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The central notion presented is that of closeness of (or difference between) two theories. In the first part, we give intuitive arguments in favor of considering topologies on the set of theories, continuous logics, and the average difference between two logics (i.e., the integral of their...
With the aid of automated reasoning techniques, we show that all previously known short single axioms for odd exponent groups are special cases of one general schema. We also demonstrate how to convert the proofs generated by an automated reasoning system into proofs understandable by a human.
This paper describes some experiments involving the automated theorem-proving program OTTER in the system TRC of illative combinatory logic. We show how OTTER can be steered to find a contradiction in an inconsistent variant of TRC, and present some experimentally discovered identities in TRC.
A backward reasoning approach is described to show that the behavioral specification of a finite-state machine satisfies some high-level input-output specification. It is based on the principles of theorem proving. The proof may require inductive reasoning. The theorem prover seeks to find out...
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