## On Constructive Negation in Logic Programming (1995)

Venue: | In North American Conference on Logic Programming |

Citations: | 24 - 3 self |

### BibTeX

@INPROCEEDINGS{Przymusinski95onconstructive,

author = {Teodor Przymusinski},

title = {On Constructive Negation in Logic Programming},

booktitle = {In North American Conference on Logic Programming},

year = {1995},

pages = {page},

publisher = {MIT Press}

}

### OpenURL

### Abstract

this paper we significantly extend Chan's approach and provide it with a more thorough theoretical foundation.

### Citations

1913 |
Foundations of Logic Programming
- LLoyd
- 1987
(Show Context)
Citation Context ... 6= f(y))` is valid. The inequality 8y (x 6= g(f(y)))` is satisfiable, but not valid. The inequality 8y(x 6= g(y))` is not satisfiable. From now on we assume that R is any fixed computation rule (see =-=[Llo84]-=-), i.e. a rule that selects exactly one literal from every non-empty goal G. The only restriction imposed on R is that it never selects inequalitiess8 (t 1 6= t 2 ), which are satisfiable, but not val... |

874 | The well-founded semantics for general logic programs - Gelder, Ross, et al. - 1991 |

634 | Towards a theory of declarative knowledge - Apt, Blair, et al. - 1988 |

240 | Negation in logic programming - Kunen - 1985 |

142 | Every logic program has a natural stratification and an iterated least fixed point model - Przymusinski - 1998 |

138 |
Complete axiomatizations of the algebras of finite, rational and infinite trees
- Maher
(Show Context)
Citation Context ...al forms of equality formulae, which are much easier to deal with than general equality formulae. The results contained in this section are closely related to those obtained independently by M. Maher =-=[Mah88]-=- and can also be viewed as a refinement of the previous work by Malcev [Mal71] (see also [KKu87]). Consult [She89] for an interesting comparison of various approaches. In the Appendix we define a yet ... |

132 |
Negation as failure using tight derivations for general logic programs
- Gelder
- 1988
(Show Context)
Citation Context ...erfect model semantics. The converses of these implications are false. Our second result proves that a rather broad class of programs, namely the class of programs with the bounded term property (cf. =-=[VG89]-=-), is equality-definable w.r.t. the perfect model semantics. This class includes, in particular, all functionless programs. This means that all queries about such programs admit complete answers, when... |

131 |
Constructive negation based on the completed database
- Chan
- 1988
(Show Context)
Citation Context ...ngs for query variables. Although various attempts to correct this problem have been made in the past, only recently a natural and yet powerful solution of this important problem has been proposed in =-=[Cha88]-=- for programs using Clark's completion semantics. In this paper we significantly extend Chan's approach and provide it with a more thorough theoretical foundation. 1 We first observe that query answer... |

69 | On the declarative semantics of stratified deductive databases and logic programs - Przymusinski - 1988 |

64 | On the declarative and procedural semantics of logic programs
- Przymusinski
- 1995
(Show Context)
Citation Context ... and 7 we assume that programs are stratified and that the perfect model semantics is used. We extend the SLS-resolution (Linear resolution with Selection function for Stratified programs) defined in =-=[Prz89b]-=- to SLS-resolution with Constructive negation (SLSC-resolution), by augmenting it with the constructive negation, defined similarly as in [Cha88]. Individual answers produced by SLSC-resolution (i.e. ... |

46 |
Axiomatizable classes of locally free algebras
- Malcev
- 1971
(Show Context)
Citation Context ... equality formulae. The results contained in this section are closely related to those obtained independently by M. Maher [Mah88] and can also be viewed as a refinement of the previous work by Malcev =-=[Mal71]-=- (see also [KKu87]). Consult [She89] for an interesting comparison of various approaches. In the Appendix we define a yet more narrow class of equality formulae, called strictly normal equality formul... |

29 |
Language and equality theory in logic programming
- Shepherdson
- 1988
(Show Context)
Citation Context ...tants or functions in the language L P is essential for the validity of Theorem 3.1 and Corollary 3.2 and for the validity of most of the results presented in the paper. However, as recently shown in =-=[She89]-=-, some of the results presented in this paper can be obtained without this assumption or by replacing it by some other assumptions (e.g., domain closure assumption). Generally, though, the resulting t... |

18 | Non-monotonic formalisms and logic programming - Przymusinski - 1989 |

3 |
Predicate Logic as a Computational Mechanism
- Clark
- 1979
(Show Context)
Citation Context ... means of normal equality formulae. 5 Definability of Programs vs. Their Semantics In this section we compare equality-definability for three semantics: Clark's predicate completion semantics COMP(P) =-=[Cla79]-=-, the perfect model semantics [Prz89b] and the first order logic semantics FO(P). Our first theorem shows that every formula which is equality-definable w.r.t. first order semantics is also equality-d... |

1 |
sets and negation as failure
- Answer
- 1987
(Show Context)
Citation Context .... The results contained in this section are closely related to those obtained independently by M. Maher [Mah88] and can also be viewed as a refinement of the previous work by Malcev [Mal71] (see also =-=[KKu87]-=-). Consult [She89] for an interesting comparison of various approaches. In the Appendix we define a yet more narrow class of equality formulae, called strictly normal equality formulae and we show tha... |