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Interpolation via translations
Author(s) -
Rasga João,
Carnielli Walter,
Sernadas Cristina
Publication year - 2009
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200810013
Subject(s) - interpolation (computer graphics) , translation (biology) , mathematics , style (visual arts) , linear interpolation , algebra over a field , pure mathematics , calculus (dental) , discrete mathematics , computer science , artificial intelligence , mathematical analysis , motion (physics) , history , medicine , biochemistry , chemistry , archaeology , dentistry , messenger rna , polynomial , gene
A new technique is presented for proving that a consequence system enjoys Craig interpolation or Maehara interpolation based on the fact that these properties hold in another consequence system. This technique is based on the existence of a back and forth translation satisfying some properties between the consequence systems. Some examples of translations satisfying those properties are described. Namely a translation between the global/local consequence systems induced by fragments of linear logic, a Kolmogorov‐Gentzen‐Gödel style translation, and a new translation between the global consequence systems induced by full Lambek calculus and linear logic, mixing features of a Kiriyama‐Ono style translation with features of a Kolmogorov‐Gentzen‐Gödel style translation. These translations establish a strong relationship between the logics involved and are used to obtain new results about whether Craig interpolation and Maehara interpolation hold in that logics (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)