Philosophical theories also bear upon lexical semantics. Frege's [43] distinction between sense and reference marked a turn to interest in descriptions (e.g., intensions) rather than focusing strictly on denotations (e.g., extensions). This shows up most clearly in Montague semantics to be discussed next, but it also has an influence in various knowledge representation schemes used in NLP.
For example, the text meaning representation language of Mikrokosmos [90,89] includes an operator that returns the meaning or intension of the concept bound to a particular variable.
Montague semantics [36] is an influential theory for model-theoretical semantics. For instance, the Generative Lexicon [96] approach incorporates it for modeling lexical functions; also, Helmreich [53] uses Montague semantics for a pragmatic account of word meaning. The central idea of Montague semantics is to provide for a compositional semantics by defining explicit mappings from syntax into semantics. This relies heavily on the distinction between extensional and intensional functions. Extensional functions are the traditional type of functions used in denotation, for instance, a function from ``American presidents'' to the set of American presidents. Intensional functions are intended to capture the notion of sense, for instance, the attributes associated with American presidents. However, the attributes are not represented directly (e.g., via semantic primitives); instead they are represented implicitly by mapping from contexts into the appropriate denotation. Thus intensional functions are at a higher level than extensional functions in that an intensional function maps from an expression into an extensional function. In other words, they encode the all the possible extensions an expression can have depending upon context.
Davidson [32] developed a theory of event representation to address the problem of accounting for the wide variety of event modifiers without having to postulate many different event frames or require optional arguments. Instead, he uses an event variable that is an implicit argument of each predicate. Then, modifiers appear as distinct predicates using the same event variable. This work has been influential in semantics, for example, as in the work by Higginbotham [55] discussed later.
This effect of event variables is prevalent in many logical knowledge representation schemes, either explicitly, as in the Generative Lexicon predicate expressions [96], or implicitly, as in conceptual graphs [7] or frame-based representations [90].