Fω^C: a symmetrically classic variant of System Fω
Lengrand & Miquel (2008). Greco-Roman Fω, orthogonality and symmetric candidates. Annals of Pure and Put on Logic 153:3-20.
We portray a version of system Fω, bade Fω^C, in which the layer of type
constructors is basically the traditional one of Fω, whereas provability
of types is classic. The proof-term calculus accounting for the Graeco-Roman
reasoning is a variant of Barbanera and Berardi’s symmetrical λ-calculus.
We evidence that the hale calculus is powerfully normalising. For the
layer of type constructors, we utilise Tait and Girard’s reducibility method
combined with orthogonality techniques. For the (Graeco-Roman) layer of terms,
we habituate Barbanera and Berardi’s method based on a symmetrical notion of
reducibility candidate. We show that orthogonality does not catch the
fixpoint construction of symmetrical candidates.We make the consistency of Fω^C, and connect the calculus to the
traditional system Fω, likewise when the latter is extended with axioms for
Greco-Roman logic.
