Finite Models and Full Completeness

  • Authors:
  • Jim Laird

  • Affiliations:
  • -

  • Venue:
  • Proceedings of the 14th Annual Conference of the EACSL on Computer Science Logic
  • Year:
  • 2000

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Abstract

A finite model property for fully complete denotational models of propositional logics is investigated using fully complete translations to compare programming languages and logics. The main result is that there can be no finite and fully complete models of linear or affine propositional logics. This is shown to be a consequence of Loader's result that contextual equivalence for finitary PCF is not decidable by giving a fully complete translation from finitary PCF into a Λ(Ω)ωbda-calculus for a dual affine/non-linear logic. It is shown that the non-linear part of this logic does have a finite and fully complete model, and a conservative extension of the above translation is given from finitary PCF with control (µPCF) into the non-linear fragment which shows that the fully abstract modelof µPCF is effectively presentable.