44 research outputs found
Computing Preferred Answer Sets by Meta-Interpretation in Answer Set Programming
Most recently, Answer Set Programming (ASP) is attracting interest as a new
paradigm for problem solving. An important aspect which needs to be supported
is the handling of preferences between rules, for which several approaches have
been presented. In this paper, we consider the problem of implementing
preference handling approaches by means of meta-interpreters in Answer Set
Programming. In particular, we consider the preferred answer set approaches by
Brewka and Eiter, by Delgrande, Schaub and Tompits, and by Wang, Zhou and Lin.
We present suitable meta-interpreters for these semantics using DLV, which is
an efficient engine for ASP. Moreover, we also present a meta-interpreter for
the weakly preferred answer set approach by Brewka and Eiter, which uses the
weak constraint feature of DLV as a tool for expressing and solving an
underlying optimization problem. We also consider advanced meta-interpreters,
which make use of graph-based characterizations and often allow for more
efficient computations. Our approach shows the suitability of ASP in general
and of DLV in particular for fast prototyping. This can be fruitfully exploited
for experimenting with new languages and knowledge-representation formalisms.Comment: 34 pages, appeared as a Technical Report at KBS of the Vienna
University of Technology, see http://www.kr.tuwien.ac.at/research/reports
The DLV System for Knowledge Representation and Reasoning
This paper presents the DLV system, which is widely considered the
state-of-the-art implementation of disjunctive logic programming, and addresses
several aspects. As for problem solving, we provide a formal definition of its
kernel language, function-free disjunctive logic programs (also known as
disjunctive datalog), extended by weak constraints, which are a powerful tool
to express optimization problems. We then illustrate the usage of DLV as a tool
for knowledge representation and reasoning, describing a new declarative
programming methodology which allows one to encode complex problems (up to
-complete problems) in a declarative fashion. On the foundational
side, we provide a detailed analysis of the computational complexity of the
language of DLV, and by deriving new complexity results we chart a complete
picture of the complexity of this language and important fragments thereof.
Furthermore, we illustrate the general architecture of the DLV system which
has been influenced by these results. As for applications, we overview
application front-ends which have been developed on top of DLV to solve
specific knowledge representation tasks, and we briefly describe the main
international projects investigating the potential of the system for industrial
exploitation. Finally, we report about thorough experimentation and
benchmarking, which has been carried out to assess the efficiency of the
system. The experimental results confirm the solidity of DLV and highlight its
potential for emerging application areas like knowledge management and
information integration.Comment: 56 pages, 9 figures, 6 table
Comparing the Reasoning Capabilities of Equilibrium Theories and Answer Set Programs
[Abstract] Answer Set Programming (ASP) is a well established logical approach in artificial intelligence that is widely used for knowledge representation and problem solving. Equilibrium logic extends answer set semantics to more general classes of programs and theories. When intertheory relations are studied in ASP, or in the more general form of equilibrium logic, they are usually understood in the form of comparisons of the answer sets or equilibrium models of theories or programs. This is the case for strong and uniform equivalence and their relativised and projective versions. However, there are many potential areas of application of ASP for which query answering is relevant and a comparison of programs in terms of what can be inferred from them may be important. We formulate and study some natural equivalence and entailment concepts for programs and theories that are couched in terms of inference and query answering. We show that, for the most part, these new intertheory relations coincide with their model-theoretic counterparts. We also extend some previous results on projective entailment for theories and for the new connective called fork.This research has received partial support from the European Cooperation in Science & Technology (COST) Action CA17124. The third author acknowledges the funding of project PID 2020-116201GB-I00 (Ministerio de Ciencia e Innovación, Spain) and also the financial support supplied by the ConsellerÃa de Educación, Universidade e Formación Profesional (accreditations GPC ED431B 2022/23 and 2019–2022 ED431G-2019/01). The last author has been supported by the Austrian Science Fund (FWF) grant Y698Xunta de Galicia; ED431B 2022/23Xunta de Galicia; ED431G-2019/0
Modularity in answer set programs
Answer set programming (ASP) is an approach to rule-based constraint programming allowing flexible knowledge representation in variety of application areas. The declarative nature of ASP is reflected in problem solving. First, a programmer writes down a logic program the answer sets of which correspond to the solutions of the problem. The answer sets of the program are then computed using a special purpose search engine, an ASP solver. The development of efficient ASP solvers has enabled the use of answer set programming in various application domains such as planning, product configuration, computer aided verification, and bioinformatics.
The topic of this thesis is modularity in answer set programming. While modern programming languages typically provide means to exploit modularity in a number of ways to govern the complexity of programs and their development process, relatively little attention has been paid to modularity in ASP. When designing a module architecture for ASP, it is essential to establish full compositionality of the semantics with respect to the module system. A balance is sought between introducing restrictions that guarantee the compositionality of the semantics and enforce a good programming style in ASP, and avoiding restrictions on the module hierarchy for the sake of flexibility of knowledge representation.
To justify a replacement of a module with another, that is, to be able to guarantee that changes made on the level of modules do not alter the semantics of the program when seen as an entity, a notion of equivalence for modules is provided. In close connection with the development of the compositional module architecture, a transformation from verification of equivalence to search for answer sets is developed. The translation-based approach makes it unnecessary to develop a dedicated tool for the equivalence verification task by allowing the direct use of existing ASP solvers.
Translations and transformations between different problems, program classes, and formalisms are another central theme in the thesis. To guarantee efficiency and soundness of the translation-based approach, certain syntactical and semantical properties of transformations are desirable, in terms of translation time, solution correspondence between the original and the transformed problem, and locality/globality of a particular transformation.
In certain cases a more refined notion of minimality than that inherent in ASP can make program encodings more intuitive. Lifschitz' parallel and prioritized circumscription offer a solution in which certain atoms are allowed to vary or to have fixed values while others are falsified as far as possible according to priority classes. In this thesis a linear and faithful transformation embedding parallel and prioritized circumscription into ASP is provided. This enhances the knowledge representation capabilities of answer set programming by allowing the use of existing ASP solvers for computing parallel and prioritized circumscription
Towards a unified theory of logic programming semantics: Level mapping characterizations of selector generated models
Currently, the variety of expressive extensions and different semantics
created for logic programs with negation is diverse and heterogeneous, and
there is a lack of comprehensive comparative studies which map out the
multitude of perspectives in a uniform way. Most recently, however, new
methodologies have been proposed which allow one to derive uniform
characterizations of different declarative semantics for logic programs with
negation. In this paper, we study the relationship between two of these
approaches, namely the level mapping characterizations due to [Hitzler and
Wendt 2005], and the selector generated models due to [Schwarz 2004]. We will
show that the latter can be captured by means of the former, thereby supporting
the claim that level mappings provide a very flexible framework which is
applicable to very diversely defined semantics.Comment: 17 page
Towards a Systematic Account of Different Semantics for Logic Programs
In [Hitzler and Wendt 2002, 2005], a new methodology has been proposed which
allows to derive uniform characterizations of different declarative semantics
for logic programs with negation. One result from this work is that the
well-founded semantics can formally be understood as a stratified version of
the Fitting (or Kripke-Kleene) semantics. The constructions leading to this
result, however, show a certain asymmetry which is not readily understood. We
will study this situation here with the result that we will obtain a coherent
picture of relations between different semantics for normal logic programs.Comment: 20 page