A Rule Based Theorem Prover: an Introduction to Proofs in Secondary Schools

Abstract

The introduction of automated deduction systems in secondary schools faces several bottlenecks. Beyond the problems related with the curricula and the teachers, the dissonance between the outcomes of the geometry automated theorem provers and the normal practice of conjecturing and proving in schools is a major barrier to a wider use of such tools in an educational environment.Since the early implementations of geometry automated theorem provers, applications of artificial intelligence methods, synthetic provers based on inference rules and using forward chaining reasoning are considered to be best suited for education proposes.Choosing an appropriate set of rules and an automated method that can use those rules is a major challenge. We discuss one such rule set and its implementation using the geometry deductive databases method (GDDM). The approach is tested using some chosen geometric conjectures that could be the goal of a 7th year class (≈12-year-old students). A lesson plan is presented, its goal is the introduction of formal demonstration of proving geometric theorems, trying to motivate students to that goal.

Open Source Prover in the Attic

“…Even if many of the items of such reports can be of a matter of taste and coding style, a detailed study of these messages seems unavoidable for the long term. Some recent work [1,8,9] confirm that continuing the pioneer work being put in JGEX is an important step towards the more general use of automated reasoning in the classroom. One possibility is to copy the algorithms and modify them accordingly (this way was chosen by Baeta and Quaresma, using C++), but another option (we chose this) is to use the original source code and do the modifications on it directly.…”

Towards a geometry deductive database prover

“…a method that uses the usual set of rules used on those schools and a method capable of rendering the proofs produced in the usual (in)formalism of secondary schools. As defended in [19], synthetic provers based on inference rules and using forward chaining reasoning are more suited for education proposes.…”

“…In [19] two problems, suited to a 7th year class (≈12-year-old students) are presented. An appropriated set of rules based on the set of rules [6,7] is presented and the proofs (that could be) produced (by an appropriated implementation) of the GDDM method are shown.…”

“…Unlike the algebraic methods, and the semi-synthetic methods [3], they can produce readable synthetic proofs and, depending on the chosen set of rules, more adapted to a given school audience, e.g. secondary school students [19].…”