Axiom schemata as metalevel axioms: model theory

Authors:
Timothy L. Hinrichs;Michael R. Genesereth
Affiliations:
Logic Group, Computer Science Department, Stanford University;Logic Group, Computer Science Department, Stanford University
Venue:
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
Year:
2005

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Abstract

Logicians frequently use axiom schemata to encode (potentially infinite) sets of sentences with particular syntactic form. In this paper we examine a first-order language in which it is possible to write expressions that both describe sentences and assert the truth of the sentences so described. The effect of adding such expressions to a knowledge base is the same as directly including the set of described sentences.