67 research outputs found
Towards an Intelligent Tutor for Mathematical Proofs
Computer-supported learning is an increasingly important form of study since
it allows for independent learning and individualized instruction. In this
paper, we discuss a novel approach to developing an intelligent tutoring system
for teaching textbook-style mathematical proofs. We characterize the
particularities of the domain and discuss common ITS design models. Our
approach is motivated by phenomena found in a corpus of tutorial dialogs that
were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor
for textbook-style mathematical proofs can be built on top of an adapted
assertion-level proof assistant by reusing representations and proof search
strategies originally developed for automated and interactive theorem proving.
The resulting prototype was successfully evaluated on a corpus of tutorial
dialogs and yields good results.Comment: In Proceedings THedu'11, arXiv:1202.453
The AProS project: Strategic thinking & computational logic.
Abstract The paper discusses tools for teachin
Gödelâs Philosophical Challenge (to Turing)
The incompleteness theorems constitute the mathematical core of Gödelâs philosophical challenge. They are given in their âmost satisfactory formâ, as Gödel saw it, when the formality of theories to which they apply is characterized via Turing machines. These machines codify human mechanical procedures that can be carried out without appealing to higher cognitive capacities. The question naturally arises, whether the theorems justify the claim that the human mind has mathematical abilities that are not shared by any machine. Turing admits that non-mechanical steps of intuition are needed to transcend particular formal theories. Thus, there is a substantive point in comparing Turingâs views with Gödelâs that is expressed by the assertion, âThe human mind infinitely surpasses any finite machineâ. The parallelisms and tensions between their views are taken as an inspiration for beginning to explore, computationally, the capacities of the human mathematical mind
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