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.
P \nvDash QShowing multiple non-semantic consequences in a logical argument.
A \nvDash B \quad B \nvDash C \quad A \nvDash CDemonstrating that a formula is not a valid consequence of a set of premises.
\{P \rightarrow Q, Q \rightarrow R\} \nvDash P \rightarrow R