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According to Rudolf Carnap, in logic, an interpretation is a descriptive interpretation (also called a factual interpretation) if at least one of the undefined symbols of its formal system becomes, in the interpretation, a ''descriptive sign'' (i.e., the name of single objects, or observable properties).〔Carnap, Rudolf, ''Introduction to Symbolic Logic and its Applications''〕 In his ''Introduction to Semantics'' (Harvard Uni. Press, 1942) he makes a distinction between formal interpretations which are ''logical interpretations'' (also called ''mathematical interpretation'' or ''logico-mathematical interpretation'') and ''descriptive interpretations'': a formal interpretation is a ''descriptive interpretation'' if it is not a ''logical interpretation''.〔 Attempts to axiomatize the empirical sciences, Carnap said, use a ''descriptive interpretation'' to model reality.:〔 the aim of these attempts is to construct a formal system for which reality is the only interpretation.〔The Concept and the Role of the Model in Mathematics and Natural and Social Sciences〕 - the world is an interpretation (or model) of these sciences, only insofar as these sciences are true.〔 Any non-empty set may be chosen as the domain of a descriptive interpretation, and all n-ary relations among the elements of the domain are candidates for assignment to any predicate of degree n. ==Examples== A sentence is either ''true'' or ''false'' under an ''interpretation'' which assigns values to the logical variables. We might for example make the following assignments: Individual constants * a: Socrates * b: Plato * c: Aristotle Predicates: * Fα: α is sleeping * Gαβ: α hates β * Hαβγ: α made β hit γ Sentential variables: * ''p'' "It is raining." Under this interpretation the sentences discussed above would represent the following English statements: * ''p'': "It is raining." * ''F''(''a''): "Socrates is sleeping." * ''H''(''b'',''a'',''c''): "Plato made Socrates hit Aristotle." * ''x''(''F''(''x'')): "Everybody is sleeping." * ''z''(''G''(''a'',''z'')): "Socrates hates somebody." * ''x'y'z''(''H''(''x'',''y'',''z'')): "Somebody made everybody hit somebody." * ''x'z''(''F''(''x'')''G''(''a'',''z'')): Everybody is sleeping and Socrates hates somebody. * ''x'y'z'' (''G''(''a'',''z'')''H''(''x'',''y'',''z'')): Either Socrates hates somebody or somebody made everybody hit somebody. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Descriptive interpretation」の詳細全文を読む スポンサード リンク
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