text: A*semantics*is a system for mapping expressions of a formal language to their denotations. In many 
  systems of logic, denotations are truth values. For instance, the semantics for classical propositional logic 
  assigns the formula 
   are true. From the semantic point of 
  view, a premise entails a conclusion if the conclusion is true whenever the premise is true.[102] 
  
   the denotation "true" whenever   and 
  
  A system of logic is sound when its proof system cannot derive a conclusion from a set of premises 
  unless it is semantically entailed by them. In other words, its proof system cannot lead to false 
  conclusions, as defined by the semantics. A system is complete when its proof system can derive every 
  conclusion that is semantically entailed by its premises. In other words, its proof system can lead to any 
  true conclusion, as defined by the semantics. Thus, soundness and completeness together describe a 
  system whose notions of validity and entailment line up perfectly.[103] 