Computational verb systems: Computing with verbs and applications
In the previous work, verbs were modeled by using different linear and nonlinear dynamical systems for characterizing each of them with different dynamics in different contexts. In this paper the problem of computing with verbs (verb computation) is studied. The relationship and computation between verbs are modeled by relations between different dynamics. The classical "equality" is generalized to verb equality, which is synchronization or generalized synchronization between dynamical systems. Different schemes of synchronization between dynamical systems are presented to show how rich the verb equality can be. Verb computation turns out to be another aspect of linguistic computation besides fuzzy logic. In a word, fuzzy logic answers the questions characterized by "what" while verb computation answers the questions characterized by "how". Verb computation is a model of the natural way used by human beings to cope with the dynamical aspects of complexities of the nature. Whenever (wherever) a system becomes too complex to get an exact model, and only some linguistic statements containing descriptions or implications of dynamical characteristics exist, verb computation becomes a powerful tool for coping with these complexities. Comparing with fuzzy theory, which copes with vagueness in static relations, verb computation copes with vagueness in dynamical processes. Fuzzy theory and verb computation describe two different aspects of the complexities we should cope with for our survival. To illustrate the application of verb computation, the simulation example of "understand music" is presented to show how emotions and intuitions can be transmitted through music by a process of computing with verbs. Then an actual application of verb computation to unmasking a chaotic secure communication scheme-chaotic shift keying is presented. First a reference system is chosen as the "machinself". Then the reference system "hears" the transmitted signal and "feels" different styles in the transmitted signal when different bits of the message signal are scrambled. Different feelings of the reference system reveal the scrambled message signal even though the structure and the parameters of the chaotic transmitter are unknown.
computational verb computational verb systems verb verb computation chaos computing with word chaotic synchronization