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Journal of Logic and Computation, Volume 8, Issue 2: April 1998.
Extensions for open default theories via the domain closure assumption
M Kaminski1, JA Makowsky1 and M Tiomkin2
1Department of Computer Science, Technion - Israel Institute of Technology, Haifa 32000, Israel, 2Intel Israel, MTM - Scientific Industries Center, RO.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.