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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.
Building biological models by inferring functional dependencies from experimental data is an important issue in Molecular Biology. To relieve the biologist from this traditionally manual process, various approaches have been proposed to increase the degree of automation. However, available approaches often yield a single model only, rely on specific assumptions, and/or use dedicated, heuristic algorithms that are intolerant to changing circumstances or requirements in the view of the rapid progress made in Biotechnology. Our aim is to provide a declarative solution to the problem by appeal to Answer Set Programming (ASP) overcoming these difficulties. We build upon an existing approach to Automatic Network Reconstruction proposed by part of the authors. This approach has firm mathematical foundations and is well suited for ASP due to its combinatorial flavor providing a characterization of all models explaining a set of experiments. The usage of ASP has several benefits over the existing heuristic algorithms. First, it is declarative and thus transparent for biological experts. Second, it is elaboration tolerant and thus allows for an easy exploration and incorporation of biological constraints. Third, it allows for exploring the entire space of possible models. Finally, our approach offers an excellent performance, matching existing, special-purpose systems.
Indoor position estimation constitutes a central task in home-based assisted living environments. Such environments often rely on a heterogeneous collection of low-cost sensors whose diversity and lack of precision has to be compensated by advanced techniques for localization and tracking. Although there are well established quantitative methods in robotics and neighboring fields for addressing these problems, they lack advanced knowledge representation and reasoning capacities. Such capabilities are not only useful in dealing with heterogeneous and incomplete information but moreover they allow for a better inclusion of semantic information and more general homecare and patient-related knowledge. We address this problem and investigate how state-of-the-art localization and tracking methods can be combined with Answer Set Programming, as a popular knowledge representation and reasoning formalism. We report upon a case-study and provide a first experimental evaluation of knowledge-based position estimation both in a simulated as well as in a real setting.
We present the new multi-threaded version of the state-of-the-art answer set solver clasp. We detail its component and communication architecture and illustrate how they support the principal functionalities of clasp. Also, we provide some insights into the data representation used for different constraint types handled by clasp. All this is accompanied by an extensive experimental analysis of the major features related to multi-threading in clasp.
We present the hybrid ASP solver clingcon, combining the simple modeling language and the high performance Boolean solving capacities of Answer Set Programming (ASP) with techniques for using non-Boolean constraints from the area of Constraint Programming (CP). The new clingcon system features an extended syntax supporting global constraints and optimize statements for constraint variables. The major technical innovation improves the interaction between ASP and CP solver through elaborated learning techniques based on irreducible inconsistent sets. A broad empirical evaluation shows that these techniques yield a performance improvement of an order of magnitude.
We introduce an approach to computing answer sets of logic programs, based on concepts successfully applied in Satisfiability (SAT) checking. The idea is to view inferences in Answer Set Programming (ASP) as unit propagation on nogoods. This provides us with a uniform constraint-based framework capturing diverse inferences encountered in ASP solving. Moreover, our approach allows us to apply advanced solving techniques from the area of SAT. As a result, we present the first full-fledged algorithmic framework for native conflict-driven ASP solving. Our approach is implemented in the ASP solver clasp that has demonstrated its competitiveness and versatility by winning first places at various solver contests.
We introduce formal proof systems based on tableau methods for analyzing computations in Answer Set Programming (ASP). Our approach furnishes fine-grained instruments for characterizing operations as well as strategies of ASP solvers. The granularity is detailed enough to capture a variety of propagation and choice methods of algorithms used for ASP solving, also incorporating SAT-based and conflict-driven learning approaches to some extent. This provides us with a uniform setting for identifying and comparing fundamental properties of ASP solving approaches. In particular, we investigate their proof complexities and show that the run-times of best-case computations can vary exponentially between different existing ASP solvers. Apart from providing a framework for comparing ASP solving approaches, our characterizations also contribute to their understanding by pinning down the constitutive atomic operations. Furthermore, our framework is flexible enough to integrate new inference patterns, and so to study their relation to existing ones. To this end, we generalize our approach and provide an extensible basis aiming at a modular incorporation of additional language constructs. This is exemplified by augmenting our basic tableau methods with cardinality constraints and disjunctions.
We address the problem of belief change in (nonmonotonic) logic programming under answer set semantics. Our formal techniques are analogous to those of distance-based belief revision in propositional logic. In particular, we build upon the model theory of logic programs furnished by SE interpretations, where an SE interpretation is a model of a logic program in the same way that a classical interpretation is a model of a propositional formula. Hence we extend techniques from the area of belief revision based on distance between models to belief change in logic programs.
We first consider belief revision: for logic programs P and Q, the goal is to determine a program R that corresponds to the revision of P by Q, denoted P * Q. We investigate several operators, including (logic program) expansion and two revision operators based on the distance between the SE models of logic programs. It proves to be the case that expansion is an interesting operator in its own right, unlike in classical belief revision where it is relatively uninteresting. Expansion and revision are shown to satisfy a suite of interesting properties; in particular, our revision operators satisfy all or nearly all of the AGM postulates for revision.
We next consider approaches for merging a set of logic programs, P-1,...,P-n. Again, our formal techniques are based on notions of relative distance between the SE models of the logic programs. Two approaches are examined. The first informally selects for each program P-i those models of P-i that vary the least from models of the other programs. The second approach informally selects those models of a program P-0 that are closest to the models of programs P-1,...,P-n. In this case, P-0 can be thought of as a set of database integrity constraints. We examine these operators with regards to how they satisfy relevant postulate sets.
Last, we present encodings for computing the revision as well as the merging of logic programs within the same logic programming framework. This gives rise to a direct implementation of our approach in terms of off-the-shelf answer set solvers. These encodings also reflect the fact that our change operators do not increase the complexity of the base formalism.
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.
Proposing relevant perturbations to biological signaling networks is central to many problems in biology and medicine because it allows for enabling or disabling certain biological outcomes. In contrast to quantitative methods that permit fine-grained (kinetic) analysis, qualitative approaches allow for addressing large-scale networks. This is accomplished by more abstract representations such as logical networks. We elaborate upon such a qualitative approach aiming at the computation of minimal interventions in logical signaling networks relying on Kleene's three-valued logic and fixpoint semantics. We address this problem within answer set programming and show that it greatly outperforms previous work using dedicated algorithms.
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.
We consider the problem of representing arbitrary preferences in causal reasoning and planning systems. In planning, a preference may be seen as a goal or constraint that is desirable, but not necessary, to satisfy. To begin, we define a very general query language for histories, or interleaved sequences of world states and actions. Based on this, we specify a second language in which preferences are defined. A single preference defines a binary relation on histories, indicating that one history is preferred to the other. From this, one can define global preference orderings on the set of histories, the maximal elements of which are the preferred histories. The approach is very general and flexible; thus it constitutes a base language in terms of which higher-level preferences may be defined. To this end, we investigate two fundamental types of preferences that we call choice and temporal preferences. We consider concrete strategies for these types of preferences and encode them in terms of our framework. We suggest how to express aggregates in the approach, allowing, e.g. the expression of a preference for histories with lowest total action costs. Last, our approach can be used to express other approaches and so serves as a common framework in which such approaches can be expressed and compared. We illustrate this by indicating how an approach due to Son and Pontelli can be encoded in our approach, as well as the language PDDL3.
Circumscribing inconsistency
(1997)
Compressions and extensions
(1998)
The family of default logics
(1998)
Significant inferences
(2000)
A polynomial translation of logic programs with nested expressions into disjunctive logic programs
(2002)
Preferred well-founded semantics for logic programming by alternating fixpoints : preliminary report
(2002)
The integration of preferences into answer set programming constitutes an important practical device for distinguishing certain preferred answer sets from non-preferred ones. To this end, we elaborate upon rule dependency graphs and their colorings for characterizing different preference handling strategies found in the literature. We start from a characterization of (three types of) preferred answer sets in terms of totally colored dependency graphs. In particular, we demonstrate that this approach allows us to capture all three approaches to preferences in a uniform setting by means of the concept of a height function. In turn, we exemplarily develop an operational characterization of preferred answer sets in terms of operators on partial colorings for one particular strategy. In analogy to the notion of a derivation in proof theory, our operational characterization is expressed as a (non-deterministically formed) sequence of colorings, gradually turning an uncolored graph into a totally colored one
Antwortmengenprogrammierung
(2003)