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A formal system for Euclid's Elements
, 2009
"... We present a formal system, E, which provides a faithful model of the proofs in Euclid’s Elements, including the use of diagrammatic reasoning. ..."
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We present a formal system, E, which provides a faithful model of the proofs in Euclid’s Elements, including the use of diagrammatic reasoning.
Automating Theories in Intuitionistic Logic
 in "7th International Symposium on Frontiers of Combining Systems FroCoS’09, Italie
"... Abstract. Deduction modulo consists in applying the inference rules of a deductive system modulo a rewrite system over terms and formulæ. This is equivalent to proving within a socalled compatible theory. Conversely, given a firstorder theory, one may want to internalize it into a rewrite system t ..."
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Cited by 4 (2 self)
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Abstract. Deduction modulo consists in applying the inference rules of a deductive system modulo a rewrite system over terms and formulæ. This is equivalent to proving within a socalled compatible theory. Conversely, given a firstorder theory, one may want to internalize it into a rewrite system that can be used in deduction modulo, in order to get an analytic deductive system for that theory. In a recent paper, we have shown how this can be done in classical logic. In intuitionistic logic, however, we show here not only that this may be impossible, but also that the set of theories that can be transformed into a rewrite system with an analytic sequent calculus modulo is not corecursively enumerable. We nonetheless propose a procedure to transform a large class of theories into compatible rewrite systems. We then extend this class by working in conservative extensions, in particular using Skolemization. 1
Regular bohm trees
, 1996
"... We give a decision procedure for the extensional equality of total Böhm trees presented by regular systems of recursion equations. 1. Böhm trees presentations Böhm trees are the natural infinite generalisations of normal forms in pure λcalculus. ..."
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Cited by 1 (1 self)
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We give a decision procedure for the extensional equality of total Böhm trees presented by regular systems of recursion equations. 1. Böhm trees presentations Böhm trees are the natural infinite generalisations of normal forms in pure λcalculus.
What Does Euclid Have To Say About The Foundations Of Computer Science
"... It is fair to say that Euclid's Elements has been a driving factor in the developmentof mathematics and mathematical logic for twentythree centuries. The author's own love affair with mathematics and logic start with the Elements. ..."
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It is fair to say that Euclid's Elements has been a driving factor in the developmentof mathematics and mathematical logic for twentythree centuries. The author's own love affair with mathematics and logic start with the Elements.