Interpolation via translations

Author(s)

Rasga, Joao ^[1] ; Carnielli, Walter ^[2] ; Sernadas, Cristina ^[1]

Affiliation

^[1] Univ Tecn Lisboa, IST, DM, Lisbon - Portugal

^[2] Univ Estadual Campinas, CLE & IFCH, Campinas, SP - Brazil

• Document type: Journal article
• Source: MATHEMATICAL LOGIC QUARTERLY; v. 55, n. 5, p. 515-534, OCT 2009.
• Web of Science Citations: 1

Abstract

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-Godel 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-Godel 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. (c) 2009 WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim (AU)

• FAPESP's process: 04/14107-2 - Logical consequence and combinations of logics: fundaments and efficient applications
• Grantee: Walter Alexandre Carnielli
• Support Opportunities: Research Projects - Thematic Grants