R. Blute and P. J. Scott. Linear Lauchli Semantics. Annals of Pure and Applied Logic, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... for now is that this can indeed be done using suitable uniformity and preservation properties in a number of semantic settings; this is the content of the various full completeness theorems for Multiplicative Linear Logic which have appeared over the past few years, starting with [AJ92b] see e.g. [HO92, BS96, Loa94a, Hag00]) The question is, how can this view of the multiplicatives, which has no scope for expressing causal dependencies (this is exactly the sense in which it is asynchronous) be reconciled with the additives, which as we have seen are essentially concerned with choice and causality We can in ....

.... , and a Full Completeness theorem was proved for a game semantics of Multiplicative Linear Logic (with the MIX rule) This was followed by a series of papers which established full completeness results for a variety of models with respect to various versions of Multiplicative Linear Logic, e.g. [HO92, BS96, Loa94a, Loa94b, Tan97, DHPP99, Hag00]. The proofs of full completeness which have appeared to date fall into two broad classes: Proofs using decomposition arguments There were a number of signi cant precursors, as noted in [AJ92b] including representation theorems in category theory [FS91] full abstraction results in ....

R. Blute and P. J. Scott. Linear Lauchli Semantics. Annals of Pure and Applied Logic 77:101-142, 1996.

.... for now is that this can indeed be done using suitable uniformity and preservation properties in a number of semantic settings; this is the content of the various full completeness theorems for Multiplicative Linear Logic which have appeared over the past few years, starting with [AJ92b] see e.g. [HO92, BS96, Loa94a, Hag00]) The question is, how can this view of the multiplicatives, which has no scope for expressing causal dependencies (this is exactly the sense in which it is asynchronous) be reconciled with the additives, which as we have seen are essentially concerned with choice and causality 1 We can in ....

.... 2 , and a Full Completeness theorem was proved for a game semantics of Multiplicative Linear Logic (with the MIX rule) This was followed by a series of papers which established full completeness results for a variety of models with respect to various versions of Multiplicative Linear Logic, e.g. [HO92, BS96, Loa94a, Loa94b, Tan97, DHPP99, Hag00]. The proofs of full completeness which have appeared to date fall into two broad classes: Proofs using decomposition arguments 2 There were a number of signi cant precursors, as noted in [AJ92b] including representation theorems in category theory [FS91] full abstraction results in ....

R. Blute and P. J. Scott. Linear Lauchli Semantics. Annals of Pure and Applied Logic 77:101-142, 1996.

....problems for the semantics of programming languages. Full completeness is also of considerable interest for logic itself, and in fact this paper spawned a (still growing) literature on full completeness results for the same or similar fragments of Linear Logic with respect to a variety of models [HO92, Loa94, BS96]. Full Abstraction for PCF Motivated by the full completeness results, it became of compelling interest to re examine perhaps the best known open problem in the semantics of programming languages, namely the Full Abstraction problem for PCF , using the new tools provided by game semantics. 2 ....

R. Blute and P. J. Scott. Linear Lauchli Semantics. Annals of Pure and Applied Logic, 1996.

.... and a Full Completeness theorem was proved for a game semantics of Multiplicative Linear Logic (with the MIX rule) This was followed by a series of papers which established full completeness results for a variety of models with respect to various versions of Multiplicative Linear Logic (MLL) [HO92, BS96, Loa94a, Loa94b]. However, there have been no results for logics beyond the (very weak) multiplicative fragment of Linear Logic. In this paper, we make a first significant extension beyond the multiplicative fragment, by proving that the concurrent games model is fully complete for Multiplicative Additive Linear ....

R. Blute and P. J. Scott. Linear Lauchli Semantics. Annals of Pure and Applied Logic, 1996.

....evolved largely during this century, is truth invariance for all value assignments of the parameters of the theorem, possibly subject to given axioms. More recently analogous semantic notions of abstract constructive proof have begun to appear, in particular natural and dinatural transformations [LS86, BS96] and related notions such as logical transformations [Plo80] game strategies [AJ94, HO93] and uniformity conditions [Loa94] The naturality condition expresses transformational invariance for all transformations of the parameters of the proof, again possibly subject to given axioms. The ....

R.F. Blute and P.J. Scott. Linear Lauchli semantics. Annals of Pure and Applied Logic, 77:101--142, 1996.

.... cut free proofs (understood suitably abstractly) of multiplicative linear logic without MIX, a full completeness result in the sense of Abramsky and Jagadeesan [1] and Hyland and Pratt Ong [11] but with their game semantics replaced by dinaturality semantics along the lines of Blute and Scott [4,5]. This summer with Gordon Plotkin we have been able to remove the restriction on two variables. This entailed strengthening dinaturality to logicality, necessitated by the presence of at least four dinaturals from A GammaffiA to itself, only one of which was accounted for by Girard s system. The ....

R.F. Blute and P.J. Scott. Linear Lauchli semantics. Annals of Pure and Applied Logic, 77:101--142, 1996.

.... and a Full Completeness theorem was proved for a game semantics of Multiplicative Linear Logic (with the MIX rule) This was followed by a series of papers which established full completeness results for a variety of models with respect to various versions of Multiplicative Linear Logic (MLL) [HO92, BS96, Loa94a, Loa94b]. However, there have been no results for logics beyond the (very weak) multiplicative fragment of Linear Logic. In this paper, we make a first significant extension beyond the multiplicative fragment, by proving that the concurrent games model is fully complete for Multiplicative Additive Linear ....

R. Blute and P. J. Scott. Linear Lauchli Semantics. Annals of Pure and Applied Logic, 1996.

....Whereas ordinary logic axiomatizes theorems, linear logic axiomatizes proofs. The semantic criterion for theoremhood is validity: the truth function denoted by a formula is required to be universally true. Following Lambek and Scott [11] and (as applied to linear logic) Blute and Scott [3, 4], we shall take the semantic criterion for proofhood to be naturality: the transformation denoted by a proof is required to commute with all morphisms of the ambient category. Dinaturality is a small but important generalization of naturality accommodating mixed variance, the possibility of a ....

....disallowing certain plays they characterize as unfair. Game semantics imbues linear logic with a computationally appealing procedural quality. From a mathematical standpoint however the definitions appear contrived when contrasted with the more fundamental notion of naturality. Blute and Scott [3, 4] have treated the problem of full completeness of linear logic using Lauchli semantics, invariance under (continuous) group actions, dinaturality, and logical relations. It seems to us that completeness results based on naturality are of deeper significance than those based on game semantics. In ....

R.F. Blute and P.J. Scott. Linear Lauchli semantics. Annals of Pure and Applied Logic, 77:101--142, 1996.

....taken to be natural transformations. However linear logic contains functors of mixed variance 1 such as A GammaffiA, for which mere naturality is not enough. Elsewhere [Pra97] we have shown that when the morphisms are taken to be ordinary dinatural transformations, as done by Blute and Scott [BS96a, BS96b] for their Lauchli semantics of linear logic, then Girard s MIX free axiomatization of multiplicative linear logic is sound and fully complete for the fragment admitting at most two occurrences of each atom. In Section 3 we show that this result cannot be extended to four occurrences. This is not ....

R.F. Blute and P.J. Scott. Linear Lauchli semantics. Annals of Pure and Applied Logic, 77:101--142, 1996.

....a simplification of that work by showing that the invariance criterion is actually a consequence of dinaturality. The passage from groups to Hopf algebras corresponds to the passage from commutative to noncommutative logic. 1 Introduction This paper is a continuation of a program initiated in [13], where a linear version of Lauchli s semantics for intuitionistic logic is presented. In that paper, we consider actions of the additive group of integers on a category of topological vector spaces. We associate to any sequent in Multiplicative Linear Logic (MLL) a vector space of dinatural ....

....form a basis and not just a spanning set means that our interpretation is faithful, as well as full. In fact, we have a fully faithful representation of a free autonomous category, canonically enriched over vector spaces. This will be discussed in Remark 2.16 below. It was observed at the end of [13] that this semantics might be expanded to noncommutative logics by replacing groups with Hopf algebras. In [12] the representation theory of Hopf algebras is presented as a unifying framework for the analysis of a number of variants of linear logic. By varying the Hopf structure, one obtains ....

[Article contains additional citation context not shown here]

R.F. Blute, P.J. Scott, Linear Lauchli Semantics, Annals of Pure and Applied Logic 77, (1996), pp.101-142.

....spaces: maybe too easily, since the tensor and the cotensor are identified, and sum and product as well. In infinite 4 Jean Yves Girard dimension the two multiplicatives are distinct, but the spaces are no longer equal to their second dual ; this is why Blute and Philip Scott in their paper [2] used an old trick of Lefschetz to cope with infinite dimension, namely to introduce a topology to cut the size of the dual, so as to preserve involutivity. Again this topological trick belongs more to the spirit of algebra than to the spirit of topology. The paper [2] basically deals with ....

....Philip Scott in their paper [2] used an old trick of Lefschetz to cope with infinite dimension, namely to introduce a topology to cut the size of the dual, so as to preserve involutivity. Again this topological trick belongs more to the spirit of algebra than to the spirit of topology. The paper [2] basically deals with multiplicatives ; in order to separate the two additives the authors realized (work in progress, see the forthcoming [3] that normed spaces can do it, e.g. using the distinction 1 1 , which is consistent with the very contents of our paper. 1.2 Coherent Banach ....

R. Blute and P. Scott. Linear Lauchli semantics. Annals of Pure and Applied Logic, 77:101--142, 1996.

....values in a Lie group. They are useful in the representation theory of gauge groups. Finally, we hope to take advantage of the fact that distributions form a D module, that is to say they provide representations of the Weyl algebra [20] It would be interesting to attempt to extend the work of [16, 17], where full completeness theorems are obtained by considering representations of the additive group of integers and a noncocommutative Hopf algebra. ....

R. Blute, P. Scott. Linear Lauchli semantics. Annals of Pure and Applied Logic, 77:101-142, 1996.

....the category has biproducts acting as tensor and par, then it is not hard to show that all ( nite) biproducts of the unit will also be in the core. This may then be a non trivial category. An example of this phenomenon is given by the category RTVec of re exive linear topological vector spaces [L63,Ba76,BS96], i.e. vector spaces equipped with a linear topology which are isomorphic to their double duals. In this category, all nite dimensional vector spaces are in the core but in nite dimensional vector spaces are not in the core. ii) As another example, consider the category of sup lattices, where ....

R.F. Blute and P.J. Scott \Linear Lauchli semantics", Annals of Pure and Applied Logic, 77 (1996) 101-142.

No context found.

R. Blute and P. J. Scott. Linear Lauchli Semantics. Annals of Pure and Applied Logic, 1996.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC