Paraconsistent Constructive Modal Logic
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909751675191296 |
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| author | Gao, Han Kozhemiachenko, Daniil Olivetti, Nicola |
| author_facet | Gao, Han Kozhemiachenko, Daniil Olivetti, Nicola |
| contents | We present a family of paraconsistent counterparts of the constructive modal logic CK. These logics aim to formalise reasoning about contradictory but non-trivial propositional attitudes like beliefs or obligations. We define their Kripke-style semantics based on intuitionistic frames with two valuations which provide independent support for truth and falsity; they are connected by strong negation as defined in Nelson's logic. A family of systems is obtained depending on whether both modal operators are defined using the same or by different accessibility relations for their positive and negative support. We propose Hilbert-style axiomatisations for all logics determined by this semantic framework. We also propose a~family of modular cut-free sequent calculi that we use to establish decidability. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_17758 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Paraconsistent Constructive Modal Logic Gao, Han Kozhemiachenko, Daniil Olivetti, Nicola Logic in Computer Science We present a family of paraconsistent counterparts of the constructive modal logic CK. These logics aim to formalise reasoning about contradictory but non-trivial propositional attitudes like beliefs or obligations. We define their Kripke-style semantics based on intuitionistic frames with two valuations which provide independent support for truth and falsity; they are connected by strong negation as defined in Nelson's logic. A family of systems is obtained depending on whether both modal operators are defined using the same or by different accessibility relations for their positive and negative support. We propose Hilbert-style axiomatisations for all logics determined by this semantic framework. We also propose a~family of modular cut-free sequent calculi that we use to establish decidability. |
| title | Paraconsistent Constructive Modal Logic |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2508.17758 |