Abstract. We propose a generalization of the well-known Magic Sets technique to Datalog ¬ programs with (possibly unstratified) negation under stable model semantics. Our technique produces a new program whose evaluation is generally more efficient (due to a smaller instantiation), while preserving soundness under cautious reasoning. Importantly, if the original program is consistent, then full query-equivalence is guaranteed for both brave and cautious reasoning, which turn out to be sound and complete. In order to formally prove the correctness of our Magic Sets transformation, we introduce a novel notion of modularity for Datalog ¬ under the stable model semantics, which is relevant per se. We prove that a module can be evaluated independently from the rest of the program, while preserving soundness under cautious reasoning. For consistent programs, both soundness and completeness are guaranteed for brave reasoning and cautious reasoning as well. Our Magic Sets optimization constitutes an effective method for enhancing the performance of data-integration systems in which query-answering is carried out by means of cautious reasoning over Datalog ¬ programs. In fact, preliminary results of experiments in the EU project INFOMIX, show that Magic Sets are fundamental for the scalability of the system. 1

Abstract. Consistent Query Answering (CQA) is the problem of computing from a database the answers to a query that are consistent with respect to certain integrity constraints that the database, as a whole, may fail to satisfy. Consistent answers have been characterized as those that are invariant under certain minimal forms of restoration of the database consistency. In this paper we investigate algorithmic and complexity theoretic issues of CQA under database repairs that minimally depart-wrt the cardinality of the symmetric difference- from the original database. Research on this kind of repairs has been suggested in the literature, but no systematic study had been done. Here we obtain first tight complexity bounds. We also address, considering for the first time a dynamic scenario for CQA, the problem of incremental complexity of CQA, that naturally occurs when an originally consistent database becomes inconsistent after the execution of a sequence of update operations. Tight bounds on incremental complexity are provided for various semantics under denial constraints, e.g. (a) minimum tuple-based repairs wrt cardinality, (b) minimal tuple-based repairs wrt set inclusion, and (c) minimum numerical aggregation of attribute-based repairs. Fixed parameter tractability is also investigated in this dynamic context, where the size of the update sequence becomes the relevant parameter. 1

In recent research on nonmonotonic logic programming, repeatedly strong equivalence of logic programs P and Q has been considered, which holds if the programs P ∪ R and Q ∪ R have the same answer sets for any other program R. This property strengthens the equivalence of P and Q with respect to answer sets (which is the particular case for R =∅), and has its applications in program optimization, verification, and modular logic programming. In this article, we consider more liberal notions of strong equivalence, in which the actual form of R may be syntactically restricted. On the one hand, we consider uniform equivalence where R is a set of facts, rather than a set of rules. This notion, which is well-known in the area of deductive databases, is particularly useful for assessing whether programs P and Q are equivalent as components of a logic program which is modularly structured. On the other hand, we consider relativized notions of equivalence where R ranges over rules over a fixed alphabet, and thus generalize our results to relativized notions of strong and uniform equivalence. For all these notions, we consider disjunctive logic programs in the propositional (ground) case as well as some restricted classes, providing semantical characterizations and analyzing the computational complexity. Our results, which naturally extend to answer set semantics for programs with strong negation, complement the results on strong

Abstract. For several reasons a database may not satisfy a given set of integrity constraints (ICs), but most likely most of the information in it is still consistent with those ICs; and could be retrieved when queries are answered. Consistent answers to queries wrt a set of ICs have been characterized as answers that can be obtained from every possible minimally repaired consistent version of the original database. In this paper we consider databases that contain null values and are also repaired, if necessary, using null values. For this purpose, we propose first a precise semantics for IC satisfaction in a database with null values that is compatible with the way null values are treated in commercial database management systems. Next, a precise notion of repair is introduced that privileges the introduction of null values when repairing foreign key constraints, in such a way that these new values do not create an infinite cycle of new inconsistencies. Finally, we analyze how to specify this kind of repairs of a database that contains null values using disjunctive logic programs with stable model semantics. 1

Abstract. Using SAT solvers as inference engines in answer set programming systems showed to be a promising approach in building efficient systems. Nowadays SAT based answer set programming systems successfully work with nondisjunctive programs. This paper proposes a way to use SAT solvers for finding answer sets for disjunctive logic programs. We implement two different ways of SAT solver invocation used in nondisjunctive answer set programming. The algorithms are based on the definition of completion for disjunctive programs and the extension of loop formula to the disjunctive case. We propose the necessary modifications to the algorithms known for nondisjunctive programs in order to adapt them to the disjunctive case and demonstrate their implementation based on system CMODELS. 1

We present a new answer set solver, called nomore++, along with its underlying theoretical foundations. A distinguishing feature is that it treats heads and bodies equitably as computational objects. Apart from its operational foundations, we show how it improves on previous work through its new lookahead and its computational strategy of maintaining unfounded-freeness. We underpin our claims by selected experimental results.

Abstract. This paper gives a summary of the First Answer Set Programming System Competition that was held in conjunction with the Ninth International Conference on Logic Programming and Nonmonotonic Reasoning. The aims of the competition were twofold: first, to collect challenging benchmark problems, and second, to provide a platform to assess a broad variety of Answer Set Programming systems. The competition was inspired by similar events in neighboring fields, where regular benchmarking has been a major factor behind improvements in the developed systems and their ability to address practical applications. 1

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In this paper we apply computer-aided theorem discovery technique to discover theorems about strongly equivalent logic programs under the answer set semantics. Our discovered theorems capture new classes of strongly equivalent logic programs that can lead to new program simplification rules that preserve strong equivalence. Specifically, with the help of computers, we discovered exact conditions that capture the strong equivalence between a rule and the empty set, between two rules, between two rules and one of the two rules, between two rules and another rule, and between three rules and two of the three rules. 1.

We propose and study extensions of logic programming with constraints represented as generalized atoms of the form C(X), where X is a finite set of atoms and C is an abstract constraint (formally, a collection of sets of atoms). Atoms C(X) are satisfied by an interpretation (set of atoms) M , if M C. We focus here on monotone constraints, that is, those collections C that are closed under the superset. They include, in particular, weight (or pseudo-boolean) constraints studied both by the logic programming and SAT communities. We show that key concepts of the theory of normal logic programs such as the one-step provability operator, the semantics of supported and stable models, as well as several of their properties including complexity results, can be lifted to such case.