J.-Y. Girard. Multiplicatives. Rendiconti del Seminario Matematico (Torino), Universita Pol. Torino, 1988. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Sequentiality vs. Concurrency in Games and Logic - Abramsky (2001) (Correct)
....form of symbolic dynamics. The basic idea of Geometry of Interaction is that multiplicative proofs are represented by permutations acting on structures of some kind. 7. 1 Background The original version of the Geometry of Interaction was developed by Girard for the multiplicative fragment [Gir88]. This is still the best setting in which to explain the basic ideas on which the interpretation is based. Consider then the multiplicative fragment, with the restriction that the Axiom is only used for propositional atoms, Now, if we look at the cut free proofs, for example of ( ....
....more generally, 16 The idea, as with cut free proofs, is to model these transformations dynamically, by the ow of information tokens, rather than by graph rewriting. An interpretation of the multiplicative fragment can be given using just permutations on nite sets, as described in [Gir88]. The task of characterizing the space of proofs is then to pick out exactly those permutations which can arise as the denotation of (cut free) proof nets, and moreover to do so in a compositional, syntax free fashion. This is the goal of full completeness theorems, to be discussed in the next ....
J.-Y. Girard. Multiplicatives. Rendiconti del Seminario Matematico (Torino), Universita Pol. Torino, 1988.
Sequentiality vs. Concurrency in Games and Logic - Abramsky (2001) (Correct)
....form of symbolic dynamics. The basic idea of Geometry of Interaction is that multiplicative proofs are represented by permutations acting on structures of some kind. 7. 1 Background The original version of the Geometry of Interaction was developed by Girard for the multiplicative fragment [Gir88]. This is still the best setting in which to explain the basic ideas on which the interpretation is based. Consider then the multiplicative fragment, with the restriction that the Axiom is only used for propositional atoms, Now, if we look at the cut free proofs, for example of ( ....
.... The idea, as with cut free proofs, is to model these transformations dynamically, by the ow of information tokens, rather than by graph rewriting. An interpretation of the multiplicative fragment can be given using just permutations on nite sets, as described in [Gir88]. The task of characterizing the space of proofs is then to pick out exactly those permutations which can arise as the denotation of (cut free) proof nets, and moreover to do so in a compositional, syntax free fashion. This is the goal of full completeness theorems, to be discussed in the next ....
J.-Y. Girard. Multiplicatives. Rendiconti del Seminario Matematico (Torino), Universita Pol. Torino, 1988.
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