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src/Sequents/T.thy

author | paulson |

Wed, 09 Oct 1996 13:32:33 +0200 | |

changeset 2073 | fb0655539d05 |

child 17481 | 75166ebb619b |

permissions | -rw-r--r-- |

New unified treatment of sequent calculi by Sara Kalvala
combines the old LK and Modal with the new ILL (Int. Linear Logic)

(* 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