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.

💡 Research Summary

The paper reports on a four‑year experimental study in which undergraduate students were taught logical reasoning using the Gentzen‑Prawitz style of natural deduction (ND) rather than the more common Boolean‑algebra approach. The authors begin by critiquing the traditional curriculum: while Boolean algebra efficiently teaches truth‑value computation, it often neglects the procedural aspects of proof construction—how assumptions are introduced, how inference rules are applied, and how the structure of a proof evolves. To address this gap, the study introduced ND, which treats each logical connective with explicit introduction and elimination rules, thereby making the dynamics of assumption management and rule application visible to learners.

Participants comprised 180 students from computer science, electrical engineering, and mathematics programs, spanning a wide range of prior logical competence. The instructional design spanned twelve weekly sessions, each consisting of a two‑hour lecture, a one‑hour hands‑on workshop, and a one‑hour lab on proof‑assistant tools such as Coq and Lean. The first two weeks reviewed propositional logic and Boolean algebra to establish a baseline. Weeks three through six covered the basic ND rules for conjunction, disjunction, implication, and negation, with short proof exercises. Weeks seven through ten introduced quantifier rules, the handling of discharged assumptions, and proof‑tree visualisation techniques. The final two weeks culminated in a project where students modelled type‑system rules and simple program‑verification problems using ND, then mechanised the proofs in a proof assistant.

Assessment was multi‑modal: pre‑ and post‑tests measured factual knowledge; written proof assignments captured procedural skill; surveys gauged perceived difficulty and motivation; and semi‑structured interviews provided qualitative insight. The results were striking. Compared with a control group taught exclusively with Boolean algebra, the ND group (1) completed proof tasks on average 22 % faster, (2) made 35 % fewer logical errors, and (3) answered meta‑logical questions (e.g., “Why is this assumption needed?”) with 48 % higher accuracy. The most pronounced improvement stemmed from the explicit handling of assumption discharge, which helped students internalise the scope of hypotheses and avoid common pitfalls such as accidental reuse of discharged assumptions.

Survey data revealed that 87 % of ND participants found the approach “relevant to programming language type checking and verification,” and many reported increased confidence when later using proof assistants. The authors argue that this relevance is not accidental: ND mirrors the rule‑based reasoning underlying type systems, program logics, and formal verification frameworks, making it a natural pedagogical bridge for computer‑science curricula.

Nevertheless, the study acknowledges several limitations. First, the heterogeneity of students’ prior mathematical background was only partially controlled, leaving open the possibility that stronger students benefitted disproportionately. Second, the twelve‑week horizon does not allow assessment of long‑term retention of proof‑construction skills. Third, the transferability of ND to non‑technical disciplines (e.g., philosophy, law) remains unexplored.

In conclusion, the authors contend that Gentzen‑Prawitz natural deduction offers a superior alternative to Boolean algebra for teaching logical reasoning, especially for students destined for formal methods, programming language theory, and software verification. By foregrounding the procedural structure of proofs, ND cultivates meta‑logical awareness and aligns undergraduate instruction with the reasoning patterns used in contemporary computer‑science research and practice. Future work is proposed to (a) conduct longitudinal studies of skill retention, (b) test ND in a broader array of academic domains, and (c) develop integrated curricula that couple ND instruction with automated theorem‑proving environments.