nVdash

Represents a negated double vertical dash symbol used in mathematical logic to indicate non-provability or non-derivability.

Overview

Serves as a specialized notation in formal logic and proof theory, particularly when expressing negative relationships between statements or propositions.

Common in mathematical logic for denoting that a conclusion does not follow from given premises
Used in formal proofs and theorem proving to indicate non-derivability
Appears frequently in advanced logic textbooks and academic papers discussing proof systems
Often paired with its positive counterpart (\Vdash) when discussing logical consequences and formal deductions

Examples

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

p \nVdash q

p \nVdash q

Showing multiple non-consequences in a logical argument.

A \nVdash B \quad B \nVdash C \quad A \nVdash C

A \nVdash B \quad B \nVdash C \quad A \nVdash C

Demonstrating non-validity in a formal system with multiple premises.

\{p_1, p_2, \ldots, p_n\} \nVdash q

\{p_1, p_2, \ldots, p_n\} \nVdash q