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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Annals of mathematics and artificial intelligence 19 (1997), S. 97-125 
    ISSN: 1573-7470
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract While non-determinism has long been established as a key concept in logic pro-gramming, its importance in the context of deductive databases was recognized only recently. This paper provides an overview of recent results on this topic with the aim of providing an introduction to the theory and practice of non-determinism in deductive databases. In particular we (i) recall the main results linking non-deterministic constructs in database languages to the theory of data complexity and the expressibility hierarchy of query languages; (ii) provide a reasoned introduction to effective programming with non-deterministic constructs; (iii) compare the usage of non-deterministic constructs in languages such as LDL++ to that of traditional logic programming languages; (iv) discuss the link between the semantics of logic programs with non-deterministic constructs and the stable-model semantics of logic programs with negation.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Annals of mathematics and artificial intelligence 19 (1997), S. 59-96 
    ISSN: 1573-7470
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Partial stable models for deductive databases, i.e., normal function-free logic programs (also called datalog programs), have two equivalent definitions: one based on 3-valued logics and another based on the notion of unfounded set. The notion of partial stable model has been extended to disjunctive deductive databases using 3-valued logics. In this paper, a characterization of partial stable models for disjunctive datalog programs is given using a suitable extension of the notion of unfounded set. Two interesting sub-classes of partial stable models, M-stable (Maximal-stable) (also called regular models, preferred extension,and maximal stable classes) and L-stable (Least undefined-stable) models, are then extended from normal to disjunctive datalog programs. On the one hand, L-stable models are shown to be the natural relaxation of the notion of total stable model; on the other hand the less strict M-stable models, endowed with a nice modularity property, may be appealing from the programming and computational point of view. M-stable and L-stable models are also compared with the regular models for disjunctive datalog programs recently proposed in the literature.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Annals of mathematics and artificial intelligence 19 (1997), S. 147-168 
    ISSN: 1573-7470
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The partial stable models of a logic program form a class of models that include the (unique) well-founded model, total stable models and other two interesting subclasses: maximal stable models and least undefined stable models. As stable models different from the well-founded are not unique, DATALOG queries do not in general correspond to functions. The question is: what are the expressive powers of the various types of stable models when they are restricted to the class of all functional queries? The paper shows that this power does not go in practice beyond the one of stratified queries, except for least undefined stable models which, instead, capture the whole Boolean hierarchy BH. Finally, it is illustrated how the latter result can be used to design a ``functional'' language which, by means of a disciplined usage of negation, allows to achieve the desired level of expressiveness up to BH so that exponential time resolution is eventually enabled only for hard problems.
    Type of Medium: Electronic Resource
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