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Some Remarks on the Definability of Transitive Closure in First-order Logic and Datalog (2004)
BibTeX
@MISC{Keller04someremarks,
author = {Uwe Keller},
title = {Some Remarks on the Definability of Transitive Closure in First-order Logic and Datalog},
year = {2004}
}
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Abstract
In the last WSML phone conference we had a brief discussion about the expressivity of First-order Logic and Datalog resp. the relation between the expressiveness of those two languages. In particular, there has been some confusion around the description of the transitive closure R + of some binary relation R. In this short document, we want to clarify the situation and hope to remedy the confusion. 1 Starting point During the discussion in the last WSML phone conference the statement arose that Datalog with it’s particular semantics can express some things which can not be expressed in the First-order Logic (FOL) under the standard modeltheoretic (resp. Tarski) semantics [14]. As an example the transitive closure of a (binary) relation has been mentioned. Some people didn’t believe this claim because it’s a straightforward
