“Interpolation via translations”

November 4, 2009 in publications

A new paper from members of the ConsRel project:

“Interpolation via translations”
João Rasga,Walter Carnielli e Cristina Sernadas
Math. Log. Quart. 55, No. 5, 515-534 (2009) / DOI 10.1002/malq.200810013

http://www3.interscience.wiley.com/journal/117943446/grouphome/home.html

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-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.”