Nets Enriched over Closed Monoidal Structures

Abstract. We show how the firing rule of Petri nets relies on a residuation operation for the commutative monoid of natural numbers. On that basis we introduce closed monoidal structures which are residuated monoids. We identify a class of closed monoidal structures (associated with a family of idempotent group dioids) for which one can mimic the token game of Petri nets to define the behaviour of these generalized Petri nets whose flow relations and place contents are valued in the closed monoidal structure.

• Type: Conference
• Year: 2003
• Where: APN
• Authors: Eric Badouel, Jules Chenou
• Keywords: APN 2003, Artificial Intelligence, Closed Monoidal Structure, Idempotent Group Dioids, Petri Nets