Paramodulation Decision Procedures

The aim of this thesis is to present Paramodulation Operators deciding the (i) Ackermann class with Equality [FS93] and (ii) the monadic class with equality [BGW93]. Ad (i) a refinement of the Ordered Paramodulation calculus [HR91] is used to define the appropriate inference operator; ad (ii) a variant of the Superposition calculus [BG94] is employed for this purpose. It seemed natural to give a uniform presentation of these underlying equational calculi. Hence, the first part of this thesis is designed to be a uniform treatment of these calculi. In the definition of the paramodulation operator that decides the monadic class with equality ordering constraints are used. Therefor we choose to present all the inference rules that Ordered Paramodulation and Superposition define with respect to ordering constraints. These constraints are used to express the restrictions normally given with the description of an inference rule as part of the object language. Acknowledgments: I wish to thank Univ. Prof. Dr. Alexander Leitsch for the excellent education I received and the bunch of helpful comments that he told me while I was busy with this thesis. Furthermore I wish to thank Univ.-Doz. Dr. Christian Fermüller and Univ.-Ass. Dr. Gernot Salzer for all the ideas and stimulating discussions. For less helpful, but nevertheless stimulating remarks, I wish to thank Alexander, Clark, Julia, Mandana, Richard and Roman.