Abstract
The main purpose of the paper is to connect some kind of dialetheism to the use of complex truth values, with new definitions of basic truth-functional connectives that allow for p, \(\backslash \)not p to both be true. ‘True’ is interpreted as \(\left| p \right| = 1\), ‘False’ as \(\left| p \right| = 0\); other values are dispensed with. New definitions of basic truth-functional connectives then allow for “p and not p” to be true. A propositional logic is discussed with the set of connectives including negation, conjunction, disjunction, implication, concordance, discordance, complementary, and equivalence. The authors introduce truth values of propositions, which belong to a subset E, of an uncountable semi-ring F and valuations of propositions, which can be obtained from truth values with the help of a function \(V:E \rightarrow \left[ {0,1} \right] \) satisfying simple properties. Finally, a paraconsistent Boolean logic is introduced.
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Annex A. Truth Table of Principal Normal Binary Propositions
Annex A. Truth Table of Principal Normal Binary Propositions
We will represent in the following table a comparison between three logics: classical (CL), quasi-paraconsistent (QPL), and strong paraconsistent (SPL) (Table 6.4).
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Nescolarde-Selva, J., Usó-Doménech, J.L., Alonso-Stenberg, K. (2015). An Approach to Paraconsistent Multivalued Logic: Evaluation by Complex Truth Values. In: Beziau, JY., Chakraborty, M., Dutta, S. (eds) New Directions in Paraconsistent Logic. Springer Proceedings in Mathematics & Statistics, vol 152. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2719-9_6
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