Results 1 
3 of
3
A system of interaction and structure IV: The exponentials
 IN THE SECOND ROUND OF REVISION FOR MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE
, 2007
"... We study some normalisation properties of the deepinference proof system NEL, which can be seen both as 1) an extension of multiplicative exponential linear logic (MELL) by a certain noncommutative selfdual logical operator; and 2) an extension of system BV by the exponentials of linear logic. T ..."
Abstract

Cited by 16 (9 self)
 Add to MetaCart
We study some normalisation properties of the deepinference proof system NEL, which can be seen both as 1) an extension of multiplicative exponential linear logic (MELL) by a certain noncommutative selfdual logical operator; and 2) an extension of system BV by the exponentials of linear logic. The interest of NEL resides in: 1) its being Turing complete, while the same for MELL is not known, and is widely conjectured not to be the case; 2) its inclusion of a selfdual, noncommutative logical operator that, despite its simplicity, cannot be axiomatised in any analytic sequent calculus system; 3) its ability to model the sequential composition of processes. We present several decomposition results for NEL and, as a consequence of those and via a splitting theorem, cut elimination. We use, for the first time, an induction measure based on flow graphs associated to the exponentials, which captures their rather complex behaviour in the normalisation process. The results are presented in the calculus of structures, which is the first, developed formalism in deep inference.
A New Logical Notion of Partial Order Planning
"... We present a new approach to conjunctive planning where an explicit correspondence between partial order plans and multiplicative exponential linear logic proofs is established. As the underlying proof theoretical formalism, we employ the recently developed calculus of structures. This way ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
We present a new approach to conjunctive planning where an explicit correspondence between partial order plans and multiplicative exponential linear logic proofs is established. As the underlying proof theoretical formalism, we employ the recently developed calculus of structures. This way
Deep Inference and the Calculus of Structures
, 2005
"... This document gives an overview of this research e#ort ..."