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Issue title: Machines, Computations and Universality, Part I
Article type: Research Article
Authors: Fisher, John | Bezem, Marc
Affiliations: Department of Computer Science, California State Polytechnic University, Pomona, California, USA. jrfisher@csupomona.edu | Department of Computer Science, University of Bergen, Bergen, Norway. bezem@ii.uib.no
Note: [] Address for correspondence: Department of Computer Science, California State Polytechnic University, Pomona, California, USA
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 correctness and completeness. Skolem machines compute queries for the Geolog language, a rich fragment of first-order logic. The concepts of Geolog trees and complete Geolog trees are defined, and these tree concepts are used to show logical correctness and completeness of Skolem machine computations. The universality of Skolem machine computations is demonstrated. Lastly, the paper outlines implementation design issues using an abstract machine model approach.
Keywords: Finitary geometric logic, Skolem machines, Geolog language, Geolog trees, correctness, completeness, universality
DOI: 10.3233/FI-2009-0034
Journal: Fundamenta Informaticae, vol. 91, no. 1, pp. 79-103, 2009
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