Classical truth-functional semantics and almost all of its modifications have a serious problem in treating prototypes and their combinations. Though some modelling variants can account for many puzzling empirical observations, their explanatory value is seldom noteworthy. In recent work by several researchers it has been argued that this explanatory inadequacy is due to the Boolean characteristic of the underlying semantics. These researchers have suggested a proper generalization of Boolean algebras called ortho-algebras (known from quantum information theory). In five lectures, this new and exciting field of research will be discussed:
Many linguistic phenomena have a close analogue to phenomena investigated in quantum physics. Words are floating freely in a polyvalent state representing a variety of different uses. As the properties of small particles are not absolute and determined not until observing them, in language the properties of word tokens are determined not until conscious apprehension. Further, cognitive measures such as salience, typicality or cue validity cannot be modelled properly by classical probabilities. Instead, quantum probabilities were quite useful for handling such quantities. Finally, a quantum framework can be used for integrating logic programs and connectionist systems (representing the “phrase space” in a dynamic “phase space”).
The new and exciting field of quantum linguistics concerns three main areas:
Vector based retrieval of semantic information (see Widdows, Aerts)
Prototype semantics, bounded rationality, and interference effects (see Aerts, Gabora, Busemeyer, Khrennikov, Franco)
Representation theory for nonlinear dynamic automata and quantum information theory (see Atmanspacher, beim Graben, Primas)