On three-valued presentations of classical logic
| Autor: | da Ré, Bruno, Szmuc, Damian, Chemla, Emmanuel, Égré, Paul |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1017/S1755020323000114 |
| Popis: | 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. Comment: Review of Symbolic Logic |
| Databáze: | arXiv |
| Externí odkaz: |
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