src/Sequents/S4.thy
author wenzelm
Sun Sep 18 15:20:08 2005 +0200 (2005-09-18)
changeset 17481 75166ebb619b
parent 2073 fb0655539d05
child 21426 87ac12bed1ab
permissions -rw-r--r--
converted to Isar theory format;
     1 (*  Title:      Modal/S4.thy
     2     ID:         $Id$
     3     Author:     Martin Coen
     4     Copyright   1991  University of Cambridge
     5 *)
     6 
     7 theory S4
     8 imports Modal0
     9 begin
    10 
    11 axioms
    12 (* Definition of the star operation using a set of Horn clauses *)
    13 (* For system S4:  gamma * == {[]P | []P : gamma}               *)
    14 (*                 delta * == {<>P | <>P : delta}               *)
    15 
    16   lstar0:         "|L>"
    17   lstar1:         "$G |L> $H ==> []P, $G |L> []P, $H"
    18   lstar2:         "$G |L> $H ==>   P, $G |L>      $H"
    19   rstar0:         "|R>"
    20   rstar1:         "$G |R> $H ==> <>P, $G |R> <>P, $H"
    21   rstar2:         "$G |R> $H ==>   P, $G |R>      $H"
    22 
    23 (* Rules for [] and <> *)
    24 
    25   boxR:
    26    "[| $E |L> $E';  $F |R> $F';  $G |R> $G';
    27            $E'         |- $F', P, $G'|] ==> $E          |- $F, []P, $G"
    28   boxL:     "$E,P,$F,[]P |-         $G    ==> $E, []P, $F |-          $G"
    29 
    30   diaR:     "$E          |- $F,P,$G,<>P   ==> $E          |- $F, <>P, $G"
    31   diaL:
    32    "[| $E |L> $E';  $F |L> $F';  $G |R> $G';
    33            $E', P, $F' |-         $G'|] ==> $E, <>P, $F |- $G"
    34 
    35 ML {* use_legacy_bindings (the_context ()) *}
    36 
    37 end