R. Seeley. ?-autonomous categories, cofree coalgebras and linear logic. In J. W. Gray and A. Scedrov, editors, Categories in Computer Science and Logic, volume 92 of Contemporary Mathematics, pages 371--382. American Mathematical Society, 1989. 33  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)
....on the sub category G hf of history free strategies. A history free strategy oe = oe f is uniquely determined by the underlying function f on moves. In particular, all the morphisms witnessing the autonomous structure in G hf , or equivalently the interpretations of proofs in MLL MIX [See89], can be defined directly in terms of these functions. When we do so, we find that the interpretation coincides exactly with the Geometry of Interaction interpretation [Gir89b, Gir89a, Gir88] More precisely, it corresponds to a reformulation of the Geometry of Interaction, due to the present ....
....d k Delta e 2 T ] 9k) m k (d 0 ) e] d Delta e 2 ffi h : 14 3.5 autonomous categories of games 3.5.1 G hf as a autonomous category We show that G hf is a autonomous category, and thus yields an interpretation of the formulas and proofs of MLL MIX. For background, see [See89, Bar91]) We have already defined the object part of the tensor product B, the linear negation A and the tensor unit. The action of tensor on morphisms is defined as follows. If oe f : A B; g : A : B Omega is induced by h = M f g The natural isomorphisms for ....
[Article contains additional citation context not shown here]
R. Seeley. ?-autonomous categories, cofree coalgebras and linear logic. In J. W. Gray and A. Scedrov, editors, Categories in Computer Science and Logic, volume 92 of Contemporary Mathematics, pages 371--382. American Mathematical Society, 1989. 33
Denotational Completeness Revisited - Streicher (1998) (2 citations) (Correct)
....the rest of this paper. Readers not feeling at ease with general categorical models of linear logic may well think of their favourite concrete model, for example the coherence space model of [3] without missing anything essential. For a precise definition of categorical model for Linear Logic see [7] or rather the corrected version in [2] though the difference is not relevant for our purposes as we do not consider equality of proof terms) For ease of exposition we sometimes employ a 2 sided sequent calculus for linear logic because this does not make any difference w.r.t. the ....
R. Seely. -autonomous categories, cofree coalgebras and linear logic. In J. W. Gray and A. Scedrov, editors, Categories in Computer Science and Logic, volume 92 of Contemporary Mathematics, pages 371--382. American Mathematical Society, 1989.
Games and Full Completeness for Multiplicative Linear Logic - Abramsky, Jagadeesan (1992) (132 citations) (Correct)
....on the sub category G hf of history free strategies. A history free strategy oe = oe f is uniquely determined by the underlying function f on moves. In particular, all the morphisms witnessing the autonomous structure in G hf , or equivalently the interpretations of proofs in MLL MIX [See89], can be defined directly in terms of these functions. When we do so, we find that the interpretation coincides exactly with the Geometry of Interaction interpretation [Gir89b, Gir89a, Gir88] More precisely, it corresponds to a reformulation of the Geometry of Interaction, due to the present ....
....d k Delta e 2 T ] 9k) m 0 k (d 0 ) e] d Delta e 2 ffi h : 3.5 autonomous categories of games 3.5.1 G hf as a autonomous category We show that G hf is a autonomous category, and thus yields an interpretation of the formulas and proofs of MLL MIX. For background, see [See89, Bar91]) We have already defined the object part of the tensor product A Omega B, the linear negation A and the tensor unit. The action of tensor on morphisms is defined as follows. If oe f : A B; g : A 0 B 0 , then oe Omega : A Omega A 0 B Omega B 0 is induced by h = M ....
[Article contains additional citation context not shown here]
R. Seeley. ?-autonomous categories, cofree coalgebras and linear logic. In J. W. Gray and A. Scedrov, editors, Categories in Computer Science and Logic, volume 92 of Contemporary Mathematics, pages 371--382. American Mathematical Society, 1989.
Games and Full Completeness for Multiplicative Linear Logic - Abramsky, Jagadeesan (1994) (132 citations) (Correct)
....attention on the sub category G hf of history free strategies. A history free strategy oe = oe f is uniquely determined by the underlying function f on moves. In particular, all the morphisms witnessing the autonomous structure in G hf , or equivalently the interpretations of proofs in MLL MIX [See89], can be defined directly in terms of these functions. When we do so, we find that the interpretation coincides exactly with the Geometry of Interaction interpretation [Gir89b, Gir89a, Gir88] More precisely, it corresponds to a reformulation of the Geometry of Interaction, due to the present ....
....(t Delta d Delta b 1 Delta : Delta b k Delta e) A; C 2 oe f ; oe g . 3.5 autonomous categories of games 3.5.1 G hf as a autonomous category We show that G hf is a autonomous category, and thus yields an interpretation of the formulas and proofs of MLL MIX. For background, see [See89, Bar91]) We have already defined the object part of the tensor product A Omega B, the linear negation A and the tensor unit. The action of tensor on morphisms is defined as follows. If oe f : A B; g : A 0 B 0 , then oe Omega : A Omega A 0 B Omega B 0 is induced by h = M A ....
[Article contains additional citation context not shown here]
R. Seeley. ?-autonomous categories, cofree coalgebras and linear logic. In J. W. Gray and A. Scedrov, editors, Categories in Computer Science and Logic, volume 92 of Contemporary Mathematics, pages 371--382. American Mathematical Society, 1989.
Linear Types and Approximation - Huth, Jung, Keimel (1995) (Correct)
....interaction orders, bicontinuous lattices, completely distributive lattices, upper and lower powerdomains. 1 Introduction Complete lattices with maps preserving all suprema as morphisms form a autonomous category SUP [Bar79] and give rise to a model of linear logic in the standard fashion of [See89] If 2 : f0 1g denotes the two point lattice and A Gamma ffi B the linear function space of all maps f : A B preserving all suprema, ordered pointwise, we can define the multiplicatives as A : A Gamma ffi 2 ( order dual of A) 1) A Omega B : A Gamma ffi B ) AOB : A ....
R. Seely. -autonomous categories, cofree coalgebras and linear logic. In J. W. Grey and A. Scedrov, editors, Categories in Computer Science and Logic, volume 92 of Contemporary Mathematics, pages 371--382. American Mathematical Society, 1989.
Linear Types and Approximation - Huth, Jung, Keimel (1999) (Correct)
....far, we have ignored the modalities of Linear Logic and it is high time to study how they can be added to our framework. Some general comments may be in place here. From the viewpoint of autonomous categories, modalities require a further piece of structure in the form of a comonad. First Seely, See89] and later Benton, Bierman, de Paiva, and Hyland, BBHdP93, BBdPH93, Bie95] worked out the precise conditions that need to be imposed on the comonad in order to get the desired close correspondence between proof theory and categorical semantics. More recently, Benton, Ben94] came up with a ....
R. Seely. -autonomous categories, cofree coalgebras and linear logic. In J. W. Grey and A. Scedrov, editors, Categories in Computer Science and Logic, volume 92 of Contemporary Mathematics, pages 371-- 382. American Mathematical Society, 1989.
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