Zobrazeno 1 - 10
of 232
pro vyhledávání: '"PLOTKIN, GORDON"'
We study Polynomial Lawvere logic PL, a logic defined over the Lawvere quantale of extended positive reals with sum as tensor, to which we add multiplication, thereby obtaining a semiring structure. PL is designed for complex quantitative reasoning,
Externí odkaz:
http://arxiv.org/abs/2402.03543
Publikováno v:
Electronic Notes in Theoretical Informatics and Computer Science, Volume 3 - Proceedings of MFPS XXXIX (November 23, 2023) entics:12292
Lawvere showed that generalised metric spaces are categories enriched over $[0, \infty]$, the quantale of the positive extended reals. The statement of enrichment is a quantitative analogue of being a preorder. Towards seeking a logic for quantitativ
Externí odkaz:
http://arxiv.org/abs/2302.01224
Publikováno v:
Logical Methods in Computer Science, Volume 20, Issue 4 (October 29, 2024) lmcs:10761
Inspired by the seminal work of Hyland, Plotkin, and Power on the combination of algebraic computational effects via sum and tensor, we develop an analogous theory for the combination of quantitative algebraic effects. Quantitative algebraic effects
Externí odkaz:
http://arxiv.org/abs/2212.11784
Autor:
Plotkin, Gordon
We show that adding recursion does not increase the total functions definable in the typed $\lambda\beta\eta$-calculus or the partial functions definable in the $\lambda\Omega$-calculus. As a consequence, adding recursion does not increase the class
Externí odkaz:
http://arxiv.org/abs/2206.08413
Publikováno v:
36th Anual Symposium on Logics in Computer Science, ACM/IEEE LICS 2021
We develop a fixed-point extension of quantitative equational logic and give semantics in one-bounded complete quantitative algebras. Unlike previous related work about fixed-points in metric spaces, we are working with the notion of approximate equa
Externí odkaz:
http://arxiv.org/abs/2106.15932
Autor:
Abadi, Martin, Plotkin, Gordon
Publikováno v:
Logical Methods in Computer Science, Volume 19, Issue 2 (April 20, 2023) lmcs:8372
Describing systems in terms of choices and their resulting costs and rewards offers the promise of freeing algorithm designers and programmers from specifying how those choices should be made; in implementations, the choices can be realized by optimi
Externí odkaz:
http://arxiv.org/abs/2007.08926
Autor:
Plotkin, Gordon D.
We formalise the well-known rules of partial differentiation in a version of equational logic with function variables and binding constructs. We prove the resulting theory is complete with respect to polynomial interpretations. The proof makes use of
Externí odkaz:
http://arxiv.org/abs/2006.06415
Autor:
Abadi, Martin, Plotkin, Gordon D.
Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the mathematical no
Externí odkaz:
http://arxiv.org/abs/1911.04523
Autor:
Cockett, Robin, Cruttwell, Geoffrey, Gallagher, Jonathan, Lemay, Jean-Simon Pacaud, MacAdam, Benjamin, Plotkin, Gordon, Pronk, Dorette
The reverse derivative is a fundamental operation in machine learning and automatic differentiation. This paper gives a direct axiomatization of a category with a reverse derivative operation, in a similar style to that given by Cartesian differentia
Externí odkaz:
http://arxiv.org/abs/1910.07065
Quantitative algebras (QAs) are algebras over metric spaces defined by quantitative equational theories as introduced by the same authors in a related paper presented at LICS 2016. These algebras provide the mathematical foundation for metric semanti
Externí odkaz:
http://arxiv.org/abs/1804.01682