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Answer Set Programming (ASP) is an emerging paradigm for declarative programming, in which a computational problem is specified by a logic program such that particular models, called answer sets, match solutions. ASP faces a growing range of applications, demanding for high-performance tools able to solve complex problems. ASP integrates ideas from a variety of neighboring fields. In particular, automated techniques to search for answer sets are inspired by Boolean Satisfiability (SAT) solving approaches. While the latter have firm proof-theoretic foundations, ASP lacks formal frameworks for characterizing and comparing solving methods. Furthermore, sophisticated search patterns of modern SAT solvers, successfully applied in areas like, e.g., model checking and verification, are not yet established in ASP solving. We address these deficiencies by, for one, providing proof-theoretic frameworks that allow for characterizing, comparing, and analyzing approaches to answer set computation. For another, we devise modern ASP solving algorithms that integrate and extend state-of-the-art techniques for Boolean constraint solving. We thus contribute to the understanding of existing ASP solving approaches and their interconnections as well as to their enhancement by incorporating sophisticated search patterns. The central idea of our approach is to identify atomic as well as composite constituents of a propositional logic program with Boolean variables. This enables us to describe fundamental inference steps, and to selectively combine them in proof-theoretic characterizations of various ASP solving methods. In particular, we show that different concepts of case analyses applied by existing ASP solvers implicate mutual exponential separations regarding their best-case complexities. We also develop a generic proof-theoretic framework amenable to language extensions, and we point out that exponential separations can likewise be obtained due to case analyses on them. We further exploit fundamental inference steps to derive Boolean constraints characterizing answer sets. They enable the conception of ASP solving algorithms including search patterns of modern SAT solvers, while also allowing for direct technology transfers between the areas of ASP and SAT solving. Beyond the search for one answer set of a logic program, we address the enumeration of answer sets and their projections to a subvocabulary, respectively. The algorithms we develop enable repetition-free enumeration in polynomial space without being intrusive, i.e., they do not necessitate any modifications of computations before an answer set is found. Our approach to ASP solving is implemented in clasp, a state-of-the-art Boolean constraint solver that has successfully participated in recent solver competitions. Although we do here not address the implementation techniques of clasp or all of its features, we present the principles of its success in the context of ASP solving.
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.
Abstract gringo
(2015)
This paper defines the syntax and semantics of the input language of the ASP grounder gringo. The definition covers several constructs that were not discussed in earlier work on the semantics of that language, including intervals, pools, division of integers, aggregates with non-numeric values, and lparse-style aggregate expressions. The definition is abstract in the sense that it disregards some details related to representing programs by strings of ASCII characters. It serves as a specification for gringo from Version 4.5 on.
We introduce a simple approach extending the input language of Answer Set Programming (ASP) systems by multi-valued propositions. Our approach is implemented as a (prototypical) preprocessor translating logic programs with multi-valued propositions into logic programs with Boolean propositions only. Our translation is modular and heavily benefits from the expressive input language of ASP. The resulting approach, along with its implementation, allows for solving interesting constraint satisfaction problems in ASP, showing a good performance.
Many knowledge representation tasks involve trees or similar structures as abstract datatypes. However, devising compact and efficient declarative representations of such structural properties is non-obvious and can be challenging indeed. In this article, we take a number of acyclicity properties into consideration and investigate various logic-based approaches to encode them. We use answer set programming as the primary representation language but also consider mappings to related formalisms, such as propositional logic, difference logic and linear programming. We study the compactness of encodings and the resulting computational performance on benchmarks involving acyclic or tree structures.
The Potsdam answer set solving collection, or Potassco for short, bundles various tools implementing and/or applying answer set programming. The article at hand succeeds an earlier description of the Potassco project published in Gebser et al. (AI Commun 24(2):107-124, 2011). Hence, we concentrate in what follows on the major features of the most recent, fifth generation of the ASP system clingo and highlight some recent resulting application systems.
We introduce a new flexible paradigm of grounding and solving in Answer Set Programming (ASP), which we refer to as multi-shot ASP solving, and present its implementation in the ASP system clingo. Multi-shot ASP solving features grounding and solving processes that deal with continuously changing logic programs. In doing so, they remain operative and accommodate changes in a seamless way. For instance, such processes allow for advanced forms of search, as in optimization or theory solving, or interaction with an environment, as in robotics or query answering. Common to them is that the problem specification evolves during the reasoning process, either because data or constraints are added, deleted, or replaced. This evolutionary aspect adds another dimension to ASP since it brings about state changing operations. We address this issue by providing an operational semantics that characterizes grounding and solving processes in multi-shot ASP solving. This characterization provides a semantic account of grounder and solver states along with the operations manipulating them. The operative nature of multi-shot solving avoids redundancies in relaunching grounder and solver programs and benefits from the solver's learning capacities. clingo accomplishes this by complementing ASP's declarative input language with control capacities. On the declarative side, a new directive allows for structuring logic programs into named and parameterizable subprograms. The grounding and integration of these subprograms into the solving process is completely modular and fully controllable from the procedural side. To this end, clingo offers a new application programming interface that is conveniently accessible via scripting languages. By strictly separating logic and control, clingo also abolishes the need for dedicated systems for incremental and reactive reasoning, like iclingo and oclingo, respectively, and its flexibility goes well beyond the advanced yet still rigid solving processes of the latter.
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.
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.