Abstract We propose a natural deduction calculus for the modal logic S4.2. The system is designed to match as much as possible the structure and the prop- erties of the standard system of natural deduction for first-order classical logic, exploiting the formal analogy between modalities and quantifiers. The system is proved sound and complete w.r.t. the standard Hilbert-style formulation of S4.2. Normalization and its consequences are obtained in a natural way, with proofs that closely follow the analogous ones for first-order logic.
A natural deduction calculus for S4.2
Andrea Masini;Margherita Zorzi
2024-01-01
Abstract
Abstract We propose a natural deduction calculus for the modal logic S4.2. The system is designed to match as much as possible the structure and the prop- erties of the standard system of natural deduction for first-order classical logic, exploiting the formal analogy between modalities and quantifiers. The system is proved sound and complete w.r.t. the standard Hilbert-style formulation of S4.2. Normalization and its consequences are obtained in a natural way, with proofs that closely follow the analogous ones for first-order logic.
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