In this way, the truth-value of a formula is determined by the semantic values of its parts, the syntactic arrangement of the formula, and relations in the structure between those semantic values. Model theory maps sentences and their parts on to configurations of elements in the domain, or structure, of a model. The mapping reveals meaning-connections between sentences by exhibiting relations between configurations in the domain. By this mapping we can plot relations between sentences as represented by the patterns amongst the objects, properties, and relations assigned to expressions which figure in those sentences. Each set of assignments, or model, corresponds to a world in which some of those sentences are true and others are false.
Truth theory offers another version of the truth-conditional approach to meaning.
L ' is appended to a sentence S of the object language L when and only when certain conditions p obtain. Proof of each instance of T proceeds from axioms which assign references to the simple parts of the object-language sentence, together with axioms that state the consequences for truth of combining those expressions in sentences. A truth theory for a language is a finite set of such axioms. Davidson has argued that such theories can serve as theories of meaning. In the early 1980s a new paradigm, called situation semantics, was developed by Barwise and Perry.