Model-checking ecological state-transition graphs
Fig 2
Toy model illustrating the if-then rule modelling.
Modelling of the STM of Fig 1a (left) into a if-then rule model (middle: system description) from which an STG can be computed (right). Each state of the STG is a vector of three Boolean variables defined in the “variables” section of the system description: grasses (Gr), shrubs (Sh) and trees (Tr), noted with + if present and with - if absent. The initial values of the variables are noted next to their symbol in the system description, defining the initial state from which the STG is computed (Gr+,Sh-,Tr-). The “rules” section of the system description defines the if-then rules describing the transitions. For example, the first rule R1 embodies that if grasses are present (Gr+) then (>>) they can fuel a high intensity fire burning down shrubs and trees (Sh-, Tr-), as grasses resprout first they do not disappear in the fire consequence. This rule corresponds in the STG to the transitions labelled by R1 from the middle and bottom states toward the top state. The cascading applications of every rule whose condition is fulfilled and whose consequence is not to every reachable state compute the STG. Compared to the STM, the computed STG is more explicit: there are two transitions from the middle state toward the bottom one because two distinct events may lead the system from the former to the latter.