|
0
|
1 |
(* Title: 91/Modal/T
|
|
|
2 |
ID: $Id$
|
|
|
3 |
Author: Martin Coen
|
|
|
4 |
Copyright 1991 University of Cambridge
|
|
|
5 |
*)
|
|
|
6 |
|
|
|
7 |
T = Modal0 +
|
|
|
8 |
rules
|
|
|
9 |
(* Definition of the star operation using a set of Horn clauses *)
|
|
|
10 |
(* For system T: gamma * == {P | []P : gamma} *)
|
|
|
11 |
(* delta * == {P | <>P : delta} *)
|
|
|
12 |
|
|
|
13 |
lstar0 "|L>"
|
|
|
14 |
lstar1 "$G |L> $H ==> []P, $G |L> P, $H"
|
|
|
15 |
lstar2 "$G |L> $H ==> P, $G |L> $H"
|
|
|
16 |
rstar0 "|R>"
|
|
|
17 |
rstar1 "$G |R> $H ==> <>P, $G |R> P, $H"
|
|
|
18 |
rstar2 "$G |R> $H ==> P, $G |R> $H"
|
|
|
19 |
|
|
|
20 |
(* Rules for [] and <> *)
|
|
|
21 |
|
|
|
22 |
boxR
|
|
|
23 |
"[| $E |L> $E'; $F |R> $F'; $G |R> $G'; \
|
|
|
24 |
\ $E' |- $F', P, $G'|] ==> $E |- $F, []P, $G"
|
|
|
25 |
boxL "$E, P, $F |- $G ==> $E, []P, $F |- $G"
|
|
|
26 |
diaR "$E |- $F, P, $G ==> $E |- $F, <>P, $G"
|
|
|
27 |
diaL
|
|
|
28 |
"[| $E |L> $E'; $F |L> $F'; $G |R> $G'; \
|
|
|
29 |
\ $E', P, $F'|- $G'|] ==> $E, <>P, $F |- $G"
|
|
|
30 |
end
|