. T1 - Consistency-based approaches to merging knowledge based : preliminary report Y1 - 2004 UR - http://www.pims.math.ca/science/2004/NMR/papers/paper17.pdf SN - 92-990021-0-X ER - TY - JOUR A1 - Delgrande, James Patrick A1 - Schaub, Torsten H. T1 - Reasoning with sets of preferences in default logic N2 - 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 Y1 - 2004 SN - 0824-7935 ER - TY - JOUR A1 - Delgrande, James Patrick A1 - Schaub, Torsten H. T1 - Reasoning credulously and skeptically within a single extension Y1 - 2003 ER - TY - JOUR A1 - Delgrande, James Patrick A1 - Schaub, Torsten H. T1 - On the relation between Reiterïs default logic and its (major) variants Y1 - 2003 SN - 3-540- 409494-5 ER -