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On three-valued presentations of classical logic
- Publication Year :
- 2023
-
Abstract
- Given a three-valued definition of validity, which choice of three-valued truth tables for the connectives can ensure that the resulting logic coincides exactly with classical logic? We give an answer to this question for the five monotonic consequence relations $st$, $ss$, $tt$, $ss\cap tt$, and $ts$, when the connectives are negation, conjunction, and disjunction. For $ts$ and $ss\cap tt$ the answer is trivial (no scheme works), and for $ss$ and $tt$ it is straightforward (they are the collapsible schemes, in which the middle value acts like one of the classical values). For $st$, the schemes in question are the Boolean normal schemes that are either monotonic or collapsible.<br />Comment: Review of Symbolic Logic
- Subjects :
- Mathematics - Logic
03B05, 03B47, 03B50
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2312.16035
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1017/S1755020323000114