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Journal of Logic and Computation 1998 8(2):169-187; doi:10.1093/logcom/8.2.169
© 1998 by Oxford University Press
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Original Articles

Extensions for Open Default Theories via the Domain Closure Assumption

MICHAEL KAMINSKI, JOHANN A. MAKOWSKY and MICHAEL TIOMKIN

Department of Computer Science, Technion - Israel Institute of Technology Haifa 32000, Israel
Intel Israel, MTM - Scientific Industries Center P.O.B. 1659, Haifa 31015, Israel

In this paper we analyse the semantical definition of extensions for open default theories. We argue that this definition reflects the domain closure assumption and show how the domain closure assumption for countable and finite domains can be expressed in first-order default logic extended with the Carnap rule of inference. Also we give examples of the domain dependence of extensions for open default theories. In particular, we show that such extensions do not possess the minimality property.

Keywords: Default logic; infinitary logic; Herbrand semantics; open default theories; the domain closure assumption


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