A. Fleury and C. Retor'e, The MIX rule, Unpublished note, 1990 Home/Search Document Not in Database Summary Related Articles Check |
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Games and Full Completeness for Multiplicative Linear Logic - Samson Abramsky And (1994) (132 citations) (Correct)
....of proof net for this logic: this uses the Danos Regnier criterion [DR89] simply omitting the connectedness part. Thus, a proof structure will be a valid proof net for MLL MIX just if, for every switching, the corresponding graph is acyclic. This criterion was studied by Fleury and Retor e [FR90], used by Blute in his work on coherence theorems [Blu92] and adapted by Lafont for his work on interaction nets [Laf90] Now we can state our result in more precise terms. Theorem 1 Every proof net in MLL MIX denotes a uniform, history independent winning strategy for Player in our game ....
....S) is: 5 Gamma Gamma Gamma Gamma Gamma Gamma ff ff 4 ff ff 4 ff 3 ff 2 ff Definition 1 A (cut free) proof net for MLL MIX is a proof structure ( Gamma; OE) such that, for all switchings S, G( Gamma; OE; S) is acyclic. Fleury and Retor e [FR90] make a detailed study of this criterion, which is of course just a modification of the Danos Regnier criterion [DR89] to accomodate the MIX rule by dropping the connectedness condition. We can regard proof nets as the canonical representations of (cut free) proofs in MLL MIX. 3 The Game ....
A. Fleury and C. Retor'e. The MIX rule. Unpublished note, 1990.
Specifying Interaction Categories - Pavlovic, Abramsky (1997) (1 citation) (Correct)
....notations ( Theta; 1) and ( 0) for products and coproducts are often replaced respectively with (N; 1) and ( Phi; 0) cotensor B Gammaffi C in the form (B Omega C ) thus making R autonomous (i.e. closed symmetric monoidal [16, sec. 1. 5] Now a autonomous R satisfies the MIX rule [13] if and only if the duality functor ( Gamma) is lax monoidal; and it is compact closed [17] if and only if the duality is monoidal. Process specifications. All these concepts readily generalise to enriched categories [16] Process specifications are meant to be Pos enriched lax monoidal ....
A. Fleury and C. Retor'e, The MIX rule, Unpublished note, 1990
Games and Full Completeness for Multiplicative Linear Logic - Abramsky, Jagadeesan (1992) (132 citations) (Correct)
....of proof net for this logic: this uses the Danos Regnier criterion [DR89] simply omitting the connectedness part. Thus, a proof structure will be a valid proof net for MLL MIX just if, for every switching, the corresponding graph is acyclic. This criterion was studied by Fleury and Retor e [FR90], used by Blute in his work on coherence theorems [Blu92] and adapted by Lafont for his work on interaction nets [Laf90] Now we can state our result in more precise terms. Theorem 1 Every proof net in MLL MIX denotes a uniform, history independent winning strategy for Player in our game ....
.... Gamma Gamma Gamma Gamma Gamma Gamma ff 3 Omega ff 4 ff 1 0 ff 2 ff 4 ff 3 ff 2 ff 1 Definition 1 A (cut free) proof net for MLL MIX is a proof structure ( Gamma; OE) such that, for all switchings S, G( Gamma; OE; S) is acyclic. Fleury and Retor e [FR90] make a detailed study of this criterion, which is of course just a modification of the Danos Regnier criterion [DR89] to accomodate the MIX rule by dropping the connectedness condition. We can regard proof nets as the canonical representations of (cut free) proofs in MLL MIX. 3 The Game ....
A. Fleury and C. Retor'e. The MIX rule. Unpublished note, 1990.
Games and Full Completeness for Multiplicative Linear Logic - Abramsky, Jagadeesan (1994) (132 citations) (Correct)
....of proof net for this logic: this uses the Danos Regnier criterion [DR89] simply omitting the connectedness part. Thus, a proof structure will be a valid proof net for MLL MIX just if, for every switching, the corresponding graph is acyclic. This criterion was studied by Fleury and Retor e [FR90], used by Blute in his work on coherence theorems [Blu92] and adapted by Lafont for his work on interaction nets [Laf90] Now we can state our result in more precise terms. Theorem 1 Every proof net in MLL MIX denotes a uniform, history independent winning strategy for Player in our game ....
.... Gamma Gamma Gamma Gamma Gamma Gamma ff 3 Omega ff 4 ff 1 0 ff 2 ff 4 ff 3 ff 2 ff 1 Definition 1 A (cut free) proof net for MLL MIX is a proof structure ( Gamma; OE) such that, for all switchings S, G( Gamma; OE; S) is acyclic. Fleury and Retor e [FR90] make a detailed study of this criterion, which is of course just a modification of the Danos Regnier criterion [DR89] to accomodate the MIX rule by dropping the connectedness condition. We can regard proof nets as the canonical representations of (cut free) proofs in MLL MIX. 3 The Game ....
A. Fleury and C. Retor'e. The MIX rule. Unpublished note, 1990.
Specifying Interaction Categories - Pavlovi'c And Abramsky (Correct)
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A. Fleury and C. Retor'e, The MIX rule, Unpublished note, 1990
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