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nvDash

Represents a negated double vertical dash symbol used in mathematical logic to indicate non-validity or non-semantic entailment.

Overview

Serves as a critical notation in formal logic and mathematical proofs, particularly when expressing relationships between propositions or sets that do not satisfy certain conditions.

  • Common in proof theory and model theory to denote that a conclusion does not follow semantically
  • Used alongside other logical symbols to construct complex logical statements
  • Frequently appears in advanced mathematics and theoretical computer science texts
  • Pairs naturally with \Dash and other related logical notation symbols

Examples

Expressing that a statement is not a semantic consequence in mathematical logic.

PQP \nvDash Q
P \nvDash Q

Showing multiple non-semantic consequences in a logical argument.

ABBCACA \nvDash B \quad B \nvDash C \quad A \nvDash C
A \nvDash B \quad B \nvDash C \quad A \nvDash C

Demonstrating that a formula is not a valid consequence of a set of premises.

{PQ,QR}PR\{P \rightarrow Q, Q \rightarrow R\} \nvDash P \rightarrow R
\{P \rightarrow Q, Q \rightarrow R\} \nvDash P \rightarrow R