INFINITELY MANY EXTENSIONS OF FOUR-VALUED LOGICS

2026 · doi:10.22541/au.177187992.23822007/v1
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Abstract

Here, we we prove that there is a strictly increasing countable chain of finitary relatively finitely-axiomatizable extensions of ({the} truth-singular {version/extension of }) [ {the} bounded {expansion of }] first-degree entailments - (TS)[B]FDE, for short - /(relatively axiomatized by the Modus Ponens rule for material implication), in which case the chain does not contain its join, and so this, being a finitary extension of (TS)[B]FDE, is not {relatively} finitely-axiomatizable. ([As a consequence, applying one of our previous works, we immediately get a strictly decreasing chain of finitely-axiomatizable quasi-varieties of bounded De Morgan lattices with non-finitely-axiomatizable intersection.])
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Abstract

Here, we we prove that there is a strictly increasing countable chain of finitary relatively finitely-axiomatizable extensions of ({the} truth-singular {version/extension of }) [ {the} bounded {expansion of }] first-degree entailments - (TS)[B]FDE, for short - /(relatively axiomatized by the Modus Ponens rule for material implication), in which case the chain does not contain its join, and so this, being a finitary extension of (TS)[B]FDE, is not {relatively} finitely-axiomatizable. ([As a consequence, applying one of our previous works, we immediately get a strictly decreasing chain of finitely-axiomatizable quasi-varieties of bounded De Morgan lattices with non-finitely-axiomatizable intersection.]) Supplementary Material File (fde-ext-au.pdf) - Download - 184.22 KB Information & Authors Information Version history Copyright This work is licensed under a Non Exclusive No Reuse License.

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Authors Metrics & Citations Metrics Article Usage 74views 59downloads Citations Download citation Alexej P. Pynko. INFINITELY MANY EXTENSIONS OF FOUR-VALUED LOGICS. Authorea. 23 February 2026. DOI: https://doi.org/10.22541/au.177187992.23822007/v1 DOI: https://doi.org/10.22541/au.177187992.23822007/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. For more information or tips please see 'Downloading to a citation manager' in the Help menu.

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last seen: 2026-05-20T01:45:00.602351+00:00