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Does weak completeness ("If $\vDash\phi$, then $\vdash\phi$") imply strong completeness ("If $\Gamma\vDash\phi$, then $\Gamma\vdash\phi$")?

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#logic #predicate-logic #first-order-logic #metalogic
283
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Question about Existential Generalization

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#logic #predicate-logic #first-order-logic
276
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Using implication in an existentially quantified sentence

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#logic #predicate-logic #quantifiers
174
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Does there exist a first-order theory $T$ and a proof system $\vdash$ such that $T\vDash\phi$ iff $T\vdash\phi$, but $\vdash$ is not complete?

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#logic #predicate-logic #first-order-logic #metalogic
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Analyzing the logical forms of the following statements (quantifiers and conditionals)

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#logic #propositional-calculus #predicate-logic #first-order-logic
1.5k
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Negation of the Universal quantifier is an existential quantifier?

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#logic #predicate-logic
43
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Can I Write Propositional Logic Statement Using Functions Returning T/F?

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#logic #propositional-calculus #predicate-logic #first-order-logic
125
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Confusion with definition of $term$ in first order languages.

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#logic #predicate-logic #first-order-logic
1.4k
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What is meant by 'domain of interpretation' in mathematical logic?

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#logic #definition #predicate-logic
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What is the difference between 'logical symbols' and 'relation symbols' in first order logic?

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#logic #definition #predicate-logic #first-order-logic
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Translation from English to Predicate Logic

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#logic #predicate-logic #logic-translation
92
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Ambiguous Quantifiers

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#predicate-logic
68
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Composition computation

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#predicate-logic
674
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Truth trees in predicate logic

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#predicate-logic #quantifiers
225
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A Hypothetical Quantifier in Predicate Logic

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#predicate-logic #quantifiers

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