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Is it possible to prove a contradiction with natural deduction by negating the formula?

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#logic #predicate-logic #natural-deduction
113
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A question on the formality of a theory

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#logic #first-order-logic #predicate-logic #formal-languages
229
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Need help understanding variable label/scoping rules for first order logic

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#logic #first-order-logic #predicate-logic #quantifiers #convention
148
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Proof verification (formal logic): $U = \emptyset \vdash \forall A ( U \subseteq A)$

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#proof-verification #elementary-set-theory #logic #predicate-logic
785
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Convincing yourself about choice of axioms for predicate calculus

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#logic #intuition #predicate-logic
40
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Predicate logic: What are the differences between ∀ and ∃ when it comes to comparing two variables?

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#discrete-mathematics #predicate-logic #integers
68
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Counterexample for the invalidity of the following

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#examples-counterexamples #first-order-logic #predicate-logic #natural-deduction
63
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Proof using natural deduction of $\small\forall x~[A(x)\to\exists y~[B(y)\land C(y,x)]] \vdash\forall x~[\exists y~[A(x)\to(B(y)\land C(y,x))]]$

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#first-order-logic #predicate-logic #natural-deduction
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Negating statements help

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#discrete-mathematics #logic #predicate-logic
372
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What is the standard first-order language to formalize ZFC?

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#set-theory #first-order-logic #predicate-logic
212
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Show that $∀x∃yRxy ⊢ ∃zRf(a)z$

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#logic #first-order-logic #predicate-logic #quantifiers
56
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Q: on Lemma I.5.11 proof from Tourlakis 2003

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#logic #first-order-logic #predicate-logic #model-theory
389
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All Finite S-structures satisfying "characterizing" S-sentence are isomorphic

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#logic #first-order-logic #predicate-logic
331
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Intuition behind a structure of a language in mathematical logic [long read but simple]

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#logic #definition #first-order-logic #intuition #predicate-logic
309
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Defining uniqueness with quantifiers

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#discrete-mathematics #logic #predicate-logic

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