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Does the Definition of a Formal Proof in Mendelson's Book Allow for the Use of Theorem/Derived Axiom Schema in Formal Proofs?

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#propositional-calculus #first-order-logic #formal-languages #formal-proofs #formal-systems
70
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Can the Negation of a Conditional Implying the First Atomic Proposition Get Proven in Around 50 Steps?

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#logic #propositional-calculus #formal-languages #formal-proofs #formal-systems
103
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Is there a formal class theory that suffices to formalize the basic notions of category theory?

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#logic #category-theory #foundations #formal-systems
686
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Is the Russell paradox formalizable in type theories?

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#homotopy-theory #paradoxes #type-theory #formal-systems
151
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How might one prove that $x$ is an element of $\{x, y\}$ in some formal system?

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#notation #formal-systems
366
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Properties of logical systems: which field study it?

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#logic #book-recommendation #formal-systems
466
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How to find out whether the formal system is complete and sound?

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#logic #propositional-calculus #axioms #formal-systems
1.3k
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What is the difference between a formal system and first order logic?

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#logic #first-order-logic #formal-languages #formal-systems
175
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Show that a given formula is not provable without the associative rule

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#logic #first-order-logic #formal-proofs #formal-systems
134
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Which formal system (aka platform) is the best for selfstudying Category Theory?

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#soft-question #category-theory #formal-languages #formal-systems
63
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Efficiently Verifying "identities" in Arithmetic

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#arithmetic #computational-complexity #computability #formal-languages #formal-systems
64
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Given an axiom in a formal system, can we always find another formal system in which this axiom is a theorem?

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#logic #formal-languages #formal-systems
35
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Formal verification of function contract?

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#logic #formal-systems
62
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Is there a standard notion of a "theory of Turing machines"?

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#logic #reference-request #computability #formal-systems
62
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How to state the "unsolvability of quintic by radicals" in 2nd and higher order logic?

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#logic #formal-systems

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