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A Brief Guide to Linear Logic
, 1993
"... An overview of linear logic is given, including an extensive bibliography and a simple example of the close relationship between linear logic and computation. ..."
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Cited by 53 (8 self)
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An overview of linear logic is given, including an extensive bibliography and a simple example of the close relationship between linear logic and computation.
Nuclear and Trace Ideals in Tensored *Categories
, 1998
"... We generalize the notion of nuclear maps from functional analysis by defining nuclear ideals in tensored categories. The motivation for this study came from attempts to generalize the structure of the category of relations to handle what might be called "probabilistic relations". The comp ..."
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Cited by 28 (9 self)
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We generalize the notion of nuclear maps from functional analysis by defining nuclear ideals in tensored categories. The motivation for this study came from attempts to generalize the structure of the category of relations to handle what might be called "probabilistic relations". The compact closed structure associated with the category of relations does not generalize directly, instead one obtains nuclear ideals. Most tensored categories have a large class of morphisms which behave as if they were part of a compact closed category, i.e. they allow one to transfer variables between the domain and the codomain. We introduce the notion of nuclear ideals to analyze these classes of morphisms. In compact closed tensored categories, all morphisms are nuclear, and in the tensored category of Hilbert spaces, the nuclear morphisms are the HilbertSchmidt maps. We also introduce two new examples of tensored categories, in which integration plays the role of composition. In the first, mor...
Types and Dynamics in Partially Additive Categories
, 1995
"... this paper can be directly applied in order to give a semantics of reduction for the multiplicative fragment of linear logic: in order to capture larger fragments it should be extended dealing with infinitary objects and more generally, this approach allows to investigate an algebraic theory of comp ..."
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this paper can be directly applied in order to give a semantics of reduction for the multiplicative fragment of linear logic: in order to capture larger fragments it should be extended dealing with infinitary objects and more generally, this approach allows to investigate an algebraic theory of computation based on the cutelimination of proofs. 6 Conclusions and Related Works
Edinburgh, Scotland
, 1998
"... Most tensored \Lambdacategories have a large class of morphisms which behave as if they were part of a compact closed category, i.e. they allow one to transfer variables between the domain and the codomain. We introduce the notion of nuclear ideals to analyze these classes of morphisms. In compact ..."
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Most tensored \Lambdacategories have a large class of morphisms which behave as if they were part of a compact closed category, i.e. they allow one to transfer variables between the domain and the codomain. We introduce the notion of nuclear ideals to analyze these classes of morphisms. In compact closed tensored \Lambdacategories, all morphisms are nuclear, and in the tensored \Lambdacategory of Hilbert spaces, the nuclear morphisms are the HilbertSchmidt maps. We also introduce two new examples of tensored \Lambdacategories, in which integration plays the role of composition. In the first, morphisms are a special class of distributions, which we call tame distributions. We also introduce a category of probabilistic relations.
Dynamics of Algorithms
"... This paper represents an extended version of [16]. In the next section we describe partially additive categories. In section 3 we present the execution of pseudoalgorithms in the framework of the partially additive categories as a kind of iteration of endomorphisms. Moreover, we consider deadlock fr ..."
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This paper represents an extended version of [16]. In the next section we describe partially additive categories. In section 3 we present the execution of pseudoalgorithms in the framework of the partially additive categories as a kind of iteration of endomorphisms. Moreover, we consider deadlock free pseudoalgorithms as to be characterized by a summability condition; concepts about structural aspects are organized via type discipline and type compatible dynamics.