Justification Logic for Intuitionistic Modal Logic (Extended Technical Report)
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916840606793728 |
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| author | Marin, Sonia Padhiar, Paaras |
| author_facet | Marin, Sonia Padhiar, Paaras |
| contents | Justification logics are an explication of modal logic; boxes are replaced with proof terms formally through realisation theorems. This can be achieved syntactically using a cut-free proof system e.g. using sequent, hypersequent or nested sequent calculi. In constructive modal logic, boxes and diamonds are decoupled and not De Morgan dual. Kuznets, Marin and Straßburger provide a justification counterpart to constructive modal logic CK and some extensions by making diamonds explicit by introducing new terms called satisfiers. We continue the line of work to provide a justification counterpart to Fischer Servi's intuitionistic modal logic IK and its extensions with the t and 4 axioms. We: extend the syntax of proof terms to accommodate the additional axioms of intuitionistic modal logic; provide an axiomatisation of these justification logics; provide a syntactic realisation procedure using a cut-free nested sequent system for intuitionistic modal logic introduced by Straßburger. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09427 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Justification Logic for Intuitionistic Modal Logic (Extended Technical Report) Marin, Sonia Padhiar, Paaras Logic in Computer Science Logic Justification logics are an explication of modal logic; boxes are replaced with proof terms formally through realisation theorems. This can be achieved syntactically using a cut-free proof system e.g. using sequent, hypersequent or nested sequent calculi. In constructive modal logic, boxes and diamonds are decoupled and not De Morgan dual. Kuznets, Marin and Straßburger provide a justification counterpart to constructive modal logic CK and some extensions by making diamonds explicit by introducing new terms called satisfiers. We continue the line of work to provide a justification counterpart to Fischer Servi's intuitionistic modal logic IK and its extensions with the t and 4 axioms. We: extend the syntax of proof terms to accommodate the additional axioms of intuitionistic modal logic; provide an axiomatisation of these justification logics; provide a syntactic realisation procedure using a cut-free nested sequent system for intuitionistic modal logic introduced by Straßburger. |
| title | Justification Logic for Intuitionistic Modal Logic (Extended Technical Report) |
| topic | Logic in Computer Science Logic |
| url | https://arxiv.org/abs/2507.09427 |