Procedures, formal computations and models
Starting from the logical point of view we conceive procedures as formulas of a formalized algorithmic language defining functions and/or relations. The notion of formal computation is introduced in a way resembling formal proofs. Computations may serve to extend the original interpretation of the language onto symbols defined by procedures. The main result is: if a system of procedures is consistent then the computed extension of a given interpretation is the smallest model of the system. From this the principle of recursion induction can be proved. A technique transforming any system of procedures to a consistent system of conditional recursive definitions is shown.
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