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In the early 1970s, in Kiev, research on automated theorem proving started in the framework of the so-called Evidence Algorithm (EA) programme, having some general features with the Mizar project and, in particular, being oriented to the development of such a technique for inference search in various first-order logics that satisfies the following requirements: the syntactic form of a problem under...
Kolmogorov introduced an informal calculus of problems in an attempt to provide a classical semantics for intuitionistic logic. This was later formalised by Medvedev and Muchnik as what has come to be called the Medvedev and Muchnik lattices. However, they only formalised this for propositional logic, while Kolmogorov also discussed the universal quantifier. We extend the work of Medvedev to first-order...
Superdeduction is a formalism closely related to deduction modulo which permits to enrich a deduction system - especially a first-order one such as natural deduction or sequent calculus - with new inference rules automatically computed from the presentation of a theory. We give a natural encoding from every functional pure type system (PTS) into superdeduction by defining an appropriate first-order...
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