 The principle of compositionality (a.k.a. Frege principle) states that semantic attributes of a complex expression \(E\) are determined by the semantic attributes of its constituent expressions and the structure of \(E\). In particular, the semantic attribute of interest (e.g., truth) may be determined in terms of one or more auxiliary semantic attributes (e.g.,  satisfaction).[49]  Hintikka has argued that compositionality amounts to semantic context-independence: semantic attributes of a complex expression depend only on the semantic attributes of its constituent expressions, plus its structure – they do not depend on the sentential context in which the expression is embedded. Semantic context-independence makes it possible to carry out semantic analysis from inside out – from simpler expressions to more complex  ones.[50]  This is what is needed for recursive definitions of semantic attributes – such as Tarski-type definitions of truth and satisfiability – to be  possible.[51]  By contrast, the GTS analysis of sentences is an outside in process: a semantic game starts with an entire sentence, and stepwise analyzes the sentence into simpler and simpler components, eventually reaching an atomic formula (together with an appropriate variable assignment). Therefore GTS allows accounting for semantic context-dependencies that violate the principle of  compositionality.[52]