Section: New Results

Encoding Additive Connectives with Multiplicatives and Subexponentials

Participant : Kaustuv Chaudhuri.

In a recent workshop on Linearity  [55] , we have published the formal proof (that was obtained in 2009) that linear logic with three subexponentials in a certain lattice is undecidable. An extended version of this paper was submitted to a special issue on Linearity in Mathematical Structures in Computer Science and was accepted in November 2015.

The preprint of that extended paper [41] gives a direct embedding of propositional MALL (multiplicative and additive linear logic) using only multiplicative connectives and five subexponentials. This means that the additive connectives are, in fact, redundant when we have multiplicatives and subexponentials. Moreover, in the first-order case this encoding is polynomial and focally adequate, which means that MALL can be simulated at the highest fidelity – at the level of individual inference rules.