Goedel Logics: On the Elimination of The Absoluteness Operator
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911652594581504 |
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| author | Baaz, Matthias Gamsakhurdia, Mariami |
| author_facet | Baaz, Matthias Gamsakhurdia, Mariami |
| contents | We investigate the eliminability of the absoluteness operator Delta in Goedel logics. While Delta is not definable from the standard connectives and disrupts important proof-theoretic properties, we show that it becomes eliminable at the propositional level under a restricted semantics in which all propositional atoms (except the truth constant 'True') are interpreted strictly below 1. Under this semantics, every formula containing Delta is equivalent to a disjunction of chain formulas, yielding a Delta-free normal form (standard and restricted semantics coincide w.r.t. valid formulas without Delta). We further analyze the situation in the first-order setting, where Delta-elimination fails in general due to recursion-theoretic and topological constraints, but can be recovered under witnessed semantics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05016 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Goedel Logics: On the Elimination of The Absoluteness Operator Baaz, Matthias Gamsakhurdia, Mariami Logic in Computer Science We investigate the eliminability of the absoluteness operator Delta in Goedel logics. While Delta is not definable from the standard connectives and disrupts important proof-theoretic properties, we show that it becomes eliminable at the propositional level under a restricted semantics in which all propositional atoms (except the truth constant 'True') are interpreted strictly below 1. Under this semantics, every formula containing Delta is equivalent to a disjunction of chain formulas, yielding a Delta-free normal form (standard and restricted semantics coincide w.r.t. valid formulas without Delta). We further analyze the situation in the first-order setting, where Delta-elimination fails in general due to recursion-theoretic and topological constraints, but can be recovered under witnessed semantics. |
| title | Goedel Logics: On the Elimination of The Absoluteness Operator |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2605.05016 |