Bacchus: Created page with "'''Minimal logic''', or '''minimal calculus''', is the symbolic logic system originally developed by Ingebrigt Johansson. If we interpret Classical logic as a system of Natural deduction removing the rule of Double negative elimination results in Minimal logic. Then if we interpret Minimal logic as an Axiomatic system we can conservatively extend it with different Axioms resulting in a variety of Intermediate logics lying between Minimal logic and Classical..."

2023-01-27T02:17:03Z

Created page with "'''Minimal logic''', or '''minimal calculus''', is the symbolic logic system originally developed by Ingebrigt Johansson. If we interpret Classical logic as a system of Natural deduction removing the rule of Double negative elimination results in Minimal logic. Then if we interpret Minimal logic as an Axiomatic system we can conservatively extend it with different Axioms resulting in a variety of Intermediate logics lying between Minimal logic and Classical..."

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'''Minimal logic''', or '''minimal calculus''', is the [[symbolic logic]] system originally developed by Ingebrigt Johansson.

If we interpret [[Classical logic]] as a system of Natural deduction removing the rule of Double negative elimination results in Minimal logic. Then if we interpret Minimal logic as an Axiomatic system we can conservatively extend it with different Axioms resulting in a variety of [[Intermediate logics]] lying between Minimal logic and Classical logic. For example, adding the Ex falso quodlibet (EFQ, from a contradiction anything follows) results in the well-known [[Intuitionistic logic]]. These Intermediate logics all fall on a lattice with Classical logic at the "join" and Minimal logic at the "meet".<ref>Segerberg, Krister, 1968, "Propositional logics related to Heyting's and Johansson's", ''Theoria'' '''34''', 26-61.</ref><ref>Johansson, Ingebrigt, 1936, "[http://www.numdam.org/numdam-bin/item?id=CM_1937__4__119_0 Der Minimalkalkul, ein reduzierter intuitionistischer Formalismus]." ''Compositio Mathematica'' '''4''', 119-136.</ref>

==References==
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[[Category:Definitions]]
[[Category:Philosophy]]

Minimal logic - Revision history