Logic Journal of IGPL Advance Access published online on August 28, 2009
Logic Journal of IGPL, doi:10.1093/jigpal/jzp040
Problem of restricted interpolation in superintuitionistic and some modal logics
Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, 630090, Novosibirsk, RUSSIA; Novosibirsk State University, Novosibirsk, Russia.
E-mail: lmaksi{at}math.nsc.ru
A restricted interpolation property IPR is investigated in modal and superintuitionistic logics. The problem of description of logics with IPR over the intuitionistic logic Int and the modal Grzegorczyk logic Grz is solved. It is proved that in extensions of Int or Grz IPR is equivalent to the projective Beth property PB2. It follows that IPR is decidable over Int and strongly decidable over Grz.
Key Words: restricted interpolation • Beth property • modal logic • intuitionistic logic • amalgamation
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