Modeling Concept Combinations in a Quantum-theoretic Framework

We present modeling for conceptual combinations which uses the mathematical formalism of quantum theory. Our model faithfully describes a large amount of experimental data collected by different scholars on concept conjunctions and disjunctions. Furthermore, our approach sheds a new light on long standing drawbacks connected with vagueness, or fuzziness, of concepts, and puts forward a completely novel possible solution to the 'combination problem' in concept theory. Additionally, we introduce an explanation for the occurrence of quantum structures in the mechanisms and dynamics of concepts and, more generally, in cognitive and decision processes, according to which human thought is a well structured superposition of a 'logical thought' and a 'conceptual thought', and the latter usually prevails over the former, at variance with some widespread beliefsComment: 5 pages. arXiv admin note: substantial text overlap with arXiv:1311.605

Respects for contradictions

International audienceI discuss the problem of whether true contradictions of the form "x is P and not P " might be the expression of an implicit relativization to distinct respects of application of one and the same predicate P. Priest rightly claims that one should not mistake true contradictions for an expression of lexical ambiguity. However, he primarily targets cases of homophony for which lexical meanings do not overlap. There exist more subtle forms of equivocation, such as the relation of privative opposition singled out by Zwicky and Sadock in their study of ambiguity. I argue that this relation, which is basically a relation of general to more specific, underlies the logical form of true contradictions. The generalization appears to be that all true contradictions really mean "x is P in some respects/to some extent, but not in all respects/not to all extent". I relate this to the strict-tolerant account of vague predicates and outline a variant of the account to cover one-dimensional and multi-dimensional predicates

Quantum structure in cognition origins, developments, successes, and expectations

The authors provide an overview of the results they have obtained over the last decade on the identification of quantum structures in cognition and, more specifically, in the formalization and representation of natural concepts. They firstly discuss the quantum foundational reasons that led them to investigate the mechanisms of formation and combination of concepts in human reasoning, starting from the empirically observed deviations from classical, logical, and probabilistic structures. They then develop their quantum-theoretic perspective in Fock space which allows successful modeling of various sets of cognitive experiments collected by different scientists, including themselves. In addition, they formulate a unified explanatory hypothesis for the presence of quantum structures in cognitive processes, and discuss their recent discovery of further quantum aspects in concept combinations, namely, ‘entanglement’ and ‘indistinguishability.’ They finally illustrate the outlook for future research

Context and interference effects in the combinations of natural concepts

The mathematical formalism of quantum theory exhibits significant effectiveness when applied to cognitive phenomena that have resisted traditional (set theoretical) modeling. Relying on a decade of research on the operational foundations of micro-physical and conceptual entities, we present a theoretical framework for the representation of concepts and their conjunctions and disjunctions that uses the quantum formalism. This framework provides a unified solution to the ‘conceptual combinations problem’ of cognitive psychology, explaining the observed deviations from classical (Boolean, fuzzy set and Kolmogorovian) structures in terms of genuine quantum effects. In particular, natural concepts ‘interfere’ when they combine to form more complex conceptual entities, and they also exhibit a ‘quantum-type context-dependence’, which are responsible of the ‘over- and under-extension’ that are systematically observed in experiments on membership judgments