C. Retor'e, Des R'eseaux De D'emonstration Pour La Linguistique, manuscript (1996). Home/Search Document Not in Database Summary Related Articles Check |
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The Shuffle Hopf Algebra and Noncommutative Full Completeness - Blute, Scott (1996) (5 citations) (Correct)
.... linear logic (CyLL) of Yetter [38] This variant is obtained by adding the cyclic exchange rule to the fully noncommutative logic of [3] The corresponding version of proof net is also described in [38] This theory has subsequently been used substantially by Retor e in his work on linguistics [31]. The Hopf algebra which provides our semantics is an example of the incidence algebras of [22, 33] It is also refered to as a shuffle algebra in [10] which is the name we have chosen to use. Given a sequent in linear logic, we assign a vector space of dinaturals which are uniform with respect ....
....rule for this fragment, it is natural to represent the formulas of a sequent as lying on the perimeter of a circle, or as labelling radial lines on a disk. Since we will only consider such structures up to a rotation, then we will not need any explicit representation of the cyclic exchange rule [38, 31]. It is possible to represent nets by an inductive procedure analogous to that of the commutative case [17, 15, 16] Rather than describe the construction in detail, we present an example of a cyclic net in figure 1, and refer the reader to [38, 31] for the details of the definition. The net ....
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C. Retor'e, Des R'eseaux De D'emonstration Pour La Linguistique, manuscript (1996).
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