author | paulson |
Wed, 09 Oct 1996 13:32:33 +0200 | |
changeset 2073 | fb0655539d05 |
permissions | -rw-r--r-- |
2073
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New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
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(* Title: 91/Modal/ex/S43thms |
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New unified treatment of sequent calculi by Sara Kalvala
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parents:
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ID: $Id$ |
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New unified treatment of sequent calculi by Sara Kalvala
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parents:
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Author: Martin Coen |
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New unified treatment of sequent calculi by Sara Kalvala
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parents:
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Copyright 1991 University of Cambridge |
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New unified treatment of sequent calculi by Sara Kalvala
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parents:
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*) |
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New unified treatment of sequent calculi by Sara Kalvala
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parents:
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|
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New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
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(* Theorems of system S43 *) |
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New unified treatment of sequent calculi by Sara Kalvala
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|
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New unified treatment of sequent calculi by Sara Kalvala
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try "|- <>[]P --> []<>P"; |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
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try "|- <>[]P --> [][]<>P"; |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- [](<>P | <>Q) --> []<>P | []<>Q"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- <>[]P & <>[]Q --> <>([]P & []Q)"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- []([]P --> []Q) | []([]Q --> []P)"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- [](<>P --> <>Q) | [](<>Q --> <>P)"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- []([]P --> Q) | []([]Q --> P)"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- [](P --> <>Q) | [](Q --> <>P)"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- [](P --> []Q-->R) | [](P | ([]R --> Q))"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- [](P | (Q --> <>C)) | [](P --> C --> <>Q)"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- []([]P | Q) & [](P | []Q) --> []P | []Q"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- <>P & <>Q --> <>(<>P & Q) | <>(P & <>Q)"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- [](P | Q) & []([]P | Q) & [](P | []Q) --> []P | []Q"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- <>P & <>Q --> <>(P & Q) | <>(<>P & Q) | <>(P & <>Q)"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- <>[]<>P <-> []<>P"; |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- []<>[]P <-> <>[]P"; |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
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New unified treatment of sequent calculi by Sara Kalvala
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parents:
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(* These are from Hailpern, LNCS 129 *) |
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|
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New unified treatment of sequent calculi by Sara Kalvala
paulson
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try "|- [](P & Q) <-> []P & []Q"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- <>(P | Q) <-> <>P | <>Q"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- <>(P --> Q) <-> []P --> <>Q"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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|
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- [](P --> Q) --> <>P --> <>Q"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- []P --> []<>P"; |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- <>[]P --> <>P"; |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- []<>[]P --> []<>P"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- <>[]P --> <>[]<>P"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- <>[]P --> []<>P"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- []<>[]P <-> <>[]P"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- <>[]<>P <-> []<>P"; |
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New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
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try "|- []P | []Q --> [](P | Q)"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
|
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try "|- <>(P & Q) --> <>P & <>Q"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
|
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try "|- [](P | Q) --> []P | <>Q"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
|
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try "|- <>P & []Q --> <>(P & Q)"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
|
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try "|- [](P | Q) --> <>P | []Q"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
|
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try "|- [](P | Q) --> []<>P | []<>Q"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
|
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try "|- <>[]P & <>[]Q --> <>(P & Q)"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
|
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try "|- <>[](P & Q) <-> <>[]P & <>[]Q"; |
fb0655539d05
New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff
changeset
|
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try "|- []<>(P | Q) <-> []<>P | []<>Q"; |