338 research outputs found

    Investigations on a Pedagogical Calculus of Constructions

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    In the last few years appeared pedagogical propositional natural deduction systems. In these systems, one must satisfy the pedagogical constraint: the user must give an example of any introduced notion. First we expose the reasons of such a constraint and properties of these "pedagogical" calculi: the absence of negation at logical side, and the "usefulness" feature of terms at computational side (through the Curry-Howard correspondence). Then we construct a simple pedagogical restriction of the calculus of constructions (CC) called CCr. We establish logical limitations of this system, and compare its computational expressiveness to Godel system T. Finally, guided by the logical limitations of CCr, we propose a formal and general definition of what a pedagogical calculus of constructions should be.Comment: 18 page

    On Constructive Axiomatic Method

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    In this last version of the paper one may find a critical overview of some recent philosophical literature on Axiomatic Method and Genetic Method.Comment: 25 pages, no figure

    Gentzen-Prawitz Natural Deduction as a Teaching Tool

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    We report a four-years experiment in teaching reasoning to undergraduate students, ranging from weak to gifted, using Gentzen-Prawitz's style natural deduction. We argue that this pedagogical approach is a good alternative to the use of Boolean algebra for teaching reasoning, especially for computer scientists and formal methods practionners

    Toward Formalizing Teleportation of Pedagogical Artificial Agents

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    Our paradigm for the use of artificial agents to teach requires among other things that they persist through time in their interaction with human students, in such a way that they “teleport” or “migrate” from an embodiment at one time t to a different embodiment at later time t\u27. In this short paper, we report on initial steps toward the formalization of such teleportation, in order to enable an overseeing AI system to establish, mechanically, and verifiably, that the human students in question will likely believe that the very same artificial agent has persisted across such times despite the different embodiments. The system achieves this by demonstrating to the students that different embodiments share one or more privileged beliefs that only one single agent can possess

    Pedagogical lambda-cube: the λ² case

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    38 pagesIn pedagogical formal systems one needs to systematically give examples of hypotheses made. This main characteristic is not the only one needed, and a formal definition of pedagogical sub-systems of the Calculus of Constructions (CC) has already been stated. Here we give such a pedagogical sub-system of CC corresponding to the second-order pedagogical λ-calculus of Colson and Michel. It thus illustrates the appropriateness of the formal definition, and opens the study to stronger systems of the λ-cube, for which CC is the most expressive representative. In addition we study the type-checking problem for the formalisms of those pedagogical calculi of second-order

    Implementing semantic tableaux

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    This report describes implementions of the tableau calculus for first-order logic. First an extremely simple implementation, called leanTAP, is presented, which nonetheless covers the full functionality of the calculus and is also competitive with respect to performance. A second approach uses compilation techniques for proof search. Improvements inculding universal variables and lemmata are considered as well as more efficient data structures using reduced ordered binary decision diagrams. The implementation language is PROLOG. In all cases fully operational PROLOG code is given. For leanTAP a formal proof of the correctness of the implementation is given relying on the operational semantics of PROLOG as given by the SLD-tree model. This report will appear as a chapter in the Handbook of Tableau-based Methods in Automated Deduction edited by: D. Gabbay, M. D\u27Agostino, R. H\"{a}hnle, and J.Posegga published by: KLUWER ACADEMIC PUBLISHERS Electronic availability will be discontinued after final acceptance for publication is obtained
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