author | paulson |
Wed, 09 Oct 1996 13:32:33 +0200 | |
changeset 2073 | fb0655539d05 |
permissions | -rw-r--r-- |
2073
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(* Title: 91/Modal/ex/S4thms |
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ID: $Id$ |
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Author: Martin Coen |
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Copyright 1991 University of Cambridge |
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*) |
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(* Theorems of system S4 from Hughes and Cresswell, p.46 *) |
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try "|- []A --> A"; (* refexivity *) |
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try "|- []A --> [][]A"; (* transitivity *) |
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try "|- []A --> <>A"; (* seriality *) |
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try "|- <>[](<>A --> []<>A)"; |
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try "|- <>[](<>[]A --> []A)"; |
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try "|- []P <-> [][]P"; |
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try "|- <>P <-> <><>P"; |
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try "|- <>[]<>P --> <>P"; |
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try "|- []<>P <-> []<>[]<>P"; |
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try "|- <>[]P <-> <>[]<>[]P"; |
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(* Theorems for system S4 from Hughes and Cresswell, p.60 *) |
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try "|- []P | []Q <-> []([]P | []Q)"; |
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try "|- ((P>-<Q) --< R) --> ((P>-<Q) --< []R)"; |
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(* These are from Hailpern, LNCS 129 *) |
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try "|- [](P & Q) <-> []P & []Q"; |
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try "|- <>(P | Q) <-> <>P | <>Q"; |
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try "|- <>(P --> Q) <-> ([]P --> <>Q)"; |
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try "|- [](P --> Q) --> (<>P --> <>Q)"; |
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try "|- []P --> []<>P"; |
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try "|- <>[]P --> <>P"; |
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try "|- []P | []Q --> [](P | Q)"; |
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try "|- <>(P & Q) --> <>P & <>Q"; |
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try "|- [](P | Q) --> []P | <>Q"; |
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try "|- <>P & []Q --> <>(P & Q)"; |
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parents:
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try "|- [](P | Q) --> <>P | []Q"; |
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