--- a/src/Sequents/S4.thy Sun Sep 18 14:25:48 2005 +0200
+++ b/src/Sequents/S4.thy Sun Sep 18 15:20:08 2005 +0200
@@ -1,31 +1,37 @@
-(* Title: Modal/S4
+(* Title: Modal/S4.thy
ID: $Id$
Author: Martin Coen
Copyright 1991 University of Cambridge
*)
-S4 = Modal0 +
-rules
+theory S4
+imports Modal0
+begin
+
+axioms
(* Definition of the star operation using a set of Horn clauses *)
(* For system S4: gamma * == {[]P | []P : gamma} *)
(* delta * == {<>P | <>P : delta} *)
- lstar0 "|L>"
- lstar1 "$G |L> $H ==> []P, $G |L> []P, $H"
- lstar2 "$G |L> $H ==> P, $G |L> $H"
- rstar0 "|R>"
- rstar1 "$G |R> $H ==> <>P, $G |R> <>P, $H"
- rstar2 "$G |R> $H ==> P, $G |R> $H"
+ lstar0: "|L>"
+ lstar1: "$G |L> $H ==> []P, $G |L> []P, $H"
+ lstar2: "$G |L> $H ==> P, $G |L> $H"
+ rstar0: "|R>"
+ rstar1: "$G |R> $H ==> <>P, $G |R> <>P, $H"
+ rstar2: "$G |R> $H ==> P, $G |R> $H"
(* Rules for [] and <> *)
- boxR
- "[| $E |L> $E'; $F |R> $F'; $G |R> $G';
+ boxR:
+ "[| $E |L> $E'; $F |R> $F'; $G |R> $G';
$E' |- $F', P, $G'|] ==> $E |- $F, []P, $G"
- boxL "$E,P,$F,[]P |- $G ==> $E, []P, $F |- $G"
+ boxL: "$E,P,$F,[]P |- $G ==> $E, []P, $F |- $G"
- diaR "$E |- $F,P,$G,<>P ==> $E |- $F, <>P, $G"
- diaL
- "[| $E |L> $E'; $F |L> $F'; $G |R> $G';
+ diaR: "$E |- $F,P,$G,<>P ==> $E |- $F, <>P, $G"
+ diaL:
+ "[| $E |L> $E'; $F |L> $F'; $G |R> $G';
$E', P, $F' |- $G'|] ==> $E, <>P, $F |- $G"
+
+ML {* use_legacy_bindings (the_context ()) *}
+
end