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Finiteness spaces
| Content Provider | Scilit |
|---|---|
| Author | Ehrhard, Thomas |
| Copyright Year | 2005 |
| Description | We investigate a new denotational model of linear logic based on the purely relational model. In this semantics, webs are equipped with a notion of ‘finitary’ subsets satisfying a closure condition and proofs are interpreted as finitary sets. In spite of a formal similarity, this model is quite different from the usual models of linear logic (coherence semantics, hypercoherence semantics, the various existing game semantics…). In particular, the standard fix-point operators used for defining the general recursive functions are not finitary, although the primitive recursion operators are. This model can be considered as a discrete analogue of the Köthe space semantics introduced in a previous paper: we show how, given a field, each finiteness space gives rise to a vector space endowed with a linear topology, a notion introduced by Lefschetz in 1942, and we study the corresponding model where morphisms are linear continuous maps (a version of Girard's quantitative semantics with coefficients in the field). In this way we obtain a new model of the recently introduced differential lambda-calculus. |
| Related Links | http://pdfs.semanticscholar.org/1ed0/365336817baca1ec24c0061a9c1163a7af8f.pdf https://www.cambridge.org/core/services/aop-cambridge-core/content/view/E5E9CE1FA4050A56EF25CFB6F6A5754F/S0960129504004645a.pdf/div-class-title-finiteness-spaces-div.pdf |
| Ending Page | 646 |
| Page Count | 32 |
| Starting Page | 615 |
| ISSN | 09601295 |
| e-ISSN | 14698072 |
| DOI | 10.1017/s0960129504004645 |
| Journal | Mathematical Structures in Computer Science |
| Issue Number | 4 |
| Volume Number | 15 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2005-08-01 |
| Access Restriction | Open |
| Subject Keyword | Mathematical Structures in Computer Science History and Philosophy of Science Finiteness Space Coherence Semantics Linear Logic New Model Corresponding Model Usual Model Quantitative Semantics Space Semantics Hypercoherence Semantics Relational Model New Denotational Model |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics Computer Science Applications |
