Logics and quantum gravity
type: Item
instance of: scholarly article
title: Logics and quantum gravity
zbMATH Open document ID: 0818.03031
DOI: 10.1007/BF00675166
author: Frank Antonsen
published in: International Journal of Theoretical Physics
publication date: 1995-08-10T00:00:00Z
review text: The author claims here that gravitation theory (because it takes `the entire universe into account') cannot allow an observer/observed distinction, and so cannot use `quantum logic'. This claim is unfortunately not further developed but serves as the starting point for investigating a non-Boolean but distributive `quantum logic'. The bulk of this paper, section 4, is devoted to investigating the structure of such a logic, and the author adopts a relatively pseudocomplemented system in which distribution holds but both Excluded Middle and Double Negation fail, apparently an intuitionist logic represented by a Heyting algebra. The paper also includes discussion of modal extensions of the system, and of Kripke semantics developed using a non-symmetric accessibility relation. The `essential theorem' of the paper is apparently that the intuitionist logic is an `extension of quantum logics'. This seems a peculiar result given that quantum logics are by definition here non-distributive, and the author himself has commented that to lose both distributivity and complementation is uninteresting. Discussion of `quantum nets', topoi based on fuzzy sets, and Yang-Mills fields follows. This paper is very wide-ranging and here lies its greatest weakness. Certainly it is at times confused and lacking in rigour. For example we are told ``in a general Heyting algebra the list of logical connectives \(\wedge\), \(\vee\), \(\Rightarrow\), \(\Leftrightarrow\), \(\neg\), \(\forall\), \(\exists\), is not redundant as in the case of classical \hbox {logic\dots''.} Such claims are not followed up by proper clarification and there is throughout a confusion of algebraic and logical terms. In fact many foundational terms are undefined -- we are told for instance how to define a formal language with a set of rules including an alphabet and rules of formation, yet no such definitions are provided for the formal languages used here. However, the paper has many interesting excursions, including di…
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 06D20
Mathematics Subject Classification ID: 81P10
Mathematics Subject Classification ID: 03B20
zbMATH DE Number: 729688
zbMATH Keywords: non-Boolean quantum logic
zbMATH Keywords: gravitation
zbMATH Keywords: relatively pseudocomplemented system
zbMATH Keywords: intuitionist logic
zbMATH Keywords: Heyting algebra
zbMATH Keywords: Kripke semantics
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 729688