Page - 177 - in Intelligent Environments 2019 - Workshop Proceedings of the 15th International Conference on Intelligent Environments

5. Analyzing theInteroperabilityMeasurementModel In section 4.3we have derived a causalmodel for themessage passing behavior of in- teroperable processes.Wenow investigate themodel behavior in order to decideon the degree of the callee’s interoperability behavior.Wediscuss themodel’s behavior using probabilities, e.g. there is a probability that an incomingmessageM contains an oper- ationwhich the dispatcher canmap to a local one. The probability of the complement means thatM containsanunknownoperation to thedispatcher. 5.1. VariablesDependenciesandd-separation Theobservationofmessagepassingof interoperableprocesses insection4.2establishes adependencybetween the incomingandoutgoingmessage through the causal relation- ships between the variables.We analyze the paths between the nodes in the graphical causalmodel of figure 3 utilizing the process of d-separation,where one can conclude thevariabledependencies from.Wequote thedefinitionfromPearl’sbook[15],page46. Definition (d-separation). Apath p isblockedbyasetofnodesZ if andonly if 1. pcontainsachainofnodesA→B→CoraforkA←B→Csuchthat themiddle nodeB is inZ (i.e.B is conditionedon), or 2. pcontains a colliderA→B←Csuch that the collisionnodeB is not inZ, and nodescendantofB is inZ. If Z blocks every path between two nodes X andY are d-separated, conditional on Z, and thusare independent conditionalonZ. If two graph’s nodes are d-separated, the variables they represent are independent. In contrast, if twonodes are d-connected, a path exists between them, i.e. the variables aremost likelydependent. 5.2. d-separationAnalysis The analysis of d-separation in the causal graph of figure 3 let us identify the condi- tionsformessagedependencies.Concretely, thediscriminatorDshalldeterminethemes- sageM′originasa result of the incomingmessageM.Asaconsequence,we formulate: Problem. Findsetsofnodes in thecausalgraphunderwhichMandDared-connected ord-separated. Discussion of the cases, ifM,Dare d-connected. Using an empty conditioning setZ, then, according to thedefinitionabove, everypathbetweenM andD formsachainwith noblockingnode inbetween.So,M andDared-connectedand thereforedependent. In this case, the incomingmessageM affects the probability ofD. In the context of inter- operability, it is understood as follows: FormessagesM containing operations known or unknown to the dispatcher the discriminatorDyieldsD=1orD=0corresponding to theprobability the incomingmessageM contains anoperationknownorunknown to thedispatcher.AsingleoccurrenceofmessageM containinganoperationknown to the dispatcherwill yieldD=1according to thedefinedcausal relationships in section4.3. S. Kotstein and C. Decker /AnApproach for Measuring IoT Interoperability 177