On semantics of first-order justification logic with binding modalities
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914189208977408 |
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| author | Yavorskaya, Tatiana Popova, Elena |
| author_facet | Yavorskaya, Tatiana Popova, Elena |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_07994 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On semantics of first-order justification logic with binding modalities Yavorskaya, Tatiana Popova, Elena Logic in Computer Science Logic 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. |
| title | On semantics of first-order justification logic with binding modalities |
| topic | Logic in Computer Science Logic |
| url | https://arxiv.org/abs/2512.07994 |