caa a22 4500 467901708 CHVBK 20180406152820.0 cr unu---uuuuu 170328e20061201xx s 000 0 eng 10.1007/s10699-004-6248-8 doi (NATIONALLICENCE)springer-10.1007/s10699-004-6248-8 The Generalised Liar Paradox: A Quantum Model and Interpretation [Elektronische Daten] [Jan Broekaert, Diederik Aerts, Bart D'Hooghe] The formalism of abstracted quantum mechanics is applied in a model of the generalized Liar Paradox. Here, the Liar Paradox, a consistently testable configuration of logical truth properties, is considered a dynamic conceptual entity in the cognitive sphere (Aerts, Broekaert, & Smets, [Foundations of Science 1999, 4, 115-132; International Journal of Theoretical Physics, 2000, 38, 3231-3239]; Aerts and colleagues[Dialogue in Psychology, 1999, 10; Proceedings of Fundamental Approachs to Consciousness, Tokyo '99; Mind in Interaction]. Basically, the intrinsic contextuality of the truth-value of the Liar Paradox is appropriately covered by the abstracted quantum mechanical approach. The formal details of the model are explicited here for the generalized case. We prove the possibility of constructing a quantum model of the m-sentence generalizations of the Liar Paradox. This includes (i) the truth-falsehood state of the m-Liar Paradox can be represented by an embedded 2m-dimensional quantum vector in a (2m) m -dimensional complex Hilbert space, with cognitive interactions corresponding to projections, (ii) the construction of a continuous ‘time' dynamics is possible: typical truth and falsehood value oscillations are described by Schrödinger evolution, (iii) Kirchoff and von Neumann axioms are satisfied by introduction of ‘truth-value by inference' projectors, (iv) time invariance of unmeasured state. Springer, 2006 Broekaert Jan Center Leo Apostel for Interdisciplinary Studies (CLEA) Foundations of the Exact Sciences (FUND) Department of Mathematics, Vrije Universiteit Brussel, 1160, Brussels, Belgium aut Aerts Diederik Center Leo Apostel for Interdisciplinary Studies (CLEA) Foundations of the Exact Sciences (FUND) Department of Mathematics, Vrije Universiteit Brussel, 1160, Brussels, Belgium aut D'Hooghe Bart Center Leo Apostel for Interdisciplinary Studies (CLEA) Foundations of the Exact Sciences (FUND) Department of Mathematics, Vrije Universiteit Brussel, 1160, Brussels, Belgium aut Foundations of Science Kluwer Academic Publishers 11/4(2006-12-01), 399-418 1233-1821 11:4<399 2006 11 10699 https://doi.org/10.1007/s10699-004-6248-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10699-004-6248-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Broekaert Jan Center Leo Apostel for Interdisciplinary Studies (CLEA) Foundations of the Exact Sciences (FUND) Department of Mathematics, Vrije Universiteit Brussel, 1160, Brussels, Belgium aut NATIONALLICENCE 700 1- Aerts Diederik Center Leo Apostel for Interdisciplinary Studies (CLEA) Foundations of the Exact Sciences (FUND) Department of Mathematics, Vrije Universiteit Brussel, 1160, Brussels, Belgium aut NATIONALLICENCE 700 1- D'Hooghe Bart Center Leo Apostel for Interdisciplinary Studies (CLEA) Foundations of the Exact Sciences (FUND) Department of Mathematics, Vrije Universiteit Brussel, 1160, Brussels, Belgium aut NATIONALLICENCE 773 0- Foundations of Science Kluwer Academic Publishers 11/4(2006-12-01), 399-418 1233-1821 11:4<399 2006 11 10699 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer