Studia Logica

, Volume 97, Issue 3, pp 385–413 | Cite as

Tracks of Relations and Equivalences-based Reasoning

Article

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).

Keywords

elementary theories equivalence embedding procedure tracks of relation finite axiomatizability 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Odessa National Academy of TelecommunicationsOdessaUkraine
  2. 2.Odessa National Academy of TelecommunicationsOdessaUkraine

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