Kamide is in America, Moisil and Leitgeb are in Australia

It is not uncommon for a logic to be invented multiple times, hinting at its robustness. This trend is followed also by the expansion BD+ of Belnap-Dunn logic by Boolean negation. Ending up in the same logic, however, does not mean that the semantic interpretations are always the same as well. In particular, different interpretations can bring us to different logics, once the basic setting is moved from a classical one to an intuitionistic one. For BD+, two such paths seem to have been taken; one (BDi) by N. Kamide along the so-called American plan, and another (HYPE) by G. Moisil and H. Leitgeb along the so-called Australian plan. The aim of this paper is to better understand this divergence. This task is approached mainly by (i) formulating a semantics for first-order BD+ that provides an Australian view of the system; (ii) showing connections of the less explored (first-order) BDi with neighbouring systems, including an intermediate logic and variants of Nelson's logics.

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Publication Details

Journal
Electronic Proceedings in Theoretical Computer Science
Published
2024-12-28
DOI
https://doi.org/10.4204/eptcs.415.17
Citations
1
Primary Topic
Advanced Algebra and Logic
Type
article
Field-Weighted Citation Impact
0.36

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article

Kamide is in America, Moisil and Leitgeb are in Australia

Hitoshi Omori, Satoru Niki
1 citations
Electronic Proceedings in Theoretical Computer Science
Advanced Algebra and Logic
0.36
article

Kamide is in America, Moisil and Leitgeb are in Australia

Hitoshi Omori, Satoru Niki
article en
1 citations

Abstract

It is not uncommon for a logic to be invented multiple times, hinting at its robustness. This trend is followed also by the expansion BD+ of Belnap-Dunn logic by Boolean negation. Ending up in the same logic, however, does not mean that the semantic interpretations are always the same as well. In particular, different interpretations can bring us to different logics, once the basic setting is moved from a classical one to an intuitionistic one. For BD+, two such paths seem to have been taken; one (BDi) by N. Kamide along the so-called American plan, and another (HYPE) by G. Moisil and H. Leitgeb along the so-called Australian plan. The aim of this paper is to better understand this divergence. This task is approached mainly by (i) formulating a semantics for first-order BD+ that provides an Australian view of the system; (ii) showing connections of the less explored (first-order) BDi with neighbouring systems, including an intermediate logic and variants of Nelson's logics.

Electronic Proceedings in Theoretical Computer ScienceVol. 415
Tohoku University (JP), Ruhr University Bochum (DE)
European Commission
Zero hunger
Openalex Percentile: Top 32%
Advanced Algebra and Logic
0.36
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