Linear combinations of orders

This note explores some properties of a notion of linear combination of partial order relations over a given set. A bilinear form is used to represent compatibility of orders, and we study combinations up to equivalence through this form. A precise description of the quotient space is provided according to the nature of the semiring of coefficients.

[1]  J. Pin.  Tropical Semirings , 2005 .

[2]  Glynn Winskel,et al.  Event Structures , 1986, Advances in Petri Nets.

[3]  Emmanuel Beffara.  An Algebraic Process Calculus , 2008, 2008 23rd Annual IEEE Symposium on Logic in Computer Science.

[4]  Karell Bertet,et al.  Weak-order extensions of an order , 2003, Theor. Comput. Sci..

[5]  Emmanuel Beffara.  Quantitative testing semantics for non-interleaving , 2009, ArXiv.