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nVDash

Represents a negated double vertical dash relation in mathematical logic and set theory, indicating a strong form of non-implication.

Overview

Serves as a specialized logical notation primarily used in advanced mathematics and formal logic to denote specific types of non-implications or contradictions.

  • Common in proof theory and mathematical logic for expressing complex logical relationships
  • Often appears alongside other logical symbols to construct formal proofs
  • Particularly useful in set theory and abstract algebra when discussing non-implications between mathematical structures
  • Frequently used in academic papers and advanced mathematical texts where precise logical notation is essential

Examples

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

p⊯qp \nVDash q 
p \nVDash q

Showing multiple non-semantic consequences in a logical argument.

p∧q⊯r∧sp \land q \nVDash r \land s 
p \land q \nVDash r \land s

Demonstrating that a formula is not a valid consequence in modal logic.

□p⊯◊q\Box p \nVDash \Diamond q 
\Box p \nVDash \Diamond q