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User:Physis/Canonical calculus

From Wikipedia, the free encyclopedia

Canonical calculus is a formal way to derive the words of a formal language. It is motivated by the pattern of inductive definitions.

It can be used as one tool in the approach of building logic without circularity: "taming it to spiral".

Hypercalculus is a special instance of it, which enables an especially concise approach to self-referent theorems, and formulation of Gödel's incompleteness theorem.

Formal definition

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Syntax

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<calculus> ::= rule
<calculus> ::= <calculus> <rule>
<rule> ::= <term>
<rule> ::= term  <rule>
<term> ::= <symb>*
<symbol> ::= <variable>
<symbol> ::= <nonlog>

Motivating example

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Decimal form of 3-divisible natural numbers

References

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  • Ruzsa, Imre (1988). Logikai szintaxis és szemantika I. Budapest: Akadémiai Kiadó.