PP-2009-01:
Blutner, Reinhard and Strigin, Anatoli
(2009)
*Bidirectional Grammar and Bidirectional Optimization.*
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## Abstract

Recently, Gerd Niestegge developed a new approach to quantum mechanics

via conditional probabilities developing the well-known proposal to

consider the Lüders-von Neumann measurement as a non-classical

extension of probability conditionalization. I will apply his powerful

and rigorous approach to the treatment of concepts using a geometrical

model of meaning. In this model, instances are treated as vectors of a

Hilbert space H . In the present approach there are at least two

possibilities to form categories. The first possibility sees

categories as a mixture of its instances (described by a density

matrix). In the simplest case we get the classical probability theory

including the Bayesian formula. The second possibility sees categories

formed by a distinctive prototype which is the superposition of the

(weighted) instances. The construction of prototypes can be seen as

transferring a mixed quantum state into a pure quantum state freezing

the probabilistic characteristics of the superposed instances into the

structure of the formed prototype. Closely related to the idea of

forming concepts by prototypes is the existence of interference

effects. Such inference effects are typically found in macroscopic

quantum systems and I will discuss them in connection with several

puzzles of bounded rationality. The present approach nicely

generalizes earlier proposals made by authors such as Diederik Aerts,

Andrei Khrennikov, Ricardo Franco, and Jerome Busemeyer. Concluding, I

will suggest that an active dialogue between cognitive approaches to

logic and semantics and the modern approach of quantum information

science is mandatory.

Item Type: | Report |
---|---|

Report Nr: | PP-2009-01 |

Series Name: | Prepublication (PP) Series |

Year: | 2009 |

Uncontrolled Keywords: | Optimality Theory; Bidirectionality; Pragmatics; Fossilization |

Depositing User: | kblutne1 |

Date Deposited: | 12 Oct 2016 14:37 |

Last Modified: | 12 Oct 2016 14:37 |

URI: | https://eprints.illc.uva.nl/id/eprint/331 |

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