Binary connectives functionally complete by themselves in S5 modal logic
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This paper answers affirmatively the open question of Massey [1] concerning the existence of binary connectives functionally complete by themselves in two-valued truth tabular logic, i.e. in the modal theory S5. Since {∼, ⊃, ◊} is a functionally complete set of connectives (Massey [1, § 4]), the following definitions show that the binary operator ф, the semantics of which is given below, is functionally complete by itself: It is left to the reader to verify, by means of complete sets of truth tables (see Massey [1, §§ 1 and 3]), that the foregoing definitions are correct.
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1969 ◽
Vol 34
(2)
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pp. 257-263
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2014 ◽
Vol 8
(1)
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pp. 178-191
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