Theory and Practice of Logic Programming, Jul 1, 2003
Most recently, Answer Set Programming (ASP) has been attracting interest as a new paradigm for pr... more Most recently, Answer Set Programming (ASP) has been attracting interest as a new paradigm for problem solving. An important aspect, for which several approaches have been presented, is the handling of preferences between rules. 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.
ACM Transactions on Computational Logic, Apr 1, 2004
We propose a new declarative planning language, called K, which is based on principles and method... more We propose a new declarative planning language, called K, which is based on principles and methods of logic programming. In this language, transitions between states of knowledge can be described, rather than transitions between completely described states of the world, which makes the language well-suited for planning under incomplete knowledge. Furthermore, it enables the use of default principles in the planning process by supporting negation as failure. Nonetheless, K also supports the representation of transitions between states of the world (i.e., states of complete knowledge) as a special case, which shows that the language is very flexible. As we demonstrate on particular examples, the use of knowledge states may allow for a natural and compact problem representation. We then provide a thorough analysis of the computational complexity of K, and consider different planning problems, including standard planning and secure planning (also known as conformant planning) problems. We show that these problems have different complexities under various restrictions, ranging from NP to NEXPTIME in the propositional case. Our results form the theoretical basis for the DLV K system, which implements the language K on top of the DLV logic programming system.
We propose a new declarative planning language, called K, which is based on principles and method... more We propose a new declarative planning language, called K, which is based on principles and methods of logic programming. In this language, transitions between states of knowledge can be described, rather than transitions between completely described states of the world, which makes the language well-suited for planning under incomplete knowledge. Furthermore, it enables the use of default principles in the planning process by supporting negation as failure. Nonetheless, K also supports the representation of transitions between states of the world (i.e., states of complete knowledge) as a special case, which shows that the language is very flexible. As we demonstrate on particular examples, the use of knowledge states may allow for a natural and compact problem representation. We then provide a thorough analysis of the computational complexity of K, and consider different planning problems, including standard planning and secure planning (also known as conformant planning) problems. We show that these problems have different complexities under various restrictions, ranging from NP to NEXPTIME in the propositional case. Our results form the theoretical basis for the DLV K system, which implements the language K on top of the DLV logic programming system.
This chapter introduces planning and knowledge representation in the declarative action language ... more This chapter introduces planning and knowledge representation in the declarative action language K. Rooted in the area of Knowledge Representation & Reasoning, action languages like K allow the formalization of complex planning problems involving non-determinism and incomplete knowledge in a very flexible manner. By giving an overview of existing planning languages and comparing these against our language, we aim on further promoting the applicability and usefulness of high-level action languages in the area
ABSTRACT DLVK is a knowledge based planning system.It is based on the declarative language K [2],... more ABSTRACT DLVK is a knowledge based planning system.It is based on the declarative language K [2], which is similar in spirit to the logic-based language C [5], but includes some logic-programming features (e.g., default negation and strong negation).
... Editors , Proc. KR-98, Morgan Kaufmann, San Mateo, CA (1998), pp. 212–223. [32] J. McCarthy, ... more ... Editors , Proc. KR-98, Morgan Kaufmann, San Mateo, CA (1998), pp. 212–223. [32] J. McCarthy, Formalization of Common Sense. Papers by John McCarthy edited by V. Lifschitz, Ablex, Norwood, NJ (1990). [33] J. McCarthy ...
Disjunctive logic programming (DLP) with stable model semantics is a powerful nonmonotonic formal... more Disjunctive logic programming (DLP) with stable model semantics is a powerful nonmonotonic formalism for knowledge representation and reasoning. Reasoning with DLP is harder than with normal (∨-free) logic programs, because stable model checking-deciding whether a given model is a stable model of a propositional DLP program-is co-NP-complete, while it is polynomial for normal logic programs. This paper proposes a new transformation Γ M (P), which reduces stable model checking to UNSAT-i.e., to deciding whether a given CNF formula is unsatisfiable. The stability of a model M of a program P thus can be verified by calling a Satisfiability Checker on the CNF formula Γ M (P). The transformation is parsimonious (i.e., no new symbol is added), and efficiently computable, as it runs in logarithmic space (and therefore in polynomial time). Moreover, the size of the generated CNF formula never exceeds the size of the input (and is usually much smaller). We complement this transformation with modular evaluation results, which allow for efficient handling of large real-world reasoning problems. The proposed approach to stable model checking has been implemented in DLV-a state-of-theart implementation of DLP. A number of experiments and benchmarks have been run using SATZ as Satisfiability checker. The results of the experiments are very positive and confirm the usefulness of our techniques.
Journal of Artificial Intelligence Research, Aug 1, 2003
Recently, planning based on answer set programming has been proposed as an approach towards reali... more Recently, planning based on answer set programming has been proposed as an approach towards realizing declarative planning systems. In this paper, we present the language K c , which extends the declarative planning language K by action costs. K c provides the notion of admissible and optimal plans, which are plans whose overall action costs are within a given limit resp. minimum over all plans (i.e., cheapest plans). As we demonstrate, this novel language allows for expressing some nontrivial planning tasks in a declarative way. Furthermore, it can be utilized for representing planning problems under other optimality criteria, such as computing "shortest" plans (with the least number of steps), and refinement combinations of cheapest and fastest plans. We study complexity aspects of the language K c and provide a transformation to logic programs, such that planning problems are solved via answer set programming. Furthermore, we report experimental results on selected problems. Our experience is encouraging that answer set planning may be a valuable approach to expressive planning systems in which intricate planning problems can be naturally specified and solved.
We present new complexity results on answer set checking for nonground programs under a variety o... more We present new complexity results on answer set checking for nonground programs under a variety of syntactic restrictions. For several of these problems, the kind of representation of the answer set to be checked is important. In particular, we consider set-based and bitmap-based representations, which are popular in implementations of Answer Set Programming systems. Furthermore, we present new complexity results for various reasoning tasks under the assumption that predicate arities are bounded by some constant. These results imply that in such a setting-which appears to be a reasonable assumption in practicemore efficient implementations than those currently available may be feasible.
Preferred and Weakly Preferred Answer Sets are extensions to Answer Set Programming (ASP) which a... more Preferred and Weakly Preferred Answer Sets are extensions to Answer Set Programming (ASP) which allow the user to specify priorities for rules. In this paper we present a first implementation of these formalisms by means of "metainterpreters" on top of DLV, an efficient engine for Disjunctive ASP. This approach shows the suitability of ASP in general and of DLV in particular for fast prototyping and experimenting with new languages and knowledge-representation formalisms. In addition to two "straightforward" metainterpreters, we also present a graph-based meta-interpreter that often allows for more efficient computations.
Principles of Knowledge Representation and Reasoning, Jun 2, 2004
Answer Set Programming has become a host for expressing knowledge representation problems, which ... more Answer Set Programming has become a host for expressing knowledge representation problems, which reinforces the interest in efficient methods for computing answer sets of a logic program. While for propositional programs, the complexity of this task has been amply studied and is wellunderstood, less attention has been paid to the case of nonground programs, which is much more important from a KR language perspective. Existing Answer Set Programming systems employ different representations of models, but the consequences of these representations for answer set computation and reasoning tasks have not been analyzed in detail. In this paper, we present novel complexity results on answer set checking for non-ground programs under two methods for representing answer sets and a variety of syntactic restrictions. In particular, we consider set-based and bitmap-based representations, which are popular in implementations of Answer Set Programming systems. Based on these results, we also derive new complexity results for the canonical reasoning tasks over answer sets, under the assumption that predicate arities are bounded by some constant. Our results imply that in such a setting-which appears to be a reasonable assumption in practice-more efficient implementations than those currently available may be feasible.
Annals of Mathematics and Artificial Intelligence, Dec 1, 2007
Disjunctive logic programming (DLP), also called answer set programming (ASP), is a convenient pr... more Disjunctive logic programming (DLP), also called answer set programming (ASP), is a convenient programming paradigm which allows for solving problems in a simple and highly declarative way. The language of DLP is very expressive and able to represent even problems of high complexity (every problem in the complexity class P 2 = NP NP). During the last decade, efficient systems supporting DLP have become available. Virtually all of these systems internally rely on variants of the Davis-Putnam procedure (for deciding propositional satisfiability [SAT]), combined with a suitable model checker. The heuristic for the selection of the branching literal (i.e., the criterion determining the literal to be assumed true at a given stage of the computation) dramatically affects the performance of a DLP system. While heuristics for SAT have received a fair deal of research, only little work on heuristics for DLP has been done so far. In this paper, we design, implement, optimize, and experiment with a number of heuristics for DLP. We focus on different look-ahead heuristics, also called "dynamic heuristics" (the DLP equivalent of unit propagation [UP] heuristics for SAT). These are branching rules where the heuristic value of a literal Q depends on the result of taking Q true and computing its consequences. We motivate and formally define a number of look-ahead heuristics for DLP programs. Furthermore, since look-ahead heuristics are computationally expensive, we design Some results in this paper have been presented in preliminary form at IJCAI-01 [16], LPNMR'01 [17], and LPNMR'05 [18].
DLV is an efficient logic programming and nonmonotonic reasoning (LPNMR) system with advanced kno... more DLV is an efficient logic programming and nonmonotonic reasoning (LPNMR) system with advanced knowledge representation mechanisms and interfaces to classic relational database systems. Its core language is disjunctive datalog (function-free disjunctive logic programming) under the Answer Set Semantics with integrity constraints, both default and strong (or explicit) negation, and queries. Integer arithmetics and various built-in predicates are also supported. In addition DLV has several frontends, namely brave and cautious reasoning, abductive diagnosis, consistency-based diagnosis, a subset of SQL3, planning with action languages, and logic programming with inheritance.
Page 1. 99 The Diagnosis Frontend of the dlv system Thomas Eiter, Wolfgang Faber, Nicola Leone an... more Page 1. 99 The Diagnosis Frontend of the dlv system Thomas Eiter, Wolfgang Faber, Nicola Leone and Gerald Pfeifer ∗ Institut für Informationssysteme, Technische Universität Wien, A-1040 Vienna, Austria E-mail: [email protected], {faber,leone,pfeifer}@dbai.tuwien.ac.at ...
Answer Set Programming (ASP) is a novel programming paradigm, which allows to solve problems in a... more Answer Set Programming (ASP) is a novel programming paradigm, which allows to solve problems in a simple and highly declarative way. The language of ASP (function-free disjunctive logic programming) is very expressive, and allows to represent even problems of high complexity (every problem in the complexity class P2 = NPNP). As for SAT solvers, the heuristic for the selection of the branching literal (i.e., the criterion determining the literal to be assumed true at a given stage of the computation) dramatically affects the performance of an ASP system. While heuristics for SAT have received a fair deal of research in AI, only little work in heuristics for ASP has been done so far. In this paper, we extend to the ASP framework a number of heuristics which have been successfully employed in existing systems, and we compare them experimentally. To this end, we implement such heuristics in the ASP system DLV, and we evaluate their respective efficiency on a number of benchmark problems taken from various domains. The experiments show interesting results, and evidence a couple of promising heuristic criteria for ASP, which sensibly outperform the heuristic of DLV.
Theory and Practice of Logic Programming, Jul 1, 2003
Most recently, Answer Set Programming (ASP) has been attracting interest as a new paradigm for pr... more Most recently, Answer Set Programming (ASP) has been attracting interest as a new paradigm for problem solving. An important aspect, for which several approaches have been presented, is the handling of preferences between rules. 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.
ACM Transactions on Computational Logic, Apr 1, 2004
We propose a new declarative planning language, called K, which is based on principles and method... more We propose a new declarative planning language, called K, which is based on principles and methods of logic programming. In this language, transitions between states of knowledge can be described, rather than transitions between completely described states of the world, which makes the language well-suited for planning under incomplete knowledge. Furthermore, it enables the use of default principles in the planning process by supporting negation as failure. Nonetheless, K also supports the representation of transitions between states of the world (i.e., states of complete knowledge) as a special case, which shows that the language is very flexible. As we demonstrate on particular examples, the use of knowledge states may allow for a natural and compact problem representation. We then provide a thorough analysis of the computational complexity of K, and consider different planning problems, including standard planning and secure planning (also known as conformant planning) problems. We show that these problems have different complexities under various restrictions, ranging from NP to NEXPTIME in the propositional case. Our results form the theoretical basis for the DLV K system, which implements the language K on top of the DLV logic programming system.
We propose a new declarative planning language, called K, which is based on principles and method... more We propose a new declarative planning language, called K, which is based on principles and methods of logic programming. In this language, transitions between states of knowledge can be described, rather than transitions between completely described states of the world, which makes the language well-suited for planning under incomplete knowledge. Furthermore, it enables the use of default principles in the planning process by supporting negation as failure. Nonetheless, K also supports the representation of transitions between states of the world (i.e., states of complete knowledge) as a special case, which shows that the language is very flexible. As we demonstrate on particular examples, the use of knowledge states may allow for a natural and compact problem representation. We then provide a thorough analysis of the computational complexity of K, and consider different planning problems, including standard planning and secure planning (also known as conformant planning) problems. We show that these problems have different complexities under various restrictions, ranging from NP to NEXPTIME in the propositional case. Our results form the theoretical basis for the DLV K system, which implements the language K on top of the DLV logic programming system.
This chapter introduces planning and knowledge representation in the declarative action language ... more This chapter introduces planning and knowledge representation in the declarative action language K. Rooted in the area of Knowledge Representation & Reasoning, action languages like K allow the formalization of complex planning problems involving non-determinism and incomplete knowledge in a very flexible manner. By giving an overview of existing planning languages and comparing these against our language, we aim on further promoting the applicability and usefulness of high-level action languages in the area
ABSTRACT DLVK is a knowledge based planning system.It is based on the declarative language K [2],... more ABSTRACT DLVK is a knowledge based planning system.It is based on the declarative language K [2], which is similar in spirit to the logic-based language C [5], but includes some logic-programming features (e.g., default negation and strong negation).
... Editors , Proc. KR-98, Morgan Kaufmann, San Mateo, CA (1998), pp. 212–223. [32] J. McCarthy, ... more ... Editors , Proc. KR-98, Morgan Kaufmann, San Mateo, CA (1998), pp. 212–223. [32] J. McCarthy, Formalization of Common Sense. Papers by John McCarthy edited by V. Lifschitz, Ablex, Norwood, NJ (1990). [33] J. McCarthy ...
Disjunctive logic programming (DLP) with stable model semantics is a powerful nonmonotonic formal... more Disjunctive logic programming (DLP) with stable model semantics is a powerful nonmonotonic formalism for knowledge representation and reasoning. Reasoning with DLP is harder than with normal (∨-free) logic programs, because stable model checking-deciding whether a given model is a stable model of a propositional DLP program-is co-NP-complete, while it is polynomial for normal logic programs. This paper proposes a new transformation Γ M (P), which reduces stable model checking to UNSAT-i.e., to deciding whether a given CNF formula is unsatisfiable. The stability of a model M of a program P thus can be verified by calling a Satisfiability Checker on the CNF formula Γ M (P). The transformation is parsimonious (i.e., no new symbol is added), and efficiently computable, as it runs in logarithmic space (and therefore in polynomial time). Moreover, the size of the generated CNF formula never exceeds the size of the input (and is usually much smaller). We complement this transformation with modular evaluation results, which allow for efficient handling of large real-world reasoning problems. The proposed approach to stable model checking has been implemented in DLV-a state-of-theart implementation of DLP. A number of experiments and benchmarks have been run using SATZ as Satisfiability checker. The results of the experiments are very positive and confirm the usefulness of our techniques.
Journal of Artificial Intelligence Research, Aug 1, 2003
Recently, planning based on answer set programming has been proposed as an approach towards reali... more Recently, planning based on answer set programming has been proposed as an approach towards realizing declarative planning systems. In this paper, we present the language K c , which extends the declarative planning language K by action costs. K c provides the notion of admissible and optimal plans, which are plans whose overall action costs are within a given limit resp. minimum over all plans (i.e., cheapest plans). As we demonstrate, this novel language allows for expressing some nontrivial planning tasks in a declarative way. Furthermore, it can be utilized for representing planning problems under other optimality criteria, such as computing "shortest" plans (with the least number of steps), and refinement combinations of cheapest and fastest plans. We study complexity aspects of the language K c and provide a transformation to logic programs, such that planning problems are solved via answer set programming. Furthermore, we report experimental results on selected problems. Our experience is encouraging that answer set planning may be a valuable approach to expressive planning systems in which intricate planning problems can be naturally specified and solved.
We present new complexity results on answer set checking for nonground programs under a variety o... more We present new complexity results on answer set checking for nonground programs under a variety of syntactic restrictions. For several of these problems, the kind of representation of the answer set to be checked is important. In particular, we consider set-based and bitmap-based representations, which are popular in implementations of Answer Set Programming systems. Furthermore, we present new complexity results for various reasoning tasks under the assumption that predicate arities are bounded by some constant. These results imply that in such a setting-which appears to be a reasonable assumption in practicemore efficient implementations than those currently available may be feasible.
Preferred and Weakly Preferred Answer Sets are extensions to Answer Set Programming (ASP) which a... more Preferred and Weakly Preferred Answer Sets are extensions to Answer Set Programming (ASP) which allow the user to specify priorities for rules. In this paper we present a first implementation of these formalisms by means of "metainterpreters" on top of DLV, an efficient engine for Disjunctive ASP. This approach shows the suitability of ASP in general and of DLV in particular for fast prototyping and experimenting with new languages and knowledge-representation formalisms. In addition to two "straightforward" metainterpreters, we also present a graph-based meta-interpreter that often allows for more efficient computations.
Principles of Knowledge Representation and Reasoning, Jun 2, 2004
Answer Set Programming has become a host for expressing knowledge representation problems, which ... more Answer Set Programming has become a host for expressing knowledge representation problems, which reinforces the interest in efficient methods for computing answer sets of a logic program. While for propositional programs, the complexity of this task has been amply studied and is wellunderstood, less attention has been paid to the case of nonground programs, which is much more important from a KR language perspective. Existing Answer Set Programming systems employ different representations of models, but the consequences of these representations for answer set computation and reasoning tasks have not been analyzed in detail. In this paper, we present novel complexity results on answer set checking for non-ground programs under two methods for representing answer sets and a variety of syntactic restrictions. In particular, we consider set-based and bitmap-based representations, which are popular in implementations of Answer Set Programming systems. Based on these results, we also derive new complexity results for the canonical reasoning tasks over answer sets, under the assumption that predicate arities are bounded by some constant. Our results imply that in such a setting-which appears to be a reasonable assumption in practice-more efficient implementations than those currently available may be feasible.
Annals of Mathematics and Artificial Intelligence, Dec 1, 2007
Disjunctive logic programming (DLP), also called answer set programming (ASP), is a convenient pr... more Disjunctive logic programming (DLP), also called answer set programming (ASP), is a convenient programming paradigm which allows for solving problems in a simple and highly declarative way. The language of DLP is very expressive and able to represent even problems of high complexity (every problem in the complexity class P 2 = NP NP). During the last decade, efficient systems supporting DLP have become available. Virtually all of these systems internally rely on variants of the Davis-Putnam procedure (for deciding propositional satisfiability [SAT]), combined with a suitable model checker. The heuristic for the selection of the branching literal (i.e., the criterion determining the literal to be assumed true at a given stage of the computation) dramatically affects the performance of a DLP system. While heuristics for SAT have received a fair deal of research, only little work on heuristics for DLP has been done so far. In this paper, we design, implement, optimize, and experiment with a number of heuristics for DLP. We focus on different look-ahead heuristics, also called "dynamic heuristics" (the DLP equivalent of unit propagation [UP] heuristics for SAT). These are branching rules where the heuristic value of a literal Q depends on the result of taking Q true and computing its consequences. We motivate and formally define a number of look-ahead heuristics for DLP programs. Furthermore, since look-ahead heuristics are computationally expensive, we design Some results in this paper have been presented in preliminary form at IJCAI-01 [16], LPNMR'01 [17], and LPNMR'05 [18].
DLV is an efficient logic programming and nonmonotonic reasoning (LPNMR) system with advanced kno... more DLV is an efficient logic programming and nonmonotonic reasoning (LPNMR) system with advanced knowledge representation mechanisms and interfaces to classic relational database systems. Its core language is disjunctive datalog (function-free disjunctive logic programming) under the Answer Set Semantics with integrity constraints, both default and strong (or explicit) negation, and queries. Integer arithmetics and various built-in predicates are also supported. In addition DLV has several frontends, namely brave and cautious reasoning, abductive diagnosis, consistency-based diagnosis, a subset of SQL3, planning with action languages, and logic programming with inheritance.
Page 1. 99 The Diagnosis Frontend of the dlv system Thomas Eiter, Wolfgang Faber, Nicola Leone an... more Page 1. 99 The Diagnosis Frontend of the dlv system Thomas Eiter, Wolfgang Faber, Nicola Leone and Gerald Pfeifer ∗ Institut für Informationssysteme, Technische Universität Wien, A-1040 Vienna, Austria E-mail: [email protected], {faber,leone,pfeifer}@dbai.tuwien.ac.at ...
Answer Set Programming (ASP) is a novel programming paradigm, which allows to solve problems in a... more Answer Set Programming (ASP) is a novel programming paradigm, which allows to solve problems in a simple and highly declarative way. The language of ASP (function-free disjunctive logic programming) is very expressive, and allows to represent even problems of high complexity (every problem in the complexity class P2 = NPNP). As for SAT solvers, the heuristic for the selection of the branching literal (i.e., the criterion determining the literal to be assumed true at a given stage of the computation) dramatically affects the performance of an ASP system. While heuristics for SAT have received a fair deal of research in AI, only little work in heuristics for ASP has been done so far. In this paper, we extend to the ASP framework a number of heuristics which have been successfully employed in existing systems, and we compare them experimentally. To this end, we implement such heuristics in the ASP system DLV, and we evaluate their respective efficiency on a number of benchmark problems taken from various domains. The experiments show interesting results, and evidence a couple of promising heuristic criteria for ASP, which sensibly outperform the heuristic of DLV.
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Papers by Gerald Pfeifer