Jorge, Juan Pablo and Holik, Federico and Krause, Décio (2023) Un acercamiento a las semánticas Nmatriciales basadas en QST. Principia: an international journal of epistemology, 27 (3). ISSN 1414-4247

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Abstract

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 emmendments 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 indetermined 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 QST formed by rough sets. Some consequences of the given formalism for the relation of logical consequence are also analysed.

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Item Type:	Published Article or Volume
Creators:	Creators Email ORCID Jorge, Juan Pablo jorgejpablo@gmail.com 0000-0003-4517-8729 Holik, Federico olentiev2@gmail.com Krause, Décio deciokrause@gmail.com
Keywords:	Nmatrices, Quasets, Qsets, Rough Sets, Quantum Logic, ZFA
Subjects:	Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Ontology Specific Sciences > Physics > Quantum Mechanics
Depositing User:	Ms. Juan Pablo Jorge
Date Deposited:	11 Mar 2025 17:36
Last Modified:	11 Mar 2025 17:36
Item ID:	24892
Journal or Publication Title:	Principia: an international journal of epistemology
Official URL:	https://periodicos.ufsc.br/index.php/principia/art...
DOI or Unique Handle:	https://doi.org/10.5007/1808-1711.2023.e91732
Subjects:	Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics > Ontology Specific Sciences > Physics > Quantum Mechanics
Date:	18 July 2023
Volume:	27
Number:	3
ISSN:	1414-4247
URI:	https://philsci-archive.pitt.edu/id/eprint/24892

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