src/Sequents/S4.thy
author wenzelm
Tue, 13 Jun 2006 23:41:39 +0200
changeset 19876 11d447d5d68c
parent 17481 75166ebb619b
child 21426 87ac12bed1ab
permissions -rw-r--r--
tuned;
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
17481
75166ebb619b converted to Isar theory format;
wenzelm
parents: 2073
diff changeset
     1
(*  Title:      Modal/S4.thy
2073
fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff changeset
     2
    ID:         $Id$
fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff changeset
     3
    Author:     Martin Coen
fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff changeset
     4
    Copyright   1991  University of Cambridge
fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff changeset
     5
*)
fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff changeset
     6
17481
75166ebb619b converted to Isar theory format;
wenzelm
parents: 2073
diff changeset
     7
theory S4
75166ebb619b converted to Isar theory format;
wenzelm
parents: 2073
diff changeset
     8
imports Modal0
75166ebb619b converted to Isar theory format;
wenzelm
parents: 2073
diff changeset
     9
begin
75166ebb619b converted to Isar theory format;
wenzelm
parents: 2073
diff changeset
    10
75166ebb619b converted to Isar theory format;
wenzelm
parents: 2073
diff changeset
    11
axioms
2073
fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff changeset
    12
(* Definition of the star operation using a set of Horn clauses *)
fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff changeset
    13
(* For system S4:  gamma * == {[]P | []P : gamma}               *)
fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff changeset
    14
(*                 delta * == {<>P | <>P : delta}               *)
fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff changeset
    15
17481
75166ebb619b converted to Isar theory format;
wenzelm
parents: 2073
diff changeset
    16
  lstar0:         "|L>"
75166ebb619b converted to Isar theory format;
wenzelm
parents: 2073
diff changeset
    17
  lstar1:         "$G |L> $H ==> []P, $G |L> []P, $H"
75166ebb619b converted to Isar theory format;
wenzelm
parents: 2073
diff changeset
    18
  lstar2:         "$G |L> $H ==>   P, $G |L>      $H"
75166ebb619b converted to Isar theory format;
wenzelm
parents: 2073
diff changeset
    19
  rstar0:         "|R>"
75166ebb619b converted to Isar theory format;
wenzelm
parents: 2073
diff changeset
    20
  rstar1:         "$G |R> $H ==> <>P, $G |R> <>P, $H"
75166ebb619b converted to Isar theory format;
wenzelm
parents: 2073
diff changeset
    21
  rstar2:         "$G |R> $H ==>   P, $G |R>      $H"
2073
fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff changeset
    22
fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff changeset
    23
(* Rules for [] and <> *)
fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff changeset
    24
17481
75166ebb619b converted to Isar theory format;
wenzelm
parents: 2073
diff changeset
    25
  boxR:
75166ebb619b converted to Isar theory format;
wenzelm
parents: 2073
diff changeset
    26
   "[| $E |L> $E';  $F |R> $F';  $G |R> $G';
2073
fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff changeset
    27
           $E'         |- $F', P, $G'|] ==> $E          |- $F, []P, $G"
17481
75166ebb619b converted to Isar theory format;
wenzelm
parents: 2073
diff changeset
    28
  boxL:     "$E,P,$F,[]P |-         $G    ==> $E, []P, $F |-          $G"
2073
fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff changeset
    29
17481
75166ebb619b converted to Isar theory format;
wenzelm
parents: 2073
diff changeset
    30
  diaR:     "$E          |- $F,P,$G,<>P   ==> $E          |- $F, <>P, $G"
75166ebb619b converted to Isar theory format;
wenzelm
parents: 2073
diff changeset
    31
  diaL:
75166ebb619b converted to Isar theory format;
wenzelm
parents: 2073
diff changeset
    32
   "[| $E |L> $E';  $F |L> $F';  $G |R> $G';
2073
fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff changeset
    33
           $E', P, $F' |-         $G'|] ==> $E, <>P, $F |- $G"
17481
75166ebb619b converted to Isar theory format;
wenzelm
parents: 2073
diff changeset
    34
75166ebb619b converted to Isar theory format;
wenzelm
parents: 2073
diff changeset
    35
ML {* use_legacy_bindings (the_context ()) *}
75166ebb619b converted to Isar theory format;
wenzelm
parents: 2073
diff changeset
    36
2073
fb0655539d05 New unified treatment of sequent calculi by Sara Kalvala
paulson
parents:
diff changeset
    37
end