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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 114 (13 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.
Loop Formulas for Disjunctive Logic Programs
 In Proc. ICLP03
, 2003
"... We extend Clark's de nition of a completed program and the de nition of a loop formula due to Lin and Zhao to disjunctive logic programs. Our main result, generalizing the Lin/Zhao theorem, shows that answer sets for a disjunctive program can be characterized as the models of its completion th ..."
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Cited by 47 (9 self)
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We extend Clark's de nition of a completed program and the de nition of a loop formula due to Lin and Zhao to disjunctive logic programs. Our main result, generalizing the Lin/Zhao theorem, shows that answer sets for a disjunctive program can be characterized as the models of its completion that satisfy the loop formulas. The concept of a tight program and Fages' theorem are extended to disjunctive programs as well.
On the Effect of Default Negation on the Expressiveness of Disjunctive Rules
, 2001
"... In this paper, the expressive power of disjunctive rules involving default negation is analyzed within a framework based on polynomial, faithful and modular (PFM) translations. The analysis is restricted to the stable semantics of disjunctive logic programs. A particular interest is understanding wh ..."
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Cited by 16 (4 self)
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In this paper, the expressive power of disjunctive rules involving default negation is analyzed within a framework based on polynomial, faithful and modular (PFM) translations. The analysis is restricted to the stable semantics of disjunctive logic programs. A particular interest is understanding what is the effect if default negation is allowed in the heads of disjunctive rules. It is established in the paper that occurrences of default negation can be removed from the heads of rules using a PFM translation when default negation is allowed in the bodies of rules. In this case, we may conclude that default negation appearing in the heads of rules does not affect expressive power of rules. However, in the case that default negation may not be used in the bodies of rules, such a PFM translation is no longer possible. Moreover, there is no PFM translation for removing default negation from the bodies of rules. Consequently, disjunctive logic programs with default negation in the bodies of rules are strictly more expressive than those without.
Equivalence in abductive logic
 In Proc. IJCAI 2005
, 2005
"... We consider the problem of identifying equivalence of two knowledge bases which are capable of abductive reasoning. Here, a knowledge base is written in either firstorder logic or nonmonotonic logic programming. In this work, we will give two definitions of abductive equivalence. The first one, exp ..."
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Cited by 3 (1 self)
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We consider the problem of identifying equivalence of two knowledge bases which are capable of abductive reasoning. Here, a knowledge base is written in either firstorder logic or nonmonotonic logic programming. In this work, we will give two definitions of abductive equivalence. The first one, explainable equivalence, requires that two abductive programs have the same explainability for any observation. Another one, explanatory equivalence, guarantees that any observation has exactly the same explanations in each abductive framework. Explanatory equivalence is a stronger notion than explainable equivalence. In firstorder abduction, explainable equivalence can be verified by the notion of extensional equivalence in default theories. In nonmonotonic logic programs, explanatory equivalence can be checked by means of the notion of relative strong equivalence. We also show the complexity results for abductive equivalence. 1
Order and Negation as Failure
 In Procs. of the Intl. Conference on Logic Programming, volume 2916 of LNCS
, 2003
"... We equip ordered logic programs with negation as failure, using a simple generalization of the preferred answer set semantics for ordered programs. ..."
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Cited by 3 (2 self)
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We equip ordered logic programs with negation as failure, using a simple generalization of the preferred answer set semantics for ordered programs.
Testing the Equivalence of Disjunctive Logic Programs
, 2003
"... To solve a problem in answer set programming (ASP), one constructs a logic program so that its answer sets correspond to the solutions of the problem and computes the answer sets of the program using a special purpose search engine. The encodings are not unique, i.e. several versions of a program ca ..."
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Cited by 2 (1 self)
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To solve a problem in answer set programming (ASP), one constructs a logic program so that its answer sets correspond to the solutions of the problem and computes the answer sets of the program using a special purpose search engine. The encodings are not unique, i.e. several versions of a program can be used e.g. in optimizing the execution time or space. Since the solutions to the problem correspond to answer sets of the program, it is necessary to ensure that the different encodings yield the same output. In ASP this means that one has to check whether given two logic programs have the same answer sets, i.e., whether they are semantically equivalent.
A Logical Characterisation of Ordered Disjunction ∗
"... In this paper we consider a logical treatment for the ordered disjunction operator × introduced by Brewka, Niemelä and Syrjänen in their Logic Programs with Ordered Disjunctions (LPOD). LPODs are used to represent preferences in logic programming under the answer set semantics. Their semantics is de ..."
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In this paper we consider a logical treatment for the ordered disjunction operator × introduced by Brewka, Niemelä and Syrjänen in their Logic Programs with Ordered Disjunctions (LPOD). LPODs are used to represent preferences in logic programming under the answer set semantics. Their semantics is defined by first translating the LPOD into a set of normal programs (called split programs) and then imposing a preference relation among the answer sets of these split programs. We concentrate on the first step and show how a suitable translation of the ordered disjunction as a derived operator into the logic of HereandThere allows capturing the answer sets of the split programs in a direct way. We use this characterisation not only for providing an alternative implementation for LPODs, but also for checking several properties (under strongly equivalent transformations) of the × operator, like for instance, its distributivity with respect to conjunction or regular disjunction. We also make a comparison to an extension proposed by Kärger, Lopes, Olmedilla and Polleres, that combines × with regular disjunction. 1
Proceedings of the TwentyThird International Joint Conference on Artificial Intelligence On Condensing a Sequence of Updates in AnswerSet Programming ∗
"... Update semantics for AnswerSet Programming assign models to sequences of answerset programs which result from the iterative process of updating programs by programs. Each program in the sequence represents an update of the preceding ones. One of the enduring problems in this context is state conde ..."
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Update semantics for AnswerSet Programming assign models to sequences of answerset programs which result from the iterative process of updating programs by programs. Each program in the sequence represents an update of the preceding ones. One of the enduring problems in this context is state condensing, or the problem of determining a single logic program that faithfully represents the sequence of programs. Such logic program should 1) be written in the same alphabet, 2) have the same stable models, and 3) be equivalent to the sequence of programs when subject to further updates. It has been known for more than a decade that update semantics easily lead to nonminimal stable models, so an update sequence cannot be represented by a single nondisjunctive program. On the other hand, more expressive classes of programs were never considered, mainly because it was not clear how they could be updated further. In this paper we solve the state condensing problem for two foundational rule update semantics, using nested logic programs. Furthermore, we also show that disjunctive programs with default negation in the head can be used for the same purpose. 1