Computer Science – Logic in Computer Science
Scientific paper
2011-06-02
Computer Science
Logic in Computer Science
To be submitted
Scientific paper
Lambek's non-associative syntactic calculus (NL) excels in its resource consciousness: the usual structural rules for weakening, contraction, exchange and even associativity are all dropped. Recently, there have been proposals for conservative extensions dispensing with NL's intuitionistic bias towards sequents with single conclusions: De Groote and Lamarche's classical non-associative Lambek calculus (CNL) and the Lambek-Grishin calculus (LG) of Moortgat and associates. We demonstrate Andreoli's focalization property for said proposals: a normalization result for Cut-free sequent derivations identifying to a large extent those differing only by trivial rule permutations. In doing so, we proceed from a `uniform' sequent presentation, deriving CNL from LG through the addition of structural rules. The normalization proof proceeds by the construction of syntactic phase models wherein every `truth' has a focused proof, similar to work of Okada and of Herbelin and Lee.
No associations
LandOfFree
Focalization and phase models for classical extensions of non-associative Lambek calculus does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Focalization and phase models for classical extensions of non-associative Lambek calculus, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Focalization and phase models for classical extensions of non-associative Lambek calculus will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-495082