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# First Order Modal Logic - University of California, Berkeley - first order logic proof calculator

First-Order Modal Logic
Notes by R.J. Buehler
Based on First-Order Modal Logic by Fitting and Mendelsohn
January 5, 2015
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Contents
Preface v
1 Quantified Modal Logic 1
1.1 First-Order Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Necessity De Re and De Dicto . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Is Quantified Modal Logic Possible? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Quantifying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4.1 Constant Domain Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4.2 Varying Domain Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Existence Relativization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.6 Barcan and Converse Barcan Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
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