Abstract
A new approach to semantics, based on ordered Banach spaces, is proposed. The Banach spaces semantics arises as a generalization of the four particular cases: the Giles' approach to belief structures, its generalization to the non-Boolean case, and “fuzzy extensions” of Boolean as well as of non-Boolean semantics.
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E. M. Alfsen,Compact Convex Sets and Boundary Integrals Ergebnisse der Mathematik und ihrer Grenzgebiete Vol. 57. Springer-Verlag, Berlin 1971.
S. Bugajski,The inner language of operational quantum mechanics. In:E. Beltrametti,B. C. van Fraassen (Ed.):Current Issues in Quantum Logic, Plenum Press, New York 1981. Pp.: 283–302.
S. Bugajski,Towards non-linear quantum mechanics. Report to the 13th Symposium on Mathematical Physics, Toruń, Dec. 1980 (to be published).S. Bugajski,Nonlinear extension of “quantum logic”. Report to a Short Conference on Universal Algebra, Bern, June 1981 (to be published).
G. G. Emch,Algebraic Methods in Statistical Mechanics and Quantum Field Theory Wiley-Interscience, New York 1972.
H. R. Fischer, G. T., Rüttimann,The geometry of the state space. In:A. R. Marlow (Ed.):Mathematical Foundations of Quantum Theory Academic Press, New York 1978. Pp.: 153–176.
R. Giles, W. Harper,Non-archimedian belief structures (to be published).
R. I. Goldblatt,Metamathematics of modal logic,Reports on Mathematical Logic 6 (1976) 41–78,7 (1976) 21–52.
A. Hartkämper, H. Neumann (Ed.):Foundations of Quantum Mechanics and Ordered Linear Spaces Lecture Notes in Physics Vol. 29. Springer-Verlag, Berlin 1974.
H. Primas,Foundations of theoretical chemistry. In:R. G. Wooley (Ed.):Quantum Dynamics of Molecules: The New Experimental Challenge to Theorists Plenum Press, New York 1980.H. Primas,Chemistry, Quantum Mechanics and Reductionism, Lecture Notes in Chemistry Vol. 24. Springer-Verlag, Berlin 1981.
M. Reed, B. Simon,Methods of Modern Mathematical Physics Vol. 1. Academic Press, New York 1972.
A. P. Robertson, W. Robertson,Topological Vector Spaces Cambridge University Press, Cambridge 1964.
L. A. Zadeh,The Concept of a Linguistic Variable and Its Application to Approximate Reasoning American Elsevier, New York 1973.
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Bugajski, S. Semantics in Banach spaces. Stud Logica 42, 81–88 (1983). https://doi.org/10.1007/BF01418761
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DOI: https://doi.org/10.1007/BF01418761