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Expressing additives using multiplicatives and subexponentials

Published online by Cambridge University Press:  21 November 2016

KAUSTUV CHAUDHURI Open the ORCID record for KAUSTUV CHAUDHURI [Opens in a new window]
KAUSTUV CHAUDHURI*
Affiliation:
INRIA, Palaiseau, France Email: kaustuv.chaudhuri@inria.fr
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Abstract

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Subexponential logic is a variant of linear logic with a family of exponential connectives – called subexponentials – that are indexed and arranged in a pre-order. Each subexponential has or lacks associated structural properties of weakening and contraction. We show that a classical propositional multiplicative subexponential logic (MSEL) with one unrestricted and two linear subexponentials can encode the halting problem for two register Minsky machines, and is hence undecidable. We then show how the additive connectives can be directly simulated by giving an encoding of propositional multiplicative additive linear logic (MALL) in an MSEL with one unrestricted and four linear subexponentials.

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Type
Paper
Information
Mathematical Structures in Computer Science , Volume 28 , Special Issue 5: Linearity 2014 , May 2018 , pp. 651 - 666
Copyright
Copyright © Cambridge University Press 2016 

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