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 - Sarsakov, Vladimir A1 - Schaub, Torsten H. A1 - Tompits, Hans A1 - Woltran, Stefan T1 - A compiler for nested logic programming Y1 - 2004 SN - 3-540- 20721-x ER - TY - JOUR A1 - Delgrande, James Patrick A1 - Schaub, Torsten H. A1 - Tompits, Hans A1 - Woltran, Stefan T1 - On Computing belief change operations using quantifield boolean formulas N2 - 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 Y1 - 2004 SN - 0955-792X ER - TY - JOUR A1 - Delgrande, James Patrick A1 - Schaub, Torsten H. A1 - Tompits, Hans A1 - Woltran, Stefan T1 - On computing solutions to belief change scenarios Y1 - 2001 SN - 3-540- 42464-4 ER - TY - JOUR A1 - Pearce, David A1 - Sarsakov, Vladimir A1 - Schaub, Torsten H. A1 - Tompits, Hans A1 - Woltran, Stefan T1 - A polynomial translation of logic programs with nested expressions into disjunctive logic programs Y1 - 2002 SN - 3-540-43930-7 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 - 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 - Pearce, David A1 - Sarsakov, Vladimir A1 - Schaub, Torsten H. A1 - Tompits, Hans A1 - Woltran, Stefan T1 - A polynomial translation of logic programs with nested expressions into disjunctive logic programs : preliminary report Y1 - 2002 ER - TY - JOUR A1 - Schaub, Torsten H. A1 - Woltran, Stefan T1 - Answer set programming unleashed! JF - Künstliche Intelligenz N2 - 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)] Y1 - 2018 U6 - https://doi.org/10.1007/s13218-018-0550-z SN - 0933-1875 SN - 1610-1987 VL - 32 IS - 2-3 SP - 105 EP - 108 PB - Springer CY - Heidelberg ER - TY - GEN A1 - Schaub, Torsten H. A1 - Woltran, Stefan T1 - Special issue on answer set programming T2 - Künstliche Intelligenz Y1 - 2018 U6 - https://doi.org/10.1007/s13218-018-0554-8 SN - 0933-1875 SN - 1610-1987 VL - 32 IS - 2-3 SP - 101 EP - 103 PB - Springer CY - Heidelberg ER -