Professional scientists and engineers routinely use nonverbal reasoning processes and graphical representations to organize their thoughts and as part of the process of solving otherwise verbally presented problems. This paper presents a computational theory and an implemented system that capture some aspects of this style of reasoning. The system, consisting of a suite of computer programs collectively known as KAM, uses numerical methods as a means to shift back and forth between symbolic and geometric methods of reasoning. The KAM program has three novel features: (1) it articulates the idea that “visual mechanisms are useful for problem solving” into a workable computational theory, (2) it applies the approach to a domain of great technical difficulty, the field of complex nonlinear chaotic dynamics, and (3) it demonstrates the power of the approach by solving problems of real interest to working scientists and engineers.

This paper explores the relationships between a computational theory of temporal representation (as developed by James Allen) and a formal linguistic theory of tense (as developed by Norbert Hornstein) and aspect. It aims to provide explicit answers to four fundamental questions: (1) what is the computational justification for the primitives of a linguistic theory; (2) what is the computational explanation of the formal grammatical constraints: (3) what are the processing constraints imposed on the learnability and markedness of these theoretical constructs: and (4) what are the constraints that a linguistic theory imposes on. representations. We show that one can effectively exploit the interface between the language faculty and the cognitive faculties by using linguistic constraints to determine restructions on the cognitive representations and vice versa.Three main results are obtained: (1) We derive an explanation of an observed grammatical constraint on tense .. the Linear Order Constraint .. from the information monotonicity property of the constraint propagation algorithm of Allen's temporal system: (2) We formulate a principle of markedness for the basic tense structures based on the computational efficiency of the temporal representations: and (3) We show Allen's interval-based temporal system is not arbitrary. but it can be used to explair, independently motivated linguistic constraints on tense and aspect interpretations.We also claim that the methodology of research developed in this study .. "cross-level" investigation of independently motivated formal grammatical theory and computational models .. is a powerful paradigm with which to attack representational problems in basic cognitive domains, e.g., space. time, causality, etc.