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LOGCOM

1998

1998

Sound and complete modal propositional logic C is presented, in which 2P has the interpretation “ P is true in all states”. The interpretation is already known as the Carnapian extension of S5. A new axiomatization for C provides two insights. First, introducing an inference rule textual substitution allows seamless integration of the propositional and modal parts of the logic, giving a more practical system for writing formal proofs. Second, the two following approaches to axiomatizing a logic are shown to be not equivalent: (i) give axiom schemes that denote an inﬁnite number of axioms and (ii) write a ﬁnite number of axioms in terms of propositional variables and introduce a substitution inference rule.

Related Content

Added |
22 Dec 2010 |

Updated |
22 Dec 2010 |

Type |
Journal |

Year |
1998 |

Where |
LOGCOM |

Authors |
David Gries, Fred B. Schneider |

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