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Semantics – Overview
Interpretation – Maps symbols of the formal language (predicates, functions, variables, constants) onto objects, relations, and functions of the “world” (formally: Domain, relational Structure, or Universe)
Valuation – Assigns domain objects to variables
The Valuation function can be used for describing value assignments and constraints in case of nested quantifiers.
The Valuation function otherwise determines the satisfaction of a formula only in case of open formulae.
Constructive Semantics – Determines the semantics of complex expressions inductively, starting with basic expressions