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arXiv · 1905.02059

A Sequent Calculus Proof Search Procedure and Counter-model Generation based on Natural Deduction Bounds

Jefferson de Barros Santos·Bruno Lopes Vieira·Edward Hermann Haeusler
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Abstract

In a previously published ENTCS paper (Santos et al. (2016)), we introduced a sequent calculus called $\mathbf{LMT^{\rightarrow}}$ for Minimal Implicational Propositional Logic ($\mathbf{LMT^{\rightarrow}}$). This calculus provides a proof search procedure for $\mathbf{LMT^{\rightarrow}}$ that works in a bottom-up approach. We proved there that $\mathbf{LMT^{\rightarrow}}$ is sound and complete. We also suggested a strategy to guarantee termination of the proof search procedure. In this current paper, we refined this strategy and presented a new strategy for $\mathbf{LMT^{\rightarrow}}$ termination. Considering this new strategy, we also provide a (new) completeness proof for the system, which improves the previous version. Besides that, we present explicit upper bounds on the proof search procedure, derived from this new strategy. We also provide a full soundness proof of the system.

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Jefferson de Barros Santos, Bruno Lopes Vieira, Edward Hermann Haeusler. 2019-05-06. A Sequent Calculus Proof Search Procedure and Counter-model Generation based on Natural Deduction Bounds. https://arxiv.org/abs/1905.02059

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