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In process schematics, an arrow implies full temporalprecedence: an instance of the UOB indicated at the tail of the arrow must complete nolater than the point at which an instance of the UOB indicated at the head of the arrow5Identity may be in terms of chemical structure, mass, physical form, function, etc. For example, grapejuice becomes wine after undergoing a fermentation process. One might argue that the “stuff of” thekind grape juice is the same as that of the resulting kind wine.
Other people having differentattunements may perceive the two kinds as being entirely different based on, for example, chemicalcomposition of the two kinds. We recommend that the assumed criteria for identity be established orcharacterized when there is possible ambiguity.53begins. By contrast, in an object schematic, the arrow implies precedence only withregard to starting points: the object in the state indicated at that tail of the arrow mustbegin to be in that state before the transition to an object in the state indicated at the headof the arrow. The reason for the switch to this weaker sort of precedence in statetransition schematics is noted above: a transition only involves a change from an objectin one state to an object (possibly the same object, possibly different) in another; thoughit may typically be so, the object in the initial state of the transition needn’t cease being inthat state after the transition. To allow for this type of transition, the weaker semantics isused for the arrow in object transition schematics.ConditionsIt is important to distinguish between the characterization of an object of a given kind(or in a given state) and the conditions or rules that govern how the object comes to be ofanother kind (i.e., how it transitions to and from that state).
(Henceforth, explicitreference to kinds will be omitted, as states are the central focus of this section). Fourgeneral classes of conditions are distinguished in IDEF3: entry, transition, state, and exit.State and exit conditions are associated intrinsically with states, while entry and transitionconditions are associated with the interface between states and transition links as depictedin Figure 3-40.
Consequently, the former two are listed in the elaboration for an objectstate, while the latter two are listed in the elaborations for transition links. (Figure 3-40 isnot illustrating new graphical elements for object schematics! The purpose of the figureis to picture where each type of condition is applicable in an object schematic.)54AExit ConditionsState ConditionsTrans. ConditionsState ConditionsBEntry ConditionsExit ConditionsFigure 3-40Object Schematic ConditionsState conditions are those necessary for an object to be in the state in question.
Forexample, to be in a frozen state (at sea level), water must satisfy the condition of being ator below 32 degrees Fahrenheit (though other conditions—e.g., salinity below a certaindegree—may be required for that condition to be sufficient for water to be frozen). Notethat this information is independent of how some quantity of water might come to be inthat state. Exit conditions are simply conditions sufficient for an object in a given state tocease being in (i.e., to exit) that state. For instance, water ceases to be in a frozen state ifheated to a temperature above 32 degrees Fahrenheit.Notice that there is no implication that it is known what state, if any, an object in agiven state S transitions to upon satisfying an exit condition for S; this is the essentialdifference between an exit condition and a transition condition.
Transition conditionsapply to the “interface” between a state and an outgoing link and consist of conditionsthat are individually necessary and jointly sufficient for there to be a transition (or, atleast, an attempted transition) of an object in a given state (A in Figure 3-40) to a55(possibly different) object in the destination state of the relevant link (B in Figure 3-40).Finally, entry conditions apply to the interface between a state and an incoming link andconsist of conditions that are sufficient for an object to enter that state given a (possiblydifferent) object in the source state of that link that has met the relevant transitionconditions.Note that for any given transition from one state to another in an object schematic,there is no requirement for any determinate or identified conditions of any of the fourtypes.
In relatively simple schematics, for example, the semantics will be evident fromthe labels on the state and UOB symbols.Using Referents in IDEF3 Object SchematicsAs with process schematics, the finer details of a state transition are left to theelaborations of the object states. However, by attaching referents to arcs one can adduseful additional information about a state transition explicitly to a correspondingschematic.Referents Attached to Transition LinksReferents used in object schematics can signify either a UOB, a scenario, or atransition schematic. Intuitively, if the referent is a UOB or Scenario referent, the referentsignifies the process during which the indicated transition occurs, or at least a processinvolved in the transition.
On the other hand, if the referent is a transition schematic, thereferent indicates that the transition—from an object in state A to an object in state B, inFigure 3-41—involves transitions through the intermediate states signified in theindicated transition schematic.The syntax for the most typical case—a single referent attached to a transition arc in abasic transition schematic—is illustrated in Figure 3-41.UOB/PABFigure 3-41Basic Transition Schematic with UOB Referent56Typically, P will be the process during which the indicated transition occurs. Thus, intypical occurrences of the indicated process, there will be an object a in state A at thebeginning of an instance p of P, and subsequently an object b at some point after thebeginning of P. However, as noted, the referent in Figure 3-41 might indicate only aprocess involved in the transition from state A to state B.
Thus, the general semantics ofFigure 3-41 requires only that, in an occurrence of the indicated transition, there must bean object in state A prior to or at the start of an instance of P.This semantics of transition schematics can be presented in terms of “intervaldiagrams”—as seen in Figure 3-42—that illustrate the temporal relationships between thevarious situations that occur in an instance of the pattern of events represented by anobject schematic.
Each horizontal line in an interval diagram represents the time intervalover which a given UOB or scenario occurs, or over which a particular object is in agiven state. A vertical line represents the starting or ending point of an interval. “Aa” isshort for “a is in state A”, and likewise for “Bb”. These diagrams are useful because evena basic state transition schematic permits multiple “instantiation patterns,” multiple waysthat real world events can count as instances of the schematic. Thus, all of the intervaldiagrams in Figure 3-42 depict legitimate instantiation patterns for the schematic inFigure 3-41. Interval diagram 1 shows a case in which there is an object a in state A priorto the beginning of an instance p of P, and in which the object b to which there is atransition continues in that state until after the end of P. Interval diagram 2 indicates astate transition of an object a from A to B that is instantaneous (relative to some timegrain). Interval diagram 3 indicates two important possibilities.
First, it illustrates that pcould begin simultaneously with (but not prior to) a’s coming to be in state A. Second, itillustrates that b’s coming to be in state B might occur before a ceases to be in state A.Typically, of course, in such a case a and b will be distinct objects; a’s being in state Amight be a precondition for b’s coming to be in state B during p, as, for example, a certaincircuit (a) being open (A) might be a precondition for a certain warning light (b) toactivate (B). Finally, interval diagram 4 indicates a case in which a ceases to be in state Aprior to the start of p, and then comes to be in state B after p ends.57Instance p of P1)AaBbInstance p of P2)AaInstance p of P3)BaInstance p of P4)AaAaBaBbFigure 3-42Interval Diagrams Representing Instances of Figure 3-41Because the referent in a basic transition schematic typically indicates the process bywhich the indicated transition occurs, cases with the structure depicted in intervaldiagram 4 might seem unwarranted.
But again, the referent in Figure 3-41 need indicateonly a process involved in the transition and not necessarily the complete transitioningprocess. For example, suppose that A is the state water:frozen and B is the statewater:gaseous and P is a heating process (involving a heating element); but suppose inaddition that in the indicated process, a block of ice is allowed to melt naturally and isonly then heated by P which is operative only until the water boils, at which point theheating process is ended and the hot water is just allowed to transition into a gas naturallyby evaporation.The point of this weaker semantics is that IDEF3 is, among other things, a process(and state transition) description capture method. When describing a certain transition,one simply may not know what the full transition process involves, and in particular mayknow only about some intermediate process in the transition.
The given semantics allowssuch a possibility.It is often as important to understand what is ruled out of the semantics of a givenrepresentation as it is to understand what is permitted. Essentially, the only thing that canrule out a given course of events is the ordering of the starting points of its constituentsituations. Thus, for instance, the two interval diagrams in Figure 3-43 do not depictlegitimate instantiation patterns for Figure 3-42. Specifically, as in the first case of Figure3-43, b comes to be in state B before the instance p of P begins, and, in the second case, pbegins without a being in state A.58Instance of PInstance of PAaAaBbBbFigure 3-43Patterns Excluded by the Semantics of Figure 3-41This semantics holds regardless of whether the referent is a UOB or a Scenarioreferent; this is logical, since every scenario can be thought of as a finer-graineddecomposition of a UOB.
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