Non-associative, Non-commutative Multi-modal Linear Logic

Non-Linear / Non-Commutative Non-Abelian Monopoles

Using recently proposed non-linearly realized supersymmetry in non-Abelian gauge theory corrected to O(α′), we derive the non-linear BPS equations in the background B-field for the U(2) monopoles and instantons. We show that these non-Abelian non-linear BPS equations coincide with the non-commutative anti-self-dual equations via the Seiberg-Witten map.

A Non-commutative Extension of Classical Linear Logic

We extend the multiplicative fragment of linear logic with a non-commutative connective (called before), which, roughly speaking, corresponds to sequential composition. This lead us to a calculus where the conclusion of a proof is a Partially Ordered MultiSET of formulae. We rstly examine coherence semantics, where we introduce the before connective, and ordered products of formulae. Secondly w...

A Non-commutative Extension of Multiplicative Exponential Linear Logic

We extend multiplicative exponential linear logic (MELL) by a noncommutative, self-dual logical operator. The extended system, called NEL, is defined in the formalism of the calculus of structures, which is a generalisation of the sequent calculus and provides a more refined analysis of proofs. We are then able to extend the expressiveness of MELL by modelling a broad notion of sequentiality. W...

Simulating Computations in Second Order Non-Commutative Linear Logic

Lincoln, Scedrov and Shankar proved undecidability of intuitionistic second order multiplicative commutative linear logic by embedding LJ2 into this logic. Emms did the same for intuitionistic second order non-commutative linear logic. Recently, Lafont and Scedrov demonstrated undecidability of classical second order multiplicative commutative linear logic. As for classical second order non-com...

Dimension Computations in Non-Commutative Associative Algebras