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Learning theoretic aspects of mathematics and logic have been studied by many authors. They study how mathematical and logical objects are algorithmically \learned" (inferred) from nite data. Although they study mathematical objects, the objective of the studies is learning. In this paper, a mathematics of which foundation itself is learning theoretic will(More)
The topic of this paper is relative constructivism. We are concerned with classifying nonconstructive principles from the constructive viewpoint. We compare, up to provability in intuitionistic arithmetic, subclassical principles like Markov's principle, (a function-free version of) weak Konig's lemma, Post's theorem, excluded middle for simply existential(More)
The notion of Limit-Computable Mathematics (LCM) will be introduced. LCM is a fragment of classical mathematics in which the law of excluded middle is restricted to 1 0 2-formulas. We can give an accountable computational interpretation to the proofs of LCM. The computational content of LCM-proofs is given by Gold's limiting recur-sive functions, which is(More)
We associate to any game G, in the sense of Set Theory, a variant of it we call bck(G). We show through examples that many relevant non-constructive proofs in Algebra and Combinatorics can be interpreted by recursive winning strategy over some game of the form bck(G). We further support this claim by proving that games of the form bck(G) are a sound and(More)
Proof animation is a way of executing proofs to nd errors in the formalization of proofs. It is intended to be \testing in proof engineer-ing". Although the realizability i n terpretation as well as the functional interpretation based on limit-computations were introduced as means for proof animation, they were unrealistic as an architectural basis for(More)
We are developing a methodology of Test-Driven Development of Models (TDDM) based on an experimental UML2.0 modeling tool SMART. Our experience shows that TDDM is quite useful for agile model developments. SMART provides guidance how to build models based on compiler errors of testcases, something similar to what Quick Fix of Eclipse does. It also provides(More)