Proofs as Execution Trees for the π-Calculus
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909457486708736 |
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| author | Acclavio, Matteo Manara, Giulia |
| author_facet | Acclavio, Matteo Manara, Giulia |
| contents | In this paper, we establish the foundations of a novel logical framework for the π-calculus, based on the deduction-as-computation paradigm. Following the standard proof-theoretic interpretation of logic programming, we represent processes as formulas, and we interpret proofs as computations.
For this purpose, we define a cut-free sequent calculus for an extension of first-order multiplicative and additive linear logic. This extension includes a non-commutative and non-associative connective to faithfully model the prefix operator, and nominal quantifiers to represent name restriction. Finally, we design proof nets providing canonical representatives of derivations up to local rule permutations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08847 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Proofs as Execution Trees for the π-Calculus Acclavio, Matteo Manara, Giulia Logic in Computer Science In this paper, we establish the foundations of a novel logical framework for the π-calculus, based on the deduction-as-computation paradigm. Following the standard proof-theoretic interpretation of logic programming, we represent processes as formulas, and we interpret proofs as computations. For this purpose, we define a cut-free sequent calculus for an extension of first-order multiplicative and additive linear logic. This extension includes a non-commutative and non-associative connective to faithfully model the prefix operator, and nominal quantifiers to represent name restriction. Finally, we design proof nets providing canonical representatives of derivations up to local rule permutations. |
| title | Proofs as Execution Trees for the π-Calculus |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2411.08847 |