src/Modal/t.thy
 author clasohm Thu, 16 Sep 1993 12:20:38 +0200 changeset 0 a5a9c433f639 permissions -rw-r--r--
Initial revision
```
(*  Title: 	91/Modal/T
ID:         \$Id\$
Author: 	Martin Coen
*)

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
```