An Approach to QST-based Nmatrices Semantics


  • Juan Pablo Jorge University of Buenos Aires and Austral University
  • Federico Holik La Plata National University
  • Décio Krause Federal University of Rio de Janeiro



Nmatrices, Quasets, Rough Sets, Quantum logic, ZFA


This paper introduces the theory QST of quasets as a formal basis for the Nmatrices. The main aim is to construct a system of Nmatrices by substituting standard sets by quasets. Since QST is a conservative extension of ZFA (the Zermelo-Fraenkel set theory with Atoms), it is possible to obtain generalized Nmatrices (Q-Nmatrices). Since the original formulation of QST is not completely adequate for the developments we advance here, some possible amendments to the theory are also considered. One of the most interesting traits of such an extension is the existence of complementary quasets which admit elements with undetermined membership. Such elements can be interpreted as quantum systems in superposed states. We also present a relationship of QST with the theory of Rough Sets RST, which grants the existence of models for SQT formed by rough sets. Some consequences of the given formalism for the relation of logical consequence are also analysed.

Author Biographies

Juan Pablo Jorge, University of Buenos Aires and Austral University

Facultad de Filosofía y Letras Universidad de Buenos Aires (CABA) y Instituto de Filosofía Universidad Austral (Pilar), Buenos Aires, Argentina

Federico Holik, La Plata National University

Instituto de Física
Universidad Nacional de La Plata
La Plata, Buenos Aires

Décio Krause, Federal University of Rio de Janeiro

Programa de Pós-Graduação em Lógica e Metafísica/PPGLM

Universidade Federal do Rio de Janeiro



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