Interpolation in Proof Theory
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910025701654528 |
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| author | van der Giessen, Iris Jalali, Raheleh Kuznets, Roman |
| author_facet | van der Giessen, Iris Jalali, Raheleh Kuznets, Roman |
| contents | This chapter provides a comprehensive overview of proof-theoretic methods for establishing interpolation properties across a range of logics, including classical, intuitionistic, modal, and substructural logics. Central to the discussion are two foundational techniques: Maehara's method for Craig interpolation and Pitts' method for uniform interpolation. The chapter demonstrates how these methods lead to results on the existence of well-behaved proof systems in the contemporary framework of universal proof theory and how they provide a road map for constructing interpolation proofs using modern proof formalisms. The emphasis of the chapter is on constructive, modular, and syntax-driven techniques that illuminate deeper connections between interpolation properties and proof systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16318 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Interpolation in Proof Theory van der Giessen, Iris Jalali, Raheleh Kuznets, Roman Logic in Computer Science This chapter provides a comprehensive overview of proof-theoretic methods for establishing interpolation properties across a range of logics, including classical, intuitionistic, modal, and substructural logics. Central to the discussion are two foundational techniques: Maehara's method for Craig interpolation and Pitts' method for uniform interpolation. The chapter demonstrates how these methods lead to results on the existence of well-behaved proof systems in the contemporary framework of universal proof theory and how they provide a road map for constructing interpolation proofs using modern proof formalisms. The emphasis of the chapter is on constructive, modular, and syntax-driven techniques that illuminate deeper connections between interpolation properties and proof systems. |
| title | Interpolation in Proof Theory |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2602.16318 |