This enlarges on earlier work attempting to show in a general way how it might be possible for a machine to use symbols with `non-derivative' semantics. It elaborates on the author's earlier suggestion that computers understand symbols referring to their own internal `virtual' worlds. A machine that grasps predicate calculus notation can use a set of axioms to give a partial ,implicitly defined, semantics to non- logical symbols. Links to other symbols defined by direct causal connections within the machine reduce ambiguity. Axiom systems for which the machine's internal states do not form a model give a basis for reference to an external world without using external sensors and motors.
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