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Hochschulschrift

Superposition and Decision Procedures - Back and Forth

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44621

Hillenbrand,  Thomas
Automation of Logic, MPI for Informatics, Max Planck Society;
International Max Planck Research School, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45719

Weidenbach,  Christoph
Automation of Logic, MPI for Informatics, Max Planck Society;

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Zitation

Hillenbrand, T. (2008). Superposition and Decision Procedures - Back and Forth. PhD Thesis, Universität des Saarlandes, Saarbrücken.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-001A-21ED-0
Zusammenfassung
Two apparently different approaches to automating deduction are mentioned in the title; they are the subject of a debate on ``big engines vs.\ little engines of proof''. The contributions in this thesis advocate that these two strands of research can interplay in subtle and sometimes unexpected ways, such that mutual pervasion can lead to intriguing results: Firstly, superposition can be run on top of decision procedures. This we demonstrate for the class of Shostak theories, incorporating a little engine into a big one. As another instance of decision procedures within superposition, we show that ground confluent rewrite systems, which decide entailment problems in equational logic, can be harnessed for detecting redundancies in superposition derivations. Secondly, superposition can be employed as proof-theoretic means underneath combined decision procedures: We re-establish the correctness of the Nelson-Oppen procedure as an instance of the completeness of superposition. Thirdly, superposition can be used as a decision procedure for many interesting theories, turning a big engine into a little one. For the theory of bits and of fixed-size bitvectors, we suggest a rephrased axiomatization combined with a transformation of conjectures, based on which superposition decides the universal fragment. Furthermore, with a modification of lifting, we adapt superposition to the theory of bounded domains and give a decision procedure, which captures the Bernays-Schönfinkel class as well.