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Using Large Language Models for (De-)Formalization and Natural Argumentation Exercises for Beginner's Students
We describe two systems currently being developed that use large language models for the automatized correction of (i) exercises in translating back and forth between natural language and the languages of propositional logic and first-order predicate logic and (ii) exercises in writing simple arguments in natural language in non-mathematical scenarios.
Improving the Diproche CNL through Autoformalization via Large Language Models
The Diproche system is an automated proof checker for texts written in a controlled fragment of German, designed for didactical applications in classes introducing students to proofs for the first time.
Natural Language Proof Checking in Introduction to Proof Classes -- First Experiences with Diproche
We present and analyze the employment of the Diproche system, a natural language proof checker, within a one-semester mathematics beginners lecture with 228 participants.
Randomising Realisability
We consider a randomised version of Kleene's realisability interpretation of intuitionistic arithmetic in which computability is replaced with randomised computability with positive probability.
Logic
Automatized Evaluation of Formalization Exercises in Mathematics
We describe two systems for supporting beginner students in acquiring basic skills in expressing statements in the formalism of first-order predicate logic; the first, called "math dictations", presents users with the task of formalizing a given natural-language sentence, while the second, called "Game of Def", challenges users to give a formal description of a set of a geometric pattern displayed to them.
Using Automated Theorem Provers for Mistake Diagnosis in the Didactics of Mathematics
The Diproche system, an automated proof checker for natural language proofs specifically adapted to the context of exercises for beginner's students similar to the Naproche system by Koepke, Schr\"oder, Cramer and others, uses a modification of an automated theorem prover which uses common formal fallacies intead of sound deduction rules for mistake diagnosis.
