--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Sequents/S4.thy Wed Oct 09 13:32:33 1996 +0200
@@ -0,0 +1,31 @@
+(* Title: Modal/S4
+ ID: $Id$
+ Author: Martin Coen
+ Copyright 1991 University of Cambridge
+*)
+
+S4 = Modal0 +
+rules
+(* 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"
+
+(* Rules for [] and <> *)
+
+ 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 |- $G"
+
+ diaR "$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"
+end