Foundations of logic programming in hybrid-dynamic quantum logic
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917683742638080 |
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| author | Gaina, Daniel |
| author_facet | Gaina, Daniel |
| contents | The main contribution of the present paper is the introduction of a simple yet expressive hybrid-dynamic logic for describing quantum programs. This version of quantum logic can express quantum measurements and unitary evolutions of states in a natural way based on concepts advanced in (hybrid and dynamic) modal logics. We then study Horn clauses in the hybrid-dynamic quantum logic proposed, and develop a series of results that lead to an initial semantics theorem for sets of clauses that are satisfiable. This shows that a significant fragment of hybrid-dynamic quantum logic has good computational properties, and can serve as a basis for defining executable languages for specifying quantum programs. We set the foundations of logic programming in this fragment by proving a variant of Herbrand's theorem, which reduces the semantic entailment of a logic-programming query by a program to the search of a suitable substitution. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_02085 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Foundations of logic programming in hybrid-dynamic quantum logic Gaina, Daniel Logic in Computer Science The main contribution of the present paper is the introduction of a simple yet expressive hybrid-dynamic logic for describing quantum programs. This version of quantum logic can express quantum measurements and unitary evolutions of states in a natural way based on concepts advanced in (hybrid and dynamic) modal logics. We then study Horn clauses in the hybrid-dynamic quantum logic proposed, and develop a series of results that lead to an initial semantics theorem for sets of clauses that are satisfiable. This shows that a significant fragment of hybrid-dynamic quantum logic has good computational properties, and can serve as a basis for defining executable languages for specifying quantum programs. We set the foundations of logic programming in this fragment by proving a variant of Herbrand's theorem, which reduces the semantic entailment of a logic-programming query by a program to the search of a suitable substitution. |
| title | Foundations of logic programming in hybrid-dynamic quantum logic |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2406.02085 |