Abstract |
We recall that SBV, a proof system developed under the methodology of deep inference, extends multiplicative linear logic with the self-dual non-commutative logical operator Seq. We introduce SBVB that extends SBV by adding the self-dual binder Sdb on names. The system SBVB is consistent because we prove that (the analogous of) cut-elimination holds for it. Moreover, the resulting interplay between Seq and Sdb can model $beta$-reduction of linear $\lambda $-calculus inside the cut-free subsystem BVB of SBVB. The long-term aim is to keep developing a programme whose goal is to give pure logical accounts of computational primitives under the proof-search-as-computation analogy, by means of minimal and incremental extensions of SBV. |
@article{Roversi:2014-JLC,
author = {Roversi, Luca},
url = {http://logcom.oxfordjournals.org/content/early/2014/06/05/logcom.exu033.abstract},
title = {A deep inference system with a self-dual binder which is complete for
linear lambda calculus},
abstract = {We recall that SBV, a proof system developed under the methodology
of deep inference, extends multiplicative linear logic with the
self-dual non-commutative logical operator Seq. We introduce SBVB
that extends SBV by adding the self-dual binder Sdb on names. The
system SBVB is consistent because we prove that (the analogous of)
cut-elimination holds for it. Moreover, the resulting interplay
between Seq and Sdb can model $beta$-reduction of linear
$\lambda$-calculus inside the cut-free subsystem BVB of SBVB. The
long-term aim is to keep developing a programme whose goal is to
give pure logical accounts of computational primitives under the
proof-search-as-computation analogy, by means of minimal and
incremental extensions of SBV.},
eprint =
{http://logcom.oxfordjournals.org/content/early/2014/06/05/logcom.exu033.full.pdf+html},
year = {2014},
doi = {10.1093/logcom/exu033},
journal = {Journal of Logic and Computation},
}
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