## Computing with Infinitary Logic (1995)

Venue: | Theoretical Computer Science |

Citations: | 9 - 6 self |

### BibTeX

@ARTICLE{Abiteboul95computingwith,

author = {Serge Abiteboul and Moshe Y. Vardi and Victor Vianu},

title = {Computing with Infinitary Logic},

journal = {Theoretical Computer Science},

year = {1995},

volume = {149},

pages = {101--128}

}

### Years of Citing Articles

### OpenURL

### Abstract

Most recursive extensions of relational calculus converge around two central classes of queries: fixpoint and while. Infinitary logic (with finitely many variables) is a very powerful extension of these languages which provides an elegant unifying formalism for a wide variety of query languages. However, neither the syntax nor the semantics of infinitary logic are effective, and its connection to practical query languages has been largely unexplored. We relate infinitary logic to another powerful extension of fixpoint and while, called relational machine, which highlights the computational style of these languages. Relational machines capture the kind of computation occurring when a query language is embedded in a host programming language, as in C+SQL. The main result of this paper is that relational machines correspond to the natural effective fragment of infinitary logic. Other well-known query languages are related to infinitary logic using syntactic restrictions formula...

### Citations

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Citation Context ... we obtain a relational machine accepting models('). 2 We note that the normal form provided by (iii) above can be viewed as the effective counterpart of a similar result shown for the full L k 1! in =-=[KV92]-=-. It is also shown in [KV92] that every formula of L k 1! is equivalent to a countable disjunction of FO l -formulas, for some lsk. Furthermore, it follows from [DLW91] that this holds also for l = k.... |

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Citation Context ... the model either [AV]. As will be seen in Section 4, the expressive power is increased if queries generated by the machine can use an unbounded number of variables (such a machine is investigated in =-=[APV94]-=-). Finally, a third extension allows addressable relations, i.e. the relational store has a variable, unbounded number of relations of bounded arity. This extension does not affect expressive power ei... |