author | wenzelm |
Wed, 03 Feb 1999 17:28:02 +0100 | |
changeset 6208 | ea009b75b74e |
parent 2073 | fb0655539d05 |
child 17481 | 75166ebb619b |
permissions | -rw-r--r-- |
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(* Title: Modal/S4 |
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ID: $Id$ |
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Author: Martin Coen |
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Copyright 1991 University of Cambridge |
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*) |
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S4 = Modal0 + |
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rules |
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(* Definition of the star operation using a set of Horn clauses *) |
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(* For system S4: gamma * == {[]P | []P : gamma} *) |
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(* delta * == {<>P | <>P : delta} *) |
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lstar0 "|L>" |
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lstar1 "$G |L> $H ==> []P, $G |L> []P, $H" |
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lstar2 "$G |L> $H ==> P, $G |L> $H" |
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rstar0 "|R>" |
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rstar1 "$G |R> $H ==> <>P, $G |R> <>P, $H" |
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rstar2 "$G |R> $H ==> P, $G |R> $H" |
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(* Rules for [] and <> *) |
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boxR |
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"[| $E |L> $E'; $F |R> $F'; $G |R> $G'; |
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$E' |- $F', P, $G'|] ==> $E |- $F, []P, $G" |
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boxL "$E,P,$F,[]P |- $G ==> $E, []P, $F |- $G" |
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diaR "$E |- $F,P,$G,<>P ==> $E |- $F, <>P, $G" |
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diaL |
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"[| $E |L> $E'; $F |L> $F'; $G |R> $G'; |
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$E', P, $F' |- $G'|] ==> $E, <>P, $F |- $G" |
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end |