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Functional Programming with Names and Necessity Aleksandar Nanevski
 

Summary: Functional Programming with Names and Necessity
Aleksandar Nanevski
June 9, 2004
2
Contents
1 Constructive modal logic 11
1.1 Natural deduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.1.1 Judgments and propositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.1.2 Hypothetical judgments and implication . . . . . . . . . . . . . . . . . . . . . 13
1.1.3 Necessity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.1.4 Possibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.1.5 Summary of the system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.2 Modal -calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.2.1 Judgments and proof terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.2.2 Summary of the system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.3 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2 Partial modal logic 33
2.1 Natural deduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.1.1 Partial judgments and supports . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.1.2 Hypothetical partial judgments . . . . . . . . . . . . . . . . . . . . . . . . . . 35

  

Source: Andrews, Peter B. - Department of Mathematical Sciences, Carnegie Mellon University

 

Collections: Mathematics