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单词 verum
释义
verum

Logic
  • A propositional constant ⊤ sometimes added to a formal language as a representation of an arbitrary logical truth. Verum appears in fewer contexts than the other Church constant, i.e., its mate falsum (⊥), which plays an important role in the interpretation of intuitionistic logic. Verum appears in settings in which operations dual to intuitionistic notions are studied, e.g., while intuitionistic negation ¬φ is read as ‘φ implies ⊥’, a dual negation can be constructed by appealing to the connective of coimplication by the scheme: ‘⊤ coimplies φ’. In the context of relevant logic, verum is contrasted with a second truth constant, the Ackermann constant t. While in relevant logic, verum is considered the weakest of logical truths, t is treated as the conjunction of all logical truths—and hence, the strongest of them— although these two connectives converge in, e.g., intuitionistic and classical logic.


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