Quantum aspects of high dimensional formal representation of conceptual
  spaces
  Human cognition is a complex process facilitated by the intricate
architecture of human brain. However, human cognition is often reduced to
quantum theory based events in principle because of their correlative
conjectures for the purpose of analysis for reciprocal understanding. In this
paper, we begin our analysis of human cognition via formal methods and proceed
towards quantum theories. Human cognition often violate classic probabilities
on which formal representation of conceptual spaces are built. Further,
geometric representation of conceptual spaces proposed by Gardenfors discusses
the underlying content but lacks a systematic approach (Gardenfors, 2000; Kitto
et. al, 2012). However, the aforementioned views are not contradictory but
different perspective with a gap towards sufficient understanding of human
cognitive process. A comprehensive and systematic approach to model a
relatively complex scenario can be addressed by vector space approach of
conceptual spaces as discussed in literature. In this research, we have
proposed an approach that uses both formal representation and Gardenfors
geometric approach. The proposed model of high dimensional formal
representation of conceptual space is mathematically analysed and inferred to
exhibit quantum aspects. Also, the proposed model achieves cognition, in
particular, consciousness. We have demonstrated this process of achieving
consciousness with a constructive learning scenario. We have also proposed an
algorithm for conceptual scaling of a real world scenario under different
quality dimensions to obtain a conceptual scale.
