## 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}

}

### OpenURL

### 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

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Citation Context ... Several logics that extend FOL in certain ways have been proposed in order to deal with the lack of expressivity of FOL. In particular the last mentioned example gave rise to a logic called ID-Logic =-=[4]-=-, a logic which extends FOL with the possibility of inductive definitions. In fact, this logic seems to be naturally related to Logic Programming. With respect to the last mentioned item in the list i... |

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