Query Completeness of Skolem Machine Computations

摘要

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.