src/Sequents/T.thy

+(*  Title:      Modal/T
+    ID:         $Id$
+    Author:     Martin Coen
+    Copyright   1991  University of Cambridge
+*)
+
+T = Modal0 +
+rules
+(* Definition of the star operation using a set of Horn clauses *)
+(* For system T:  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  |-         $G    ==> $E, []P, $F |-          $G"
+  diaR     "$E         |- $F, P,  $G    ==> $E          |- $F, <>P, $G"
+  diaL
+   "[| $E |L> $E';  $F |L> $F';  $G |R> $G';  
+               $E', P, $F'|-         $G'|] ==> $E, <>P, $F |-          $G"
+end