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I edited after a comment by Andreas Blass
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Frode Alfson Bjørdal
Frode Alfson Bjørdal
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In a base for propositional logic using the Polish connective $\uparrow$ for not both, J. Nicod isolated one axiom as sufficient:

$\uparrow\uparrow p\uparrow q r\uparrow\uparrow t\uparrow tt\uparrow\uparrow s q\uparrow\uparrow p s\uparrow ps$

J. Nicod used the somewhat odd inference rule $r$ if $\uparrow p\uparrow q r$ and $p$. May we use $\uparrow p\uparrow p r$$\uparrow p\uparrow r r$ and $p$ instead of Nicod's rule, or is there some deeper reason for usingincluding $q$?

In a base for propositional logic using the Polish connective $\uparrow$ for not both, J. Nicod isolated one axiom as sufficient:

$\uparrow\uparrow p\uparrow q r\uparrow\uparrow t\uparrow tt\uparrow\uparrow s q\uparrow\uparrow p s\uparrow ps$

J. Nicod used the somewhat odd inference rule $r$ if $\uparrow p\uparrow q r$ and $p$. May we use $\uparrow p\uparrow p r$ and $p$ instead of Nicod's rule, or is there some deeper reason for using $q$?

In a base for propositional logic using the Polish connective $\uparrow$ for not both, J. Nicod isolated one axiom as sufficient:

$\uparrow\uparrow p\uparrow q r\uparrow\uparrow t\uparrow tt\uparrow\uparrow s q\uparrow\uparrow p s\uparrow ps$

J. Nicod used the somewhat odd inference rule $r$ if $\uparrow p\uparrow q r$ and $p$. May we use $\uparrow p\uparrow r r$ and $p$ instead of Nicod's rule, or is there some deeper reason for including $q$?

deleted 37 characters in body
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Frode Alfson Bjørdal
Frode Alfson Bjørdal
  • 3.6k
  • 1
  • 15
  • 35

In a base for propositional logic using the Polish connective $\uparrow$ for not both, J. Nicod isolated one axiom as sufficient:

$\uparrow\uparrow p\uparrow q r\uparrow\uparrow t\uparrow tt\uparrow\uparrow s q\uparrow\uparrow p s\uparrow ps$

J. Nicod used the somewhat odd inference rule $r$ if $\uparrow p\uparrow q r$ and $p$. May we use $\uparrow p\uparrow p r$ and $p$ instead of Nicod's rule, or is there some deeper reason for the inclusion of the seemingly superfluoususing $q$?

In a base for propositional logic using the Polish connective $\uparrow$ for not both, J. Nicod isolated one axiom as sufficient:

$\uparrow\uparrow p\uparrow q r\uparrow\uparrow t\uparrow tt\uparrow\uparrow s q\uparrow\uparrow p s\uparrow ps$

J. Nicod used the somewhat odd inference rule $r$ if $\uparrow p\uparrow q r$ and $p$. May we use $\uparrow p\uparrow p r$ and $p$ instead of Nicod's rule, or is there some deeper reason for the inclusion of the seemingly superfluous $q$?

In a base for propositional logic using the Polish connective $\uparrow$ for not both, J. Nicod isolated one axiom as sufficient:

$\uparrow\uparrow p\uparrow q r\uparrow\uparrow t\uparrow tt\uparrow\uparrow s q\uparrow\uparrow p s\uparrow ps$

J. Nicod used the somewhat odd inference rule $r$ if $\uparrow p\uparrow q r$ and $p$. May we use $\uparrow p\uparrow p r$ and $p$ instead of Nicod's rule, or is there some deeper reason for using $q$?

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Frode Alfson Bjørdal
Frode Alfson Bjørdal
  • 3.6k
  • 1
  • 15
  • 35

Representing modus ponens in a Polish propositional logic with NAND as the only connective

In a base for propositional logic using the Polish connective $\uparrow$ for not both, J. Nicod isolated one axiom as sufficient:

$\uparrow\uparrow p\uparrow q r\uparrow\uparrow t\uparrow tt\uparrow\uparrow s q\uparrow\uparrow p s\uparrow ps$

J. Nicod used the somewhat odd inference rule $r$ if $\uparrow p\uparrow q r$ and $p$. May we use $\uparrow p\uparrow p r$ and $p$ instead of Nicod's rule, or is there some deeper reason for the inclusion of the seemingly superfluous $q$?