Query completeness of Skolem machine computations

Authors:
John Fisher;Marc Bezem
Affiliations:
Department of Computer Science, California State Polytechnic University, Pomona, California;Department of Computer Science, University of Bergen, Bergen, Norway
Venue:
MCU'07 Proceedings of the 5th international conference on Machines, computations, and universality
Year:
2007

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Abstract

The Skolem machine is a Turing-complete machine model where the instructions are first-order formulas of a specific form. We introduce Skolem machines and prove their logical completeness. Skolem machines compute queries for the Geolog language, a rich fragment of first-order logic. The concept of complete Geolog trees is defined, and this tree concept is used to show logical completeness for Skolem machines: If the query for a Geolog theory is a logical consequence of the axioms then the corresponding Skolem machine halts succesfully in a configuration that supports the query.