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What is the difference between equality and logical identity?

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#logic #propositional-calculus #first-order-logic #predicate-logic #foundations
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Is there a short way to write $(\exists x. f(x)) \implies (\exists x. f(x) \land g(x))$?

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#logic #predicate-logic
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Predicate logic - Which of these formulas is equivalent to the first?

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#predicate-logic
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Does the unique existential quantifier commute with the existential quantifier?

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#logic #propositional-calculus #predicate-logic #quantifiers
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When should I classify a statement as "undefined" versus "vacuously true/false": implications for induction

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#logic #terminology #predicate-logic
83
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negating quantifiers

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#real-analysis #logic #predicate-logic
177
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Are all mathematical laws tautologies?

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#logic #soft-question #propositional-calculus #first-order-logic #predicate-logic
43
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Is it true that exists a natural number (zero excluded) that is divisible by every natural number?

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#predicate-logic
78
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Show that a Rule is Derivable in a Hilbert Calculus

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#logic #predicate-logic #solution-verification #hilbert-calculus
79
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Is it equivalent to say that a formula is logically valid and that a formula follows from the axioms?

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#logic #first-order-logic #predicate-logic #boolean-algebra
372
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First order logic: unification of Skolem constants?

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#logic #first-order-logic #predicate-logic #unification
43
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How do I write the following mathematical statement as a predicate logic formula?

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#predicate-logic
87
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What is the correct formalization of the following mathematical statement about prime numbers in a predicate logic notation?

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#predicate-logic
70
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Are these two predicates equivalent (and correctly formed)?

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#predicate-logic
139
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Predicate Logic: Truth in a Structure Under a Variable Assignment

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#logic #predicate-logic

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