The data complexity of the syllogistic fragments of English

Authors:
Camilo Thorne;Diego Calvanese
Affiliations:
KRDB Research Centre, Free University of Bozen-Bolzano, Bolzano, Italy;KRDB Research Centre, Free University of Bozen-Bolzano, Bolzano, Italy
Venue:
Proceedings of the 17th Amsterdam colloquium conference on Logic, language and meaning
Year:
2009

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Abstract

Pratt and Third's syllogistic fragments of English can be used to capture, in addition to syllogistic reasoning, many other kinds of common sense reasoning, and, in particular (i) knowledge base consistency and (ii) knowledge base query answering, modulo their FO semantic representations. We show how difficult, in terms of semantic (computational) complexity and data complexity (i.e., computational complexity w.r.t. the number of instances declared in a knowledge base), such reasoning problems are. In doing so, we pinpoint also those fragments for which the reasoning problems are tractable (in PTime) or intractable (NP-hard or coNP-hard).