2001/06/30 by Paul Benioff
Computer Science · Physics and Astronomy · #Advanced Algebra and Logic #Algebra over a field #Completeness (order theory) #Computability, Logic, AI Algorithms #Consistency (knowledge bases) #Interpretation (philosophy) #Quantum #Relation (database) #Representation (politics) #Simple (philosophy) #Word (group theory) #quant-ph #semigroups and automata theory
paper · pdf · doi:10.1088/0305-4470/35/28/305
published in Journal of Physics A Mathematical and General 35(28), 5843-5857 (Institute of Physics) · 18 pages, 1 figure, extensively revised and expanded; includes work on the basis dependence of validity and on the relation between meaning and algorithmic complexity
arxiv created 2002/02/22 · openalex publication_date 2002/07/05 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
The representation of numbers by product states in quantum mechanics can be extended to the representation of words and word sequences in languages by product states. This can be used to study quantum systems that generate text that has meaning. A simple example of such a system, based on an example described by Smullyan, is studied here. Based on a path interpretation for some word states, definitions of truth, validity, consistency and completeness are given and their properties studied. It is also shown that the relation between the potential meaning, if any, of word states and the quantum algorithmic complexity of the process generating the word states must be quite complex or nonexistent.