## A New Introduction to Modal LogicThis entirely new work guides the reader through the most basic systems of modal propositional logic up to systems of modal predicate with identity, dealing with both technical developments and discussing philosophical applications.This long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic: An Introduction to Modal Logic and A Companion to Modal Logic.A New Introduction to Modal Logic is an entirely new work, completely re-written by the authors. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing the clarity of exposition and approachability that were essential features of their earlier works.The book takes readers from the most basic systems of modal propositional logic right up to systems of modal predicate with identity. It covers both technical developments such as completeness and incompleteness, and finite and infinite models, and their philosophical applications, especially in the area of modal predicate logic. |

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### Contents

1 THE BASIC NOTIONS | 3 |

2 THE SYSTEMS K T AND D | 19 |

3 THE SYSTEMS S4 S5 B TRIV AND VER | 43 |

4 TESTING FOR VALIDITY | 61 |

5 CONJUNCTIVE NORMAL FORM | 80 |

6 COMPLETENESS | 95 |

PART II NORMAL MODAL SYSTEMS | 107 |

7 CANONICAL MODELS | 109 |

PART III MODAL PREDICATE LOGIC | 201 |

13 THE LOWER PREDICATE CALCULUS | 203 |

14 THE COMPLETENESS OF MODAL LPC | 222 |

15 EXPANDING DOMAINS | 238 |

16 MODALITY AND EXISTENCE | 252 |

17 IDENTITY AND DESCRIPTIONS | 273 |

18 INTENSIONAL OBJECTS | 288 |

19 FURTHER ISSUES | 305 |

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### Common terms and phrases

assignment atomic wff axiom axiomatic Barcan Formula called canonical model Chapter characterized class of frames completeness proof conjunction Conjunctive Normal Form consider construction contains counterpart theory derived diagram disjunction equivalent express fact false falsifying finite model property finite number given Hughes and Cresswell inclusion requirement incomplete inconsistent individual variables induction infinitely intensional objects interpretation irreflexive K-valid Kripke lemma Lemmon Lewis maximal consistent sets MCNF means modal LPC modal operators modal predicate logic model based natural deduction natural numbers negation normal modal system Note obtained PC wff PC-valid player propositional logic propositional modal logic propositional variables quantifiers rectangle reflexive frame replaced result S-consistent S5-valid satisfies seating arrangement second-order logic semantics set of wff strict implication subset substitution-instance Suppose symbols tense logic transformation rules Triv true truth-functional truth-value valid wff value-assignment values w!Rw wff of modal wff of PC x-alternative