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nvdash

Represents logical non-provability or non-derivability in formal logic and mathematical proofs.

Overview

Essential in mathematical logic and proof theory for expressing that a conclusion cannot be derived from given premises or axioms.

  • Commonly used in formal logic systems and proof writing
  • Appears frequently in papers and texts on mathematical foundations
  • Often paired with its positive counterpart \vdash to express provability relationships
  • Particularly useful in metamathematics and theoretical computer science when discussing formal systems

Examples

Showing that a logical statement is not derivable in a formal system.

pqrp \land q \nvdash r
p \land q \nvdash r

Demonstrating non-provability in mathematical logic.

x(P(x)Q(x))xP(x)\forall x (P(x) \to Q(x)) \nvdash \exists x P(x)
\forall x (P(x) \to Q(x)) \nvdash \exists x P(x)

Expressing that a set of premises does not entail a conclusion.

{A,AB,BC}D\{A, A \to B, B \to C\} \nvdash D
\{A, A \to B, B \to C\} \nvdash D