Tracks of Relations and Equivalences-based Reasoning |
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Authors: | G Shtakser L Leonenko |
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Institution: | (1) Department of Computer Sciences, University of Texas, Austin, University Station 1 MS C0500, 78712-0233 Austin, Texas, USA |
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Abstract: | It is known that the Restricted Predicate Calculus (RPC) can be embedded in an elementary theory, the signature of which consists
of exactly two equivalences. Some special models for the mentioned theory were constructed to prove this fact. Besides formal
adequacy of these models, a question may be posed concerning their conceptual simplicity, “transparency” of interpretations
they assigned to the two stated equivalences. In works known to us these interpretations are rather complex, and can be called
“technical”, serving only the purpose of embedding. We propose a conversion method, which transforms an arbitrary model of
RPC into some model of the elementary theory TR, which includes three equivalences. RPC is embeddable in TR, and it appears possible to assign some “natural” interpretations to three equivalences
using the “Track of Relation” concept (abbreviated to TR). |
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