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....his or her intentions in a cumbersome way. We do however note that the iterative fixpoint [ABW88] of a stratified program can be obtained in our language by sequentially updating the database with the strata of the program in their hierarchical order. We also note that hypothetical queries [Bon88, Gab85] and queries on recursively indefinite databases [Mey90] can be expressed through updates. The connection between hypothetical queries and updates is explored in [GM91] In Section 2 of this paper we lay the foundation of knowledgebase transformations. In Section 3 some examples of ....

A. J. Bonner. Hypothetical Datalog: complexity and expressibility. In: Proceedings of the Second International Conference on Database Theory, pages 144--160, 1988.

....completeness. It encompasses both Robinson s resolution for propositional Horn clauses and the top down resolution defined for Hereditary Harrop formulas. Moreover, a particular restriction may be considered, defining a notion of bottomup search for propositional Hereditary Harrop formulas. In [2], Bonner gives a fixpoint semantics for this logical fragment, which provides not only decidability and complexity bounds, but also an efficient bottom up evaluation procedure. It should be noted that our goal differs from Bonner s: the full theory of Hereditary Harrop formulas involves a possibly ....

....and completeness. In section 5, we focus on a particular case defining a general notion of bottom up resolution for Hereditary Harrop formulas. In a second step, we further refine this bottom up procedure into a decidable one. We show its completeness by relating it to Bonner s fixpoint semantics [2]. Conclusions and comments appear in section 6. 2 Propositional Hereditary Harrop formulas and resolution 2.1 Propositional Hereditary Harrop formulas The propositional Hereditary Harrop formulas may be defined using the following mutually recursive definitions: Delta : j A j Gamma oe A j ....

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Anthony J. Bonner. Hypothetical Datalog: complexity and expressibility. In Proceedings of the Second International Conference on Database theory, pages 144--160, 1988.

.... embedded implications [9] we have a language that can express any database query in RE [10] If we then restrict the class of embedded implications by disallowing embedded universal quantifiers, we have a language that expresses exactly the database 2 EXAMPLES 18 queries in PSPACE [6]. Additional syntactic restrictions give us a family of languages that can express the database queries at each level of the polynomial hierarchy above P [8] These results are for ordinary embedded implications, i.e. embedded implications without any use of circumscription. As soon as ....

A.J. Bonner. Hypothetical Datalog: Complexity and Expressibility. In Proceedings of the International Conference on Database Theory (ICDT), pages 144--160. Springer-Verlag, 1988. Published as volume 326 of Lecture Notes in Computer Science.

....intentions in a cumbersome way. We do however note that the iterative fixpoint [ABW88] of a stratified program can be obtained in our language by sequentially updating the database with the strata of the program in their hierarchical order. It is also interesting to note that hypothetical queries [Bon88, Gab85] and queries on re8 cursively indefinite databases [Mey90] can be expressed through updates. The connection between hypothetical queries and updates is explored in [GM95] 3 Sample Transformations In this section we present seven example transformations. First we show that the common queries of ....

A. J. Bonner. Hypothetical Datalog: complexity and expressibility. In: Proceedings of the Second International Conference on Database Theory, pages 144--160, 1988.

.... has extended this work to a larger class of formulas and established interesting semantic results [16, 17] Bonner has shown that query evaluation in such systems is data complete for PSPACE in the function free predicate case (data complete for EXPTIME when hypothetical deletions are allowed) [4]. This paper extends this line of research by developing syntactic restrictions whose data complexity is less that PSPACE. Central to these restrictions is the idea of linearity. A rule is linear if recursion occurs through only one premise. In Horn clause logic, linear rules play an important ....

....a Hamiltonian circuit. In this example, the data complexity of R 0 is both NP and coNP hard. Thus, adding a single non recursive rule to R has increased its complexity class from NP to NP [ coNP . 4 The proof of this is left as an exercise for the reader. 4 Linear Stratification In [4] it was shown that the inference system of section 3 is data complete for PSPACE. In this section, we develop syntactic restrictions with reduced complexity. Central to these restrictions are the ideas of linear recursion and stratified negation. In particular, a new notion of stratification is ....

[Article contains additional citation context not shown here]

A.J. Bonner. Hypothetical Datalog: Complexity and Expressibility. In Proceedings of the International Conference on Database Theory (ICDT), pages 144--160. Springer-Verlag, 1988. Published as volume 326 of Lecture Notes in Computer Science.

.... implications in the restricted case: Gabbay has shown that such rules have an intuitionistic semantics [10] and Miller has developed a fixpoint semantics for the predicate case [18] Bonner has shown that query evaluation in such systems is data complete for PSPACE in the function free case [4]. Furthermore, when this logic is augmented with negation as failure, any database query whose graph is in PSPACE can be expressed [4] Syntactic restrictions have also been identified which express the database queries at each level in the polynomial time hierarchy [6] Furthermore, there is a ....

.... a fixpoint semantics for the predicate case [18] Bonner has shown that query evaluation in such systems is data complete for PSPACE in the function free case [4] Furthermore, when this logic is augmented with negation as failure, any database query whose graph is in PSPACE can be expressed [4]. Syntactic restrictions have also been identified which express the database queries at each level in the polynomial time hierarchy [6] Furthermore, there is a precise sense in which some low complexity queries can be expressed with intuitionistic embedded implications but not with classical ....

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A.J. Bonner. Hypothetical Datalog: Complexity and Expressibility. In Proceedings of the International Conference on Database Theory (ICDT), pages 144--160. Springer-Verlag, 1988. Published as volume 326 of Lecture Notes in Computer Science.

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A. Bonner, Hypothetical Datalog: Complexity and Expressibility. Proceedings ICDT 1988, 144-160.

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