MAXIMALITY OF TWO-VALUED LOGICS

2025 · doi:10.22541/au.175192313.38553224/v1
preprint OA: closed
Full text JSON View at publisher

Abstract

As a key observation, we prove that any two-valued matrix with both distinguished and non-distinguished value is embedable into any submatrix of its direct power with both distinguished and non-distinguished values, in which case they define the same two-valued logic, and so this is defined by any model of it with both distinguished and non-distinguished values. As a consequence, we conclude that any fragment of the classical logic is [inferentially] maximal, whenever it has [no] theorems.
Full text 1,392 characters · extracted from oa-doi-fallback · 2 sections · click to expand

Abstract

As a key observation, we prove that any two-valued matrix with both distinguished and non-distinguished value is embedable into any submatrix of its direct power with both distinguished and non-distinguished values, in which case they define the same two-valued logic, and so this is defined by any model of it with both distinguished and non-distinguished values. As a consequence, we conclude that any fragment of the classical logic is [inferentially] maximal, whenever it has [no] theorems. Supplementary Material File (2-val-ext-au.pdf) - Download - 120.27 KB Information & Authors Information Version history Copyright This work is licensed under a Non Exclusive No Reuse License.

Keywords

Authors Metrics & Citations Metrics Article Usage 147views 92downloads Citations Download citation Alexej P. Pynko. MAXIMALITY OF TWO-VALUED LOGICS. Authorea. 07 July 2025. DOI: https://doi.org/10.22541/au.175192313.38553224/v1 DOI: https://doi.org/10.22541/au.175192313.38553224/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.

Text is read by the "Ask this paper" AI Q&A widget below. Extraction quality varies by source — PMC NXML preserves structure cleanly, OA-HTML may include some navigation residue, and OA-PDF can have broken hyphenation. The publisher copy (via DOI) is the canonical version.

My notes (saved in your browser only)

⚙ Ask this paper AI returns verbatim quotes from the full text · source: oa-doi-fallback ⓘ

Answers must be backed by verbatim quotes from this paper's full text. Hallucinated quotes are dropped automatically; if no verbatim passage answers the question, we say so. How this works

Citation neighborhood (no data yet)

We don't have any in-corpus citations linked to this paper yet. This is a recent paper (2025) — citers typically take a year or two to land, and the OpenAlex reference graph may still be filling in.

Source provenance

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