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title TARGET DECK FILE TAGS tags
Proof Systems Obsidian::STEM formal-system
formal-system
logic

Overview

A deductive system found in certain formal systems. Proof systems are syntactic in nature. Proofs are sequences of WFFs, each of which are entailed from previous ones in the sequence. A theorem is then the last WFF in any valid sequence of WFFs.

%%ANKI Basic Why do we say formal systems using proof systems are purely syntactic? Back: No meaning is attached to the WFFs of the formal language. Reference: “Formal System,” in Wikipedia, May 10, 2024, https://en.wikipedia.org/w/index.php?title=Formal_system.

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%%ANKI Cloze Proof systems are {syntactic}, not {semantic}. Reference: “Formal System,” in Wikipedia, May 10, 2024, https://en.wikipedia.org/w/index.php?title=Formal_system.

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%%ANKI Basic How is it purely syntactic proof systems can produce theorems? Back: Inference rules define how to produce theorems from sequences of WFFs. Reference: “Formal System,” in Wikipedia, May 10, 2024, https://en.wikipedia.org/w/index.php?title=Formal_system.

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%%ANKI Basic What kind of deductive system is natural deduction usually categorized as? Back: A proof system. Reference: “Formal System,” in Wikipedia, May 10, 2024, https://en.wikipedia.org/w/index.php?title=Formal_system.

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%%ANKI Basic In a proof system, a proof is used to produce what? Back: A theorem. Reference: “Formal System,” in Wikipedia, May 10, 2024, https://en.wikipedia.org/w/index.php?title=Formal_system.

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%%ANKI Basic In a proof system, a proof is a sequence of what? Back: Well-formed formulas. Reference: “Formal System,” in Wikipedia, May 10, 2024, https://en.wikipedia.org/w/index.php?title=Formal_system.

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%%ANKI Basic In a proof system, how are WFFs produced from one another? Back: Via inference rules. Reference: “Formal System,” in Wikipedia, May 10, 2024, https://en.wikipedia.org/w/index.php?title=Formal_system.

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Bibliography