arXiv:1805.11813 Abstract | arXiv Analytics

arXiv:1805.11813 [math.LO]Abstract References Reviews Resources

Derivatives of Turing machines in Linear Logic

Published 2018-05-30Version 1

We calculate denotations under the Sweedler semantics of the Ehrhard-Regnier derivatives of various encodings of Turing machines into linear logic. We show that these derivatives calculate the rate of change of probabilities naturally arising in the Sweedler semantics of linear logic proofs. The resulting theory is applied to the problem of synthesising Turing machines by gradient descent.

Comments: 60 pages

Categories: math.LO

Keywords: sweedler semantics, linear logic proofs, ehrhard-regnier derivatives, gradient descent, probabilities

Related articles: Most relevant | Search more

arXiv:2003.07408 [math.LO] (Published 2020-03-16)

Probabilities with Gaps and Gluts

Dominik Klein, Ondrej Majer, Soroush Rafiee Rad

arXiv:1405.5139 [math.LO] (Published 2014-05-20, updated 2017-04-12)

Algorithmic identification of probabilities is hard

Laurent Bienvenu, Santiago Figueira, Benoit Monin, Alexander Shen

arXiv:2402.12953 [math.LO] (Published 2024-02-20, updated 2024-11-05)

Two-layered logics for probabilities and belief functions over Belnap--Dunn logic