Scenario durations characterization of t-timed Petri nets using linear logic

The objective of this communication is: • Characterize partial order relations in a scenario – resulting from the structure of the Petri net – resulting from the initial and the final markings (reachability) • Derive an algebraic formulae of the duration of the scenario – how long to go from the initial marking to the final one – a duration is attached to each transition – within the framework of t-timed Petri net (firing duration which may be imprecise or fuzzy), also valid for t-time (enabling duration) Relationships between Petri nets and linear logic • Equivalence between reachability and provability – some sequent is provable in intuitionist linear logic sequent calculus – there exists a firing sequence leading from a marking M to M' • More than one way for representing PN in linear logic – Gelhot's approaches is based on proper axioms for representing transitions – markings are not explicitly represented – we represent transitions by formulas with a linear implication – markings (and Pre(t) and Post(t)) are monomial in ⊗