Isomorphism Theorems between Models of Mixed Choice (Revised)
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913914557562880 |
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| author | Goubault-Larrecq, Jean |
| author_facet | Goubault-Larrecq, Jean |
| contents | We relate the so-called powercone models of mixed non-deterministic and probabilistic choice proposed by Tix, Keimel, Plotkin, Mislove, Ouaknine, Worrell, Morgan, and McIver, to our own models of previsions. Under suitable topological assumptions, we show that they are isomorphic. We rely on Keimel's cone-theoretic variants of the classical Hahn-Banach separation theorems, using functional analytic methods, and on the Schröder-Simpson Theorem. Lemma 3.4 in the original 2017 version, published at MSCS, had a wrong proof, and we prove a repaired, albeit slightly less general version here. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_13500 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Isomorphism Theorems between Models of Mixed Choice (Revised) Goubault-Larrecq, Jean Logic in Computer Science Functional Analysis Probability 46E27, 60B05, 68Q87, 28C05, 46T99 F.3.2 We relate the so-called powercone models of mixed non-deterministic and probabilistic choice proposed by Tix, Keimel, Plotkin, Mislove, Ouaknine, Worrell, Morgan, and McIver, to our own models of previsions. Under suitable topological assumptions, we show that they are isomorphic. We rely on Keimel's cone-theoretic variants of the classical Hahn-Banach separation theorems, using functional analytic methods, and on the Schröder-Simpson Theorem. Lemma 3.4 in the original 2017 version, published at MSCS, had a wrong proof, and we prove a repaired, albeit slightly less general version here. |
| title | Isomorphism Theorems between Models of Mixed Choice (Revised) |
| topic | Logic in Computer Science Functional Analysis Probability 46E27, 60B05, 68Q87, 28C05, 46T99 F.3.2 |
| url | https://arxiv.org/abs/2411.13500 |