In this paper we provide a semantical meta-theory that will support the development of higher-order calculi for automated theorem proving like the corresponding methodology has in first-order logic. To reach this goal, we establish classes of models that adequately characterize the existing theorem-proving calculi, that is, so that they are sound and complete to these calculi, and a standard methodology of abstract consistency methods (by providing the necessary model existence theorems) needed to analyze completeness of machine-oriented calculi.
We present a distributed system, Dott, for approximately solving the Trav-eling Salesman Problem (TSP) based on the Teamwork method. So-calledexperts and specialists work independently and in parallel for given time pe-riods. For TSP, specialists are tour construction algorithms and experts usemodified genetic algorithms in which after each application of a genetic operatorthe resulting tour is locally optimized before it is added to the population. Aftera given time period the work of each expert and specialist is judged by a referee.A new start population, including selected individuals from each expert and spe-cialist, is generated by the supervisor, based on the judgments of the referees.Our system is able to find better tours than each of the experts or specialistsworking alone. Also results comparable to those of single runs can be found muchfaster by a team.
This paper provides a description of PLATIN. With PLATIN we present an imple-mented system for planning inductive theorem proofs in equational theories that arebased on rewrite methods. We provide a survey of the underlying architecture ofPLATIN and then concentrate on details and experiences of the current implementa-tion.