  Tarskian Semantics. Standard model theoretic semantics for the languages of predicate logic deriving from the work of Tarski (1933,  1944) is the paradigmatic semantic theory for extensional logics.  Given a standard first-order language ℒ, a Tarskian  interpretation I for ℒ specifies a set D for the quantifiers of ℒ to range over (typically, some set of things that ℒ has been designed to describe) and assigns, to each  term (constant or variable) τ of ℒ, a referent  aτ ∈ D and, to each n-place  predicate π of ℒ, an appropriate extension  Eπ — a truth value (TRUE or FALSE) if  n = 0, a subset of D if n = 1, and a set of  n-tuples of members of D if n &gt; 1. Given these  assignments, sentences are evaluated as true under the interpretation I — trueI, for short — according to a more or less familiar set of clauses. To facilitate the definition, let I[ν/a] be the interpretation that assigns the individual a to the variable ν and is otherwise exactly like I. Then we have: 