Shortest Path in a Combined Public Transportation Network

Location Based Services that assist travelers in wayfinding are a prime application for expert system techniques. The use of public transportation leads nearly always to a combination of different services from different transportation companies (multi-modal transportation). Information systems must combine data for the different services and produce advice to navigate in space and to obtain the right tickets, reservations, etc. This information can be seen as the combination of two (or more) state-transition diagrams: one for the spatial navigation and one for the business (ticketing, validation, reservation) rules. A (categorical) product combines two state-transition diagrams. The implementation is immediate using an intuitionistic logic reasoner built into the programming language, which infers typing for second order, polymorphic functions and allows their safe execution. The shortest path algorithm in this combined network produces sound advice and reminds the user to acquire tickets and plans the necessary navigation to ticket vending machines, etc. The analysis shows how to specify the connections between the two graphs optimally. The approach combines typical expert system technologies like inference engines with object-oriented programing; recent advances increase the level of reasoning possible during compilation. The use of a high-level programming language with substantial inference power facilitates the formalization of domain knowledge and is a viable alternative to the classical expert system architecture. ”(Playing Chopin’s etudes) taught me a lifelong lesson: that phenomena perceived to be magical are always the outcome of complex patterns of nonmagical activities taking place at a level below perception. In other words, the magic behind magic is pattern.” Douglas Hofstadter, SCIENTIFIC AMERICAN, April, 1982, p. 17.