338 research outputs found
Investigations on a Pedagogical Calculus of Constructions
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
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
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
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
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
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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