A Real-Analytic Approach to Differential-Algebraic Dynamic Logic
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913858275246080 |
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| author | Hellwig, Jonathan Platzer, André |
| author_facet | Hellwig, Jonathan Platzer, André |
| contents | This paper introduces a proof calculus for real-analytic differential-algebraic dynamic logic, enabling correct transformations of differential-algebraic equations. Applications include index reductions from differential-algebraic equations to ordinary differential equations. The calculus ensures compatibility between differential-algebraic equation proof principles and (differential-form) differential dynamic logic for hybrid systems. One key contribution is ghost switching which establishes precise conditions that decompose multi-modal systems into hybrid systems, thereby correctly hybridizing sophisticated differential-algebraic dynamics. The calculus is demonstrated in a proof of equivalence for a Euclidean pendulum to index reduced form. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_19323 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Real-Analytic Approach to Differential-Algebraic Dynamic Logic Hellwig, Jonathan Platzer, André Logic in Computer Science F.3.1; F.4.1 This paper introduces a proof calculus for real-analytic differential-algebraic dynamic logic, enabling correct transformations of differential-algebraic equations. Applications include index reductions from differential-algebraic equations to ordinary differential equations. The calculus ensures compatibility between differential-algebraic equation proof principles and (differential-form) differential dynamic logic for hybrid systems. One key contribution is ghost switching which establishes precise conditions that decompose multi-modal systems into hybrid systems, thereby correctly hybridizing sophisticated differential-algebraic dynamics. The calculus is demonstrated in a proof of equivalence for a Euclidean pendulum to index reduced form. |
| title | A Real-Analytic Approach to Differential-Algebraic Dynamic Logic |
| topic | Logic in Computer Science F.3.1; F.4.1 |
| url | https://arxiv.org/abs/2505.19323 |