EXTENSIONS OF KLEENE'S THREE-VALUED LOGIC

EXTENSIONS OF KLEENE'S THREE-VALUED LOGIC | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 8 January 2026 V1 Latest version Share on EXTENSIONS OF KLEENE'S THREE-VALUED LOGIC Author : Alexej P. Pynko 0000-0002-3478-9850 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.176790888.88784351/v1 222 views 89 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract Here, we prove that proper extensions of Kleene's three-valued logic K3 form a four-element diamond lattice, the classical logic and the consistent but inferentially inconsistent one, defined by any matrix without distinguished values, being incomparable proper extensions of K3. As a by-product of auxiliary tools elaborated for solving the main problem, we also show that K3 is minimally three-valued and has a unique classical extension, while any three-valued matrices defining K3 are isomorphic, whereas any three-valued expansion of K3 is defined by an expansion of any three-valued matrix defining K3. Supplementary Material File (k3-ext-au.pdf) Download 143.28 KB Information & Authors Information Version history V1 Version 1 08 January 2026 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords extension lattice logic matrix model Authors Affiliations Alexej P. Pynko 0000-0002-3478-9850 [email protected] Department of Digital Automata Theory (100), V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine View all articles by this author Metrics & Citations Metrics Article Usage 222 views 89 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Alexej P. Pynko. EXTENSIONS OF KLEENE'S THREE-VALUED LOGIC. Authorea . 08 January 2026. DOI: https://doi.org/10.22541/au.176790888.88784351/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. 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