@article{oai:nuis.repo.nii.ac.jp:00003298,
 author = {石井, 忠夫 and ISHII, Tadao},
 journal = {新潟国際情報大学経営情報学部紀要, Journal of Niigata University of International and Information Studies Faculty of Business and Informatics},
 month = {Apr},
 note = {In this paper, we will investigate how to introduce the complex number notation for the
truth value in logic. The truth value in a logic is used to interpret whether a given
proposition is valid or not. The proposition are notated by formulas, which are constructed
from the set of atomic propo-sitional variables V AR by the standard truth functional
connectives: ¬(negation), ∧ (conjunction), ∨ (disjunction) and → (material implication). So, to
interpret a formula, we need at first to define a truth assignment function v : V AR → { 0, 1 }.
Here { 0, 1 } is a set of truth values in 2-valued logic. As the valid formulas in 2-valued logic,
law of excluded middle, law of noncontradiction, law of double negation, De Morgan’s laws
and Lewis principles are well-known. On the other hand, there exists a situation in which
2-valued logic, i.e. law of excluded middle A∨¬A was not valid. To interpret such a
situation, there are proposed several kinds of non-standard logics, intuitionistic logic, De
Morgan logic and Ł- ukasiewicz 3-valued logic, for instance. The validity of formulas in nonstandard
logics, are defined on the order relation among the truth value set of many
numerical elements. Therefore, in order to exploit the strong analytical property of complex
number domain, we will propose the complex number notation, precisely v(B) = v(A)eiθ as
the interpretation of a pair sentence (A, B), instead of using natural number or real number
as the truth value notation in logic.},
 pages = {1--13},
 title = {論理における真理値の複素数表記},
 volume = {4},
 year = {2021},
 yomi = {イシイ, タダオ}
}