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of a temporal constraint network is a set of variable assignments that satisfy the temporal constraints.  A variable assignment is a function V 
a temporal variable. A temporal constraint network is consistent if it admits a non empty interpretation. The notation, denotes the subset of - - where the variable i is mapped to the interval value j.

It is now possible to interpret generic concept expressions. onsider the e uations introduced in  igure  . An interpretation function v t , based on a variable assignment V, an interval and a set of constraints
}          over the assignments of inner variables, extends the primitive interpretation function in such a way that the e uations of igure are satisfied. Intuitively, the interpretation of a concept v t, is the set of entities of the domain that are of type at the time interval , with the assignment for the free temporal variables in given by V g see g @ y t, and with the constraints for the assignment of variables in the scope of the outermost temporal   uantifiers given by Note that, interprets the variable renaming due to the temporal substitutive   ualifier and it takes e  ect during the choice of a variable assignment, as the see Q 
e uation for v t shows.

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In absence of free variables in the concept expression with the exception of for notational simplification the natural interpretation function     being e uivalent to the interpretation function v,t, with any V such that V 
0 is introduced. The set of interpretations v t     obtained by varying I V   with a fixed    is maximal wrt set 0, i.e., the set of natural interpretations includes any set of interpretations inclusion if with a fixed I I I
unconstrained set is the larger one. Note that, for feature interpretation only the natural one is used since it is not admitted to temporally ualify them.