Classical Concepts in Quantum Contexts

Diederik Aerts, Liane M. Gabora

Purpose To elaborate a theory for modeling concepts that incorporates how a context influences the typicality of a single exemplar and the applicability of a single property of a concept. To investigate the structure of the sets of contexts and properties. Design/methodology/approach The effect of context on the typicality of an exemplar and the applicability of a property is accounted for by introducing the notion of “state of a concept”, and making use of the state‐context‐property formalism (SCOP), a generalization of the quantum formalism, whose basic notions are states, contexts and properties. Findings The paper proves that the set of context and the set of properties of a concept is a complete orthocomplemented lattice, i.e. a set with a partial order relation, such that for each subset there exists a greatest lower bound and a least upper bound, and such that for each element there exists an orthocomplement. This structure describes the “and”, “or”, and “not”, respectively for contexts and properties. It shows that the context lattice as well as the property lattice are non‐classical, i.e. quantum‐like, lattices. Originality/value Although the effect of context on concepts is widely acknowledged, formal mathematical structures of theories that incorporate this effect have not been successful. The study of this formal structure is a preparation for the elaboration of a theory of concepts that allows the description of the combination of concepts.

W. F. G. Swann

Fabio Bagarello, Francesco Gargano

Juan Manuel Burgos

We introduce the concept of quantum reliability as an extension of the concept of network reliability in the context of quantum networks. We show that this concept is intimately related to the concept of quantum reliability operator that we also introduce and show a Negami like splitting formula for it. Considering that the simple factorization formula for classical networks which is the basis of most of the calculation algorithms does not hold in the quantum context due to entanglement, a Negami like splitting for the quantum reliability operator becomes relevant.

F. A. Kaempffer

Cheng Su

This paper , based on Bohm' s ontological view of quantum measurement process and the concept of quantum potential and active information, analyses Bohm s comprehension about the ontological context of quantum object and the holistic context to comprehend the quantum measurement process, thus revealing the differences and links between Bohm' s holistic concept of quantum measurement process and Bohr's holistic concept of quantum measurement phenomenon. In addition, this paper analyses the similar and different relations between microcosmic particle and classical particle in the Bohm's interpretative