The B4-valued propositional logic with unary logical connectives ∼1 / ∼2

Wei LI, Yuefei SUI

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PDF(264 KB)
Front. Comput. Sci. ›› 2017, Vol. 11 ›› Issue (5) : 887-894. DOI: 10.1007/s11704-016-5299-7
RESEARCH ARTICLE

The B4-valued propositional logic with unary logical connectives ∼1 / ∼2

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Abstract

A B4-valued propositional logic will be proposed in this paper which there are three unary logical connectives ∼1, ∼2, ¬ and two binary logical connectives ∧, ∨, and a Gentzen-typed deduction system will be given so that the system is sound and complete with B4-valued semantics, where B4 is a Boolean algebra.

Keywords

the Belnap logic / modality / the soundness / the completeness

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Wei LI, Yuefei SUI. The B4-valued propositional logic with unary logical connectives ∼1 / ∼2 /¬. Front. Comput. Sci., 2017, 11(5): 887‒894 https://doi.org/10.1007/s11704-016-5299-7

References

[1]
BelnapN. How a computer should think. In: Ryle G, ed. Contemporary Aspects of Philosophy. Stocksfield: Oriel Press, 1977, 30–56
[2]
BelnapN. A useful four-valued logic. In: Dunn J M, Epstein G, eds. Modern Uses of Multiple-valued Logic. Dordrecht: D. Reidel, 1977, 8–37
CrossRef Google scholar
[3]
BergstraJ A, PonseA. Kleene’s three-valued logic and process algebra. Information Processing Letters, 1998, 67(2): 95–103
CrossRef Google scholar
[4]
BergstraJ A, PonseA. Process algebra with four-valued logic. Journal of Applied Non-Classical Logics, 2000, 10(1): 27–53
CrossRef Google scholar
[5]
RodriguesO, RussoA. A translation method for Belnap logic. Imperial College RR DoC98/7, 1998
[6]
PonseA, van der Zwaag M B. A generalization of ACP using Belnap’s logic. Electronic Notes in Theoretical Computer Science, 2006, 162: 287–293
CrossRef Google scholar
[7]
LiW. Mathematical Logic, Foundations for Information Science (Progress in Computer Science and Applied Logic). Berlin: Birkhäuser, 2010
[8]
PynkoA P. On Priest’s logic of paradox. Journal of Applied Non- Classical Logics, 1995, 5(2): 219–225
[9]
PynkoA P. Characterizing Belnap’s logic via De Morgan’s laws. Mathematical Logic Quarterly, 1995, 41(4): 442–454
CrossRef Google scholar
[10]
PynkoA P.Implicational classes of DeMorgan lattices. Discrete mathematics, 1999, 205(1): 171–181
CrossRef Google scholar
[11]
FontJ M. Belnap’s four-valued logic and De Morgan lattices. Logic Journal of the I.G.P.L., 1997, 5(3): 413–440
CrossRef Google scholar
[12]
GottwaldS. A Treatise on Many-Valued Logics (Studies in Logic and Computation). Baldock: Research Studies Press Ltd, 2001
[13]
UrquhartA. Basic many-valued logic. In: Gabbay D, Guenthner F, eds. Handbook of Philosophical Logic, Vol. 2. 2nd ed. Dordrecht: Kluwer, 2001, 249–295
CrossRef Google scholar

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