Context and Interference Effects in the Combinations of Natural Concepts

Philosophers and psychologists have always been interested in the deep nature of human concepts, how they are formed, how they combine to create more complex conceptual structures, as expressed by sentences and texts, and how meaning is created in these processes. Unveiling aspects of these mysteries is bound to have a massive impact on a variety of domains, from knowledge representation to natural language processing, machine learning and artificial intelligence. The original idea of a concept as a'container of objects', called'instantiations', which can be traced back to Aristotle, was challenged by the first cognitive tests by Eleanor Rosch, which revealed that concepts exhibit aspects, like'context-dependence', 'vagueness' and'graded typicality', that prevent a too naïve definition of a concept as a'set of defining properties that are either possessed or not possessed by individual exemplars' [1, 2]. More, these tests infused the suspicion that concepts do not combine by following the algebraic rules of classical logic. A first attempt to preserve a set theoretical modeling came from the'fuzzy set approach': concepts would be represented by fuzzy sets, while their conjunction (disjunction) satisfies the'minimum (maximum) rule of fuzzy set conjunction (disjunction)' [3]. However, also this approach was confuted by a whole set of experiments by cognitive psychologists, including Osherson and Smith, who identified the'Guppy effect' (or'Pet-Fish problem') in typicality judgments [4], James Hampton, who discovered'overextension' and'underextension' effects in membership judgments [5, 6], and Alxatib and Pelletier, who detected'borderline contradictions' in simple propositions of the form "John is tall and John is not tall" [7]. More recently, some of us proved that these data violate Kolmogorov's axioms of classical probability theory [8], thus revealing that classical structures,