src/Modal/ex/S4thms.ML
changeset 0 a5a9c433f639
child 1461 6bcb44e4d6e5
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/src/Modal/ex/S4thms.ML	Thu Sep 16 12:20:38 1993 +0200
     1.3 @@ -0,0 +1,40 @@
     1.4 +(*  Title: 	91/Modal/ex/S4thms
     1.5 +    ID:         $Id$
     1.6 +    Author: 	Martin Coen
     1.7 +    Copyright   1991  University of Cambridge
     1.8 +*)
     1.9 +
    1.10 +(* Theorems of system S4 from Hughes and Cresswell, p.46 *)
    1.11 +
    1.12 +try "|- []A --> A";             (* refexivity *)
    1.13 +try "|- []A --> [][]A";         (* transitivity *)
    1.14 +try "|- []A --> <>A";           (* seriality *)
    1.15 +try "|- <>[](<>A --> []<>A)";
    1.16 +try "|- <>[](<>[]A --> []A)";
    1.17 +try "|- []P <-> [][]P";
    1.18 +try "|- <>P <-> <><>P";
    1.19 +try "|- <>[]<>P --> <>P";
    1.20 +try "|- []<>P <-> []<>[]<>P";
    1.21 +try "|- <>[]P <-> <>[]<>[]P";
    1.22 +
    1.23 +(* Theorems for system S4 from Hughes and Cresswell, p.60 *)
    1.24 +
    1.25 +try "|- []P | []Q <-> []([]P | []Q)";
    1.26 +try "|- ((P>-<Q) --< R) --> ((P>-<Q) --< []R)";
    1.27 +
    1.28 +(* These are from Hailpern, LNCS 129 *)
    1.29 +
    1.30 +try "|- [](P & Q) <-> []P & []Q";
    1.31 +try "|- <>(P | Q) <-> <>P | <>Q";
    1.32 +try "|- <>(P --> Q) <-> ([]P --> <>Q)";
    1.33 +
    1.34 +try "|- [](P --> Q) --> (<>P --> <>Q)";
    1.35 +try "|- []P --> []<>P";
    1.36 +try "|- <>[]P --> <>P";
    1.37 +
    1.38 +try "|- []P | []Q --> [](P | Q)";
    1.39 +try "|- <>(P & Q) --> <>P & <>Q";
    1.40 +try "|- [](P | Q) --> []P | <>Q";
    1.41 +try "|- <>P & []Q --> <>(P & Q)";
    1.42 +try "|- [](P | Q) --> <>P | []Q";
    1.43 +