Mikheil Rukhaia

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Sequent calculus is widely used for formalizing proofs. However, due to the proliferation of data, understanding the proofs of even simple mathematical arguments soon becomes impossible. Graphical user interfaces help in this matter, but since they normally utilize Gentzen’s original notation, some of the problems persist. In this paper, we introduce a(More)
The cut-elimination method CERES (for firstand higherorder classical logic) is based on the notion of a characteristic clause set, which is extracted from an LK-proof and is always unsatisfiable. A resolution refutation of this clause set can be used as a skeleton for a proof with atomic cuts only (atomic cut normal form). This is achieved by replacing(More)
Computer-generated proofs are usually difficult to grasp for a human reader. In this paper we present an approach to understanding resolution proofs through Herbrand’s theorem and the implementation of a tool based on that approach. The information we take as primitive is which instances have been chosen for which quantifiers, in other words: an expansion(More)
This paper introduces PROOFTOOL, the graphical user interface for the General Architecture for Proof Theory (GAPT) framework. Its features are described with a focus not only on the visualization but also on the analysis and transformation of proofs and related tree-like structures, and its implementation is explained. Finally, PROOFTOOL is compared with(More)
This paper describes the implementation, as well as the features, of the graphical user interface, more specifically defined as a proof viewer, for the General Architecture for Proof Theory (GAPT) framework. It contains methods to render classical and schematic sequent calculus proofs as well as resolution proofs and other tree-like structures in a flexible(More)
This paper describes a new feature of the GAPT framework, namely the ability to import refutations obtained from external automated theorem provers. To cope with coarsegrained, under-specified and non-standard inference rules used by various theorem provers, the technique of proof replaying is employed. The refutations provided by external theorem provers(More)
The axiomatization of arithmetical properties in theorem proving creates many straightforward inference steps. In analyzing mathematical proofs with the CERES (Cut-Elimination by Resolution) system, it is convenient to hide these inferences. The central topic of the thesis is the extension of the CERES method to allow reasoning modulo equational theories.(More)
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