## Comparing the Expressive Powers of Some Syntactically Restricted Classes of Logic Programs (2000)

Venue: | In Proc. 1st International Conference on Computational Logic |

Citations: | 9 - 3 self |

### BibTeX

@INPROCEEDINGS{Janhunen00comparingthe,

author = {Tomi Janhunen},

title = {Comparing the Expressive Powers of Some Syntactically Restricted Classes of Logic Programs},

booktitle = {In Proc. 1st International Conference on Computational Logic},

year = {2000},

pages = {852--866},

publisher = {Springer Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper studies the expressive powers of classes of logic programs that are obtained by restricting the number of positive literals (atoms) in the bodies of the rules. Three kinds of restrictions are considered, giving rise to the classes of atomic, unary and binary logic programs. The expressive powers of these classes of logic programs are compared by analyzing the existence of polynomial, faithful, and modular (PFM) translation functions between the classes. This analysis leads to a strict ordering of the classes of logic programs. The main result is that binary and unary rules are strictly more expressive than unary and atomic rules, respectively. This is the case even if we consider normal logic programs where negative literals may appear in the bodies of rules. Practical implications of the results are discussed in the context of a particular implementation technique for the stable model semantics of normal logic programs, namely contrapositive reasoning with rules. 1

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Citation Context ...ic programs, namely contrapositive reasoning with rules. 1 Introduction In logic programming [20], a simple rule-based language is used for knowledge representation in a declarative fashion (see e.g. =-=[12]-=- for an extensive study and [18] for programming methodology). To enhance the knowledge representation capabilities of logic programs, Clark [2] proposed a form of negation, namely negation as failure... |

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Citation Context ...logic programs with richer syntax (see [5, 6]) and dierent semantics (see [21]). Our recent results on the relationship of partial stable models and total stable models of disjunctive logic programs [=-=11]-=- provide a promising starting point in this respect. Acknowledgments The author wishes to thank Mirek Truszczyski for his suggestion to apply techniques from [9] to the research problem addressed in t... |

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Citation Context ... on related work at rst. Partial evaluation techniques have been introduced to unfold rules of programs in a semantics preserving way. A good example in this respect is the approach by Brass and Dix [=-=1]-=-. They propose equivalence transformations for normal and disjunctive logic programs under the stable semantics. Let us describe these transformations by restricting to the case of normal logic progra... |

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Citation Context ... i such that a 2 TP " i (;). 3 Translations The author has analyzed the expressive powers of non-monotonic logics in a systematic fashion [9, 10] extending previous work by Imielinski [8] and Got=-=tlob [7]-=-. Roughly speaking, the comparison is performed for any pair of non-monotonic logics by analyzing the existence of certain kinds of translation functions between the logics. As a result of such pairwi... |

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Citation Context ...much due to implementation techniques that have dramatically improved during the past decade. The basic technique is to use well-founded models [21] as approximations in the branch and bound approach =-=[19-=-]. However, it is possible to rene well-founded models in order to obtain even tighter approximations. For instance, Niemel and Simons [16] use additional principles in their implementation (known by ... |

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(Show Context)
Citation Context ...t natural number i such that a 2 TP " i (;). 3 Translations The author has analyzed the expressive powers of non-monotonic logics in a systematic fashion [9, 10] extending previous work by Imieli=-=nski [8]-=- and Gottlob [7]. Roughly speaking, the comparison is performed for any pair of non-monotonic logics by analyzing the existence of certain kinds of translation functions between the logics. As a resul... |

16 |
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Citation Context ...ls (or answer sets [5]) for logic programs rather than using a resolution procedure for query answering. Nowadays, stable model semantics is considered as a constraint programming paradigm of its own =-=[14, 15]-=-. The success of the stable model semantics is much due to implementation techniques that have dramatically improved during the past decade. The basic technique is to use well-founded models [21] as a... |

15 |
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Citation Context ...a 2 Mm(P ), denoted by l(a), which is the least natural number i such that a 2 TP " i (;). 3 Translations The author has analyzed the expressive powers of non-monotonic logics in a systematic fas=-=hion [9, 10]-=- extending previous work by Imielinski [8] and Gottlob [7]. Roughly speaking, the comparison is performed for any pair of non-monotonic logics by analyzing the existence of certain kinds of translatio... |

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(Show Context)
Citation Context ...a 2 Mm(P ), denoted by l(a), which is the least natural number i such that a 2 TP " i (;). 3 Translations The author has analyzed the expressive powers of non-monotonic logics in a systematic fas=-=hion [9, 10]-=- extending previous work by Imielinski [8] and Gottlob [7]. Roughly speaking, the comparison is performed for any pair of non-monotonic logics by analyzing the existence of certain kinds of translatio... |

3 |
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Citation Context ...ve reasoning with rules. 1 Introduction In logic programming [20], a simple rule-based language is used for knowledge representation in a declarative fashion (see e.g. [12] for an extensive study and =-=[18]-=- for programming methodology). To enhance the knowledge representation capabilities of logic programs, Clark [2] proposed a form of negation, namely negation as failure to prove. Logic programs that i... |