Graph Theoretic Models for Reasoning About Time

Reasoning about time is a very ancient discipline, perhaps as old as prehistoric man. These ancient humans had discovered how long to roast their hunted meat and how to dry and age the skins of animals. They learned how and when to plant seeds, and where guided by the cycles of the sun, moon and the seasons. Our ancestors knew that day followed night and night followed day, and they had some notion of duration of day and night. This basic temporal knowledge was exploited to develop a sense of planning, taking advantage of observation and experience. For example, they would have observed that deer drink at the river at a certain time of the day, or that fish are easier to catch in the early morning. Early humans could recognize the changing seasons, and adapted their behavior in order to expect and avoid some of the dangers of cold and hunger by preparing in advance. If we start our solar-earth stopwatch at 100-200 thousand years ago, and follow it through to the beginning of recorded history, we will see the evolution of human understanding of time. Reasoning about time is an integral component of every advance of mankind. The annual flooding of the Nile brought fertile soil to the river banks long before the Egyptian kingdoms existed, but the quantum leap in exploiting and controlling this natural phenomenon did not happen until the great empires had been formed. As Persia, Mesopotamia, Egypt, China and India developed writing and scholarship, the process of human knowledge and reasoning entered a new era. The seasonal planter became the seasonal shipper, and our temporal planner skipped past a thousand generations. Our current notions of reasoning about time are not very different from the ideas of the “literate elite” among those of the ancient Greeks, Hebrews, Romans, Confucians. With today’s reasoning algorithms and techniques, temporal models and logics, and advances in philosophy, cognitive science and psychology, the