Rewriting recursive aggregates in answer set programming: back to monotonicity

Aggregation functions are widely used in answer set programming for representing and reasoning on knowledge involving sets of objects collectively. Current implementations simplify the structure of programs in order to optimize the overall performance. In particular, aggregates are rewritten into simpler forms known as monotone aggregates. Since the evaluation of normal programs with monotone aggregates is in general on a lower complexity level than the evaluation of normal programs with arbitrary aggregates, any faithful translation function must introduce disjunction in rule heads in some cases. However, no function of this kind is known. The paper closes this gap by introducing a polynomial, faithful, and modular translation for rewriting common aggregation functions into the simpler form accepted by current solvers. A prototype system allows for experimenting with arbitrary recursive aggregates, which are also supported in the recent version 4.5 of the grounder gringo, using the methods presented in this paper

The Pyglaf Argumentation Reasoner

The pyglaf reasoner takes advantage of circumscription to solve computational problems of abstract argumentation frameworks. In fact, many of these problems are reduced to circumscription by means of linear encodings, and a few others are solved by means of a sequence of calls to an oracle for circumscription. Within pyglaf, Python is used to build the encodings and to control the execution of the external circumscription solver, which extends the SAT solver glucose and implements an algorithm based on unsatisfiable core analysis

Dynamic Magic Sets for Disjunctive Datalog Programs

Answer set programming (ASP) is a powerful formalism for knowledge representation and common sense reasoning that allows disjunction in rule heads and nonmonotonic negation in bodies. Magic Sets are a technique for optimizing query answering over logic programs and have been originally defined for standard Datalog, that is, ASP without disjunction and negation. Essentially, the input program is rewritten in order to identify a subset of the program instantiation which is sufficient for answering the query. Dynamic Magic Sets (DMS) are an extension of this technique to ASP. The optimization provided by DMS can be exploited also during the nondeterministic phase of ASP systems. In particular, after some assumptions have been made during the computation, parts of the program may become irrelevant to a query (because of these assumptions). This allows for dynamic pruning of the search space, which may result in exponential performance gains. DMS has been implemented in the dlv system and experimental results confirm the effectiveness of the technique

Anytime Computation of Cautious Consequences in Answer Set Programming

Query answering in Answer Set Programming (ASP) is usually solved by computing (a subset of) the cautious consequences of a logic program. This task is computationally very hard, and there are programs for which computing cautious consequences is not viable in reasonable time. However, current ASP solvers produce the (whole) set of cautious consequences only at the end of their computation. This paper reports on strategies for computing cautious consequences, also introducing anytime algorithms able to produce sound answers during the computation.Comment: To appear in Theory and Practice of Logic Programmin

Effectively Solving NP-SPEC Encodings by Translation to ASP

NP-SPEC is a language for specifying problems in NP in a declarative way. Despite the fact that the semantics of the language was given by referring to Datalog with circumscription, which is very close to ASP, so far the only existing implementations are by means of ECLiPSe Prolog and via Boolean satisfiability solvers. In this paper, we present translations from NP-SPEC into ASP, and provide an experimental evaluation of existing implementations and the proposed translations to ASP using various ASP solvers. The results show that translating to ASP clearly has an edge over the existing translation into SAT, which involves an intrinsic grounding process. We also argue that it might be useful to incorporate certain language constructs of NPSPEC into mainstream ASP