##  [Valuation](/valuation) 

  ##  [Valuation](https://mathlogic.quantumdictionary.io/valuation-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A function (often called a valuation or truth assignment) that maps propositional variables or atomic formulas to truth values in a given semantic setting and extends to complex formulas according to the logic's semantic clauses.

 

 

 

 

 





 

 



 ##  [Valuation](https://puremath.quantumdictionary.io/valuation-1) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A function v from a field or a ring to a totally ordered abelian group (often R∪{∞} or Z∪{∞}) that measures size or divisibility, is multiplicative (v(xy)=v(x)+v(y) in additive notation) and satisfies a triangle-like inequality v(x+y) ≥ min(v(x),v(y)) in the non-archimedean case.