In linguistics and philosophy, the denotation of an expression is its literal meaning. For instance, the English word "warm" denotes the property of being warm. Denotation is contrasted with other aspects of meaning including connotation. For instance, the word "warm" may evoke calmness or cosiness, but these associations are not part of the word's denotation. Similarly, an expression's denotation is separate from pragmatic inferences it may trigger. For instance, describing something as "warm" often implicates that it is not hot, but this is once again not part of the word's denotation. Denotation plays a major role in several fields. Within philosophy of language, denotation is studied as an important aspect of meaning. In mathematics and computer science, assignments of denotations are assigned to expressions are a crucial step in defining interpreted formal languages. The main task of formal semantics is to reverse engineer the computational system which assigns denotations to expressions of natural languages. In linguistic semantics In natural language semantics, denotations are conceived of as the outputs of the semantic component of the grammar. For example, the denotation of the word "blue" is the property of being blue and the denotation of the word "Barack Obama" is the person who goes by that name. Phrases also have denotations which are computed according to the principle of compositionality. For instance, the verb phrase "passed the class" denotes the property of having passed the class. Depending on one's particular theory of semantics, denotations may be identified either with terms' extensions, intensions, or other structures such as context change potentials. When uttered in discourse, expressions may convey other associations which are not computed by the grammar and thus are not part of its denotation. For instance, depending on the context, saying "I ran five miles" may convey that you ran exactly five miles and not more. This content is not part of the sentence's denotation, but is rather pragmatic inferences arrived at by applying social cognition to its denotation. Denotation, meaning, and reference Linguistic discussion of the differences between denotation, meaning, and reference is rooted in the work of Ferdinand de Saussure, specifically in his theory of semiotics written in the book Course in General Linguistics. Philosophers Gottlob Frege and Bertrand Russell have also made influential contributions to this subject. Denotation and reference Although they have similar meanings, denotation should not be confused with reference. A reference is a specific person, place,