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The hilbert type axiomatization of some three‐valued propositional logic
Author(s) -
Zbrzezny Andrzej
Publication year - 1990
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19900360506
Subject(s) - mathematics , propositional calculus , citation , type (biology) , algebra over a field , linguistics , calculus (dental) , mathematics education , discrete mathematics , computer science , pure mathematics , library science , philosophy , medicine , ecology , dentistry , biology
Let L = be the propositional language determined by an infinite denumerable set of propositional variables and by the following propositional connectives: ∧,∨, and ¬. The elements of the set L will be denoted by letters A,B, C, D. Capital Greek letters Γ and ∆ will be used for denoting sequents i.e. finite (possibly empty) sets of formulae. The notation Γ, A1, . . . , An is an abbreviation of Γ ∪ {A1, . . . , An}. The notation Γ, ∆ is treated analogously. Now let us consider two sets: K = {0, 1, 2}, and K∗ = {1, 2}. We define the operators ∧,∨, and ¬ on the set K by means of the following tables: