- Omega: Towards a Mathematical Assistant (1999)
- -mega is a mixed-initiative system with the ultimate pur-pose of supporting theorem proving in main-stream mathematics andmathematics education. The current system consists of a proof plannerand an integrated collection of tools for formulating problems, provingsubproblems, and proof presentation.
- Henkin Completeness of Higher-Order Resolution (1999)
- In this paper we present an extensional higher-order resolution calculus that iscomplete relative to Henkin model semantics. The treatment of the extensionality princi-ples - necessary for the completeness result - by specialized (goal-directed) inference rulesis of practical applicability, as an implentation of the calculus in the Leo-System shows.Furthermore, we prove the long-standing conjecture, that it is sufficient to restrict the orderof primitive substitutions to the order of input formulae.
- Model Existence for Higher Order Logic (1997)
- 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.