dorsal/arxiv
View SchemaAn exercise in "anhomomorphic logic"
| Authors | Rafael D. Sorkin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0703276 |
| URL | https://arxiv.org/abs/quant-ph/0703276 |
| DOI | 10.1088/1742-6596/67/1/012018 |
| Journal | J.Phys.Conf.Ser.67:012018,2007 |
Abstract
A classical logic exhibits a threefold inner structure comprising an algebra of propositions `A', a space of ``truth values'' `V', and a distinguished family of mappings `phi' from propositions to truth values. Classically A is a Boolean algebra, V=Z_2, and the admissible maps phi:A-->Z_2 are {\it homomorphisms}. If one admits a larger set of maps, one obtains an anhomomorphic logic that seems better suited to quantal reality (and the needs of quantum gravity). I explain these ideas and illustrate them with three simple examples.
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"abstract": "A classical logic exhibits a threefold inner structure comprising an algebra\nof propositions `A\u0027, a space of ``truth values\u0027\u0027 `V\u0027, and a distinguished\nfamily of mappings `phi\u0027 from propositions to truth values. Classically A is a\nBoolean algebra, V=Z_2, and the admissible maps phi:A--\u003eZ_2 are {\\it\nhomomorphisms}. If one admits a larger set of maps, one obtains an\nanhomomorphic logic that seems better suited to quantal reality (and the needs\nof quantum gravity). I explain these ideas and illustrate them with three\nsimple examples.",
"arxiv_id": "quant-ph/0703276",
"authors": [
"Rafael D. Sorkin"
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"quant-ph",
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"doi": "10.1088/1742-6596/67/1/012018",
"journal_ref": "J.Phys.Conf.Ser.67:012018,2007",
"title": "An exercise in \"anhomomorphic logic\"",
"url": "https://arxiv.org/abs/quant-ph/0703276"
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