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I have this assignment about different types of formal logic systems, like Lewis S5, Fuzzy Logic and some others, but now they ask me to search for any non logicist system, but I've search a lot and didn't find any example or clue about this type of systems, can anyone give me a clue or an example?

My research:

I've search something about this at the Stanford Encyclopedia of Philosophy(and some google search) but got nothing else than the definition and some story. They defined us a formal logicist system as one that has 1) Logic constants. 2)Logic axioms, 3) that the inference rules must be true for any given interpretation of a logic symbol.

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  • $\begingroup$ What do you mean with "non logicist system" ? Maybe Natural Deduction or Sequent Calculus or Semantic tableau (also called : truth tree)... $\endgroup$ – Mauro ALLEGRANZA Jun 6 '16 at 8:54
  • $\begingroup$ @MauroALLEGRANZA Like I mention in "my research", they defined us what a formal logicist system is, so I asume that a "non logicist system" doesn't satisfy any of the 3 requirements I mentioned. $\endgroup$ – Alejandro Cortes Jun 6 '16 at 8:59
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    $\begingroup$ @MauroALLEGRANZA Would you mind posting those as the answer so I can mark it as solved? And Thanks for your time! $\endgroup$ – Alejandro Cortes Jun 6 '16 at 10:15
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Natural Deduction and Sequent Calculus are examples of logical systems without logical axioms: only rules.

You may consider also Post canonical systems or Formal languages as examples of formal systems that do not manage logical constants.

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