On semantics of first-order justification logic with binding modalities

Tatiana Yavorskaya; Elena Popova

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arXiv · 2512.07994

On semantics of first-order justification logic with binding modalities

Tatiana Yavorskaya·Elena Popova

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Abstract

We introduce the first order logic of proofs $FOLP^\Box$ in the joint language combining justification terms and binding modalities. The main issue is Kripke--style semantics for this logic. We describe models for $FOLP^\Box$ in terms of valuations of individual variables instead of introducing constants to the language. This approach requires a new format of the evidence function. This allows us to assign semantic meaning to formulas that contain free variables. The main results are soundness and completeness of $FOLP^\Box$ with respect to the described semantics.

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Tatiana Yavorskaya, Elena Popova. 2025-12-08. On semantics of first-order justification logic with binding modalities. https://arxiv.org/abs/2512.07994

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