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Answer Set Planning
"... In "answer set programming," solutions to a problem are represented by answer sets, and not by answer substitutions produced in response to a query, as in conventional logic programming. Instead of Prolog, answer set programming uses software systems capable of computing answer sets. This ..."
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Cited by 168 (5 self)
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In "answer set programming," solutions to a problem are represented by answer sets, and not by answer substitutions produced in response to a query, as in conventional logic programming. Instead of Prolog, answer set programming uses software systems capable of computing answer sets. This paper is about applications of this idea to planning.
Propositional Semantics for Disjunctive Logic Programs
 Annals of Mathematics and Artificial Intelligence
, 1994
"... In this paper we study the properties of the class of headcyclefree extended disjunctive logic programs (HEDLPs), which includes, as a special case, all nondisjunctive extended logic programs. We show that any propositional HEDLP can be mapped in polynomial time into a propositional theory such th ..."
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Cited by 161 (2 self)
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In this paper we study the properties of the class of headcyclefree extended disjunctive logic programs (HEDLPs), which includes, as a special case, all nondisjunctive extended logic programs. We show that any propositional HEDLP can be mapped in polynomial time into a propositional theory such that each model of the latter corresponds to an answer set, as defined by stable model semantics, of the former. Using this mapping, we show that many queries over HEDLPs can be determined by solving propositional satisfiability problems. Our mapping has several important implications: It establishes the NPcompleteness of this class of disjunctive logic programs; it allows existing algorithms and tractable subsets for the satisfiability problem to be used in logic programming; it facilitates evaluation of the expressive power of disjunctive logic programs; and it leads to the discovery of useful similarities between stable model semantics and Clark's predicate completion. 1 Introduction ...
Preferred Answer Sets for Extended Logic Programs
 ARTIFICIAL INTELLIGENCE
, 1998
"... In this paper, we address the issue of how Gelfond and Lifschitz's answer set semantics for extended logic programs can be suitably modified to handle prioritized programs. In such programs an ordering on the program rules is used to express preferences. We show how this ordering can be used ..."
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Cited by 156 (20 self)
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In this paper, we address the issue of how Gelfond and Lifschitz's answer set semantics for extended logic programs can be suitably modified to handle prioritized programs. In such programs an ordering on the program rules is used to express preferences. We show how this ordering can be used to define preferred answer sets and thus to increase the set of consequences of a program. We define a strong and a weak notion of preferred answer sets. The first takes preferences more seriously, while the second guarantees the existence of a preferred answer set for programs possessing at least one answer set. Adding priorities
On the Computational Cost of Disjunctive Logic Programming: Propositional Case
, 1995
"... This paper addresses complexity issues for important problems arising with disjunctive logic programming. In particular, the complexity of deciding whether a disjunctive logic program is consistent is investigated for a variety of wellknown semantics, as well as the complexity of deciding whethe ..."
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Cited by 140 (26 self)
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This paper addresses complexity issues for important problems arising with disjunctive logic programming. In particular, the complexity of deciding whether a disjunctive logic program is consistent is investigated for a variety of wellknown semantics, as well as the complexity of deciding whether a propositional formula is satised by all models according to a given semantics. We concentrate on nite propositional disjunctive programs with as wells as without integrity constraints, i.e., clauses with empty heads; the problems are located in appropriate slots of the polynomial hierarchy. In particular, we show that the consistency check is P 2 complete for the disjunctive stable model semantics (in the total as well as partial version), the iterated closed world assumption, and the perfect model semantics, and we show that the inference problem for these semantics is P 2 complete; analogous results are derived for the an
Nested expressions in logic programs
 Annals of Mathematics and Artificial Intelligence
, 1999
"... We extend the answer set semantics to a class of logic programs with nested expressions permitted in the bodies and heads of rules. These expressions are formed from literals using negation as failure, conjunction (,) and disjunction (;) that can be nested arbitrarily. Conditional expressions are in ..."
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Cited by 135 (12 self)
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We extend the answer set semantics to a class of logic programs with nested expressions permitted in the bodies and heads of rules. These expressions are formed from literals using negation as failure, conjunction (,) and disjunction (;) that can be nested arbitrarily. Conditional expressions are introduced as abbreviations. The study of equivalent transformations of programs with nested expressions shows that any such program is equivalent to a set of disjunctive rules, possibly with negation as failure in the heads. The generalized answer set semantics is related to the LloydTopor generalization of Clark's completion and to the logic of minimal belief and negation as failure.
DL+log: Tight integration of description logics and disjunctive datalog
 In KR2006
, 2006
"... The integration of Description Logics and Datalog rules presents many semantic and computational problems. In particular, reasoning in a system fully integrating Description Logics knowledge bases (DLKBs) and Datalog programs is undecidable. Many proposals have overcomed this problem through a “saf ..."
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Cited by 112 (6 self)
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The integration of Description Logics and Datalog rules presents many semantic and computational problems. In particular, reasoning in a system fully integrating Description Logics knowledge bases (DLKBs) and Datalog programs is undecidable. Many proposals have overcomed this problem through a “safeness ” condition that limits the interaction between the DLKB and the Datalog rules. Such a safe integration of Description Logics and Datalog provides for systems with decidable reasoning, at the price of a strong limitation in terms of expressive power. In this paper we define DL+log, a general framework for the integration of Description Logics and disjunctive Datalog. From the knowledge representation viewpoint, DL+log extends previous proposals, since it allows for a tighter form of integration between DLKBs and Datalog rules which overcomes the main representational limits of the approaches based on the safeness condition. From the reasoning viewpoint, we present algorithms for reasoning in DL+log, and prove decidability and complexity of reasoning in DL+log for several Description Logics. To the best of our knowledge, DL+log constitutes the most powerful decidable combination of Description Logics and disjunctive Datalog rules proposed so far.
A Deductive System for Nonmonotonic Reasoning
 In
, 1997
"... Abstract. Disjunctive Deductive Databases (DDDBs) functionfree disjunctive logic programs with negation in rule bodies allowed have been recently recognized as a powerful tool for knowledge representation and commonsense reasoning. Much research as been spent on issues like semantics and comple ..."
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Cited by 110 (21 self)
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Abstract. Disjunctive Deductive Databases (DDDBs) functionfree disjunctive logic programs with negation in rule bodies allowed have been recently recognized as a powerful tool for knowledge representation and commonsense reasoning. Much research as been spent on issues like semantics and complexity of DDDBs, but the important area of implementing DDDBs has been less addressed so far. However, a thorough investigation thereof is a basic requirement for building systems which render previous foundational work on DDDBs useful for practice. This paper presents the architecture ofa DDDB system currently developed at TU Vienna in the FWF project P11580MAT '~A Query System for Disjunctive Deductive Databases". 1 In t roduct ion The study of integrating databases with logic programming opened in the past the field of deductive databases. Basically, a deductive database is a functionfree logic program, i.e., a datalog program (possibly extended with negation). Several advanced eductive database systems utilize logic programming and extensions thereof or querying relational databases, e.g. [14, 21, 24]. The need for representing disjunctive (or incomplete) information led to Disjunctive Deductive Databases (DDDBs) [18]. They can be seen as functionfree disjunctive logic programs, i.e., disjunctive datalog programs [19, 12]. DDDBs are nowadays widely recognized as a valuable tool for knowledge representation a d reasoning [1, 17, 30, 13, 19]. The strong interest in enhancing deductive databases by disjunction is documented by a number of publications (cf. [17]) and special workshops dedicated to this subject (cf. [30]). An important merit of DDDBs over normal (i.e., disjunctionfree) logic programming is its capability to model incomplete knowledge [1, 17].
Answer Sets in General Nonmonotonic Reasoning
, 1992
"... Languages of declarative logic programming differ from other modal nonmonotonic formalisms by lack of syntactic uniformity. For instance, negation as failure can be used in the body of a rule, but not in the head; in disjunctive programs, disjunction is used in the head of a rule, but not in the bod ..."
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Cited by 105 (8 self)
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Languages of declarative logic programming differ from other modal nonmonotonic formalisms by lack of syntactic uniformity. For instance, negation as failure can be used in the body of a rule, but not in the head; in disjunctive programs, disjunction is used in the head of a rule, but not in the body; in extended programs, negation as failure can be used on top of classical negation, but not the other way around. We argue that this lack of uniformity should not be viewed as a distinguishing feature of logic programming in general. As a starting point, we take a translation from the language of disjunctive programs with negation as failure and classical negation into MBNFthe logic of minimal belief and negation as failure. A class of theories based on this logic is defined, theories with protected literals, which is syntactically uniform and contains the translations of all programs. We show that theories with protected literals have a semantics similar to the answer set semantics us...
A Logic Programming Approach to KnowledgeState Planning, II: The DLV System
, 2001
"... In Part I of this series of papers, we have proposed a new logicbased planning language, called K. This language facilitates the description of transitions between states of knowledge and it is well suited for planning under incomplete knowledge. Nonetheless, K also supports the representation of t ..."
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Cited by 103 (33 self)
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In Part I of this series of papers, we have proposed a new logicbased planning language, called K. This language facilitates the description of transitions between states of knowledge and it is well suited for planning under incomplete knowledge. Nonetheless, K also supports the representation of transitions between states of the world (i.e., states of complete knowledge) as a special case, proving to be very flexible. In the present Part II, we describe the DLV planning system, which implements K on top of the disjunctive logic programming system DLV. This novel planning system allows for solving hard planning problems, including secure planning under incomplete initial states (often called conformant planning in the literature), which cannot be solved at all by other logicbased planning systems such as traditional satisfiability planners. We present a detailed comparison of the system to several stateoftheart conformant planning systems, both at the level of system features and on benchmark problems. Our results indicate that, thanks to the power of knowledgestate problem encoding, the DLV system is competitive even with special purpose conformant planning systems, and it often supplies a more natural and simple representation of the planning problems.