Matching logic -- a new axiomatization

Laurenţiu Leuştean; Dafina Trufaş

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arXiv · 2506.13801

Matching logic -- a new axiomatization

Laurenţiu Leuştean·Dafina Trufaş

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Abstract

In these notes we propose a new, simpler proof system for first-order matching logic with application and definedness. The new proof system is inspired by Tarski's axiomatization for first order-logic with equality (simplified by Kalish and Montague), that does not involve the notions of a free variable and free substitution. We give also a proof system for first-order matching logic with application, obtained by adapting to matching logic G\"{o}del's proof system for first-order intuitionistic logic.

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Laurenţiu Leuştean, Dafina Trufaş. 2025-06-13. Matching logic -- a new axiomatization. https://arxiv.org/abs/2506.13801

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