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lunes, 25 de junio de 2012

New logical perspectives on physics Johan van Benthem · Sonja Smets

Synthese (2012) 186:615–617
DOI 10.1007/s11229-011-9911-y

This special issue is situated at the interface between Logic and the Foundations of
Physics. This interface, though not as active as the logical foundations of mathematics,
has long existed—with highlights such as “quantum logic”, or studies of the general
logical structure of physical theories. In recent years, more themes have come to the
fore, and we may be witnessing a revival. The papers presented here emanate from a
symposium held at the University of Utrecht in January 2008 with the aim of charting
established as well as new connections between the two fields. One of the main questions
discussedwas whether and howmodern techniques coming from logic, computer
science and information theory might be combined with state-of-the-art insights in the
philosophy of physics to gain a better understanding of the main foundational issues
and open problems in modern physics. The success of this symposium has shown that
there are several possible answers to this question. The invited papers in this issue
present the reader with an overview of the main topics at play right now. A common

feature is that all authors make essential use of logical and formal methods in physics
and point out new interesting connections between the two fields.
Research in logic has made essential progress in the last decades, along many
dimensions that seem relevant to the foundations of physics. One conspicuous strand
concerns mathematical depth. Much traditional research in the foundations of mathematics
has now begun to blend with powerful more mainstream mathematical developments
in algebra, category theory and other fields, making logical techniques more
widely available inmathematics and, in principle also, mathematical physics. Another
noticeable trend is an ever-growing amalgam of logic and formal theories of computation
and processes—perhaps the bulk of logic research as pursued today—ranging
from modal logics (spatial logic, dynamic logic and temporal logic of actions) to prooftheory-
inspired linear logic and other resource-sensitive logics, game logics, process
algebras, coalgebraic logics, etcetera. Finally, there has also been an extension of
descriptive coverage in another direction, with what has been called a “dynamic turn”
toward interaction and communication between intelligent agents, bringing logic in
touch with artificial intelligence, game theory, social choice theory, linguistics, cognitive
science, and other disciplines modeling human behaviour in an exact manner.
The papers in this volume testify to the vitality of logic in this modern sense. For
instance, modal and spatial logics can provide efficient formal tools to talk about the
qualitative temporal and spatial evolution of dynamical systems. These logics can
handle a large variety of interactive properties of processes and they can also be used
to formalize various conceptions of space. The paper by M. Aiello, G. Bezhanishvili,
I. Bloch and V. Goranko on “Logic for Physical Space” gives an overview of some
of these developments by highlighting new logical perspectives on spatial structures.
This reflects the larger emerging area documented in the “Handbook of Spatial Logics”,
edited by M. Aiello, J. van Benthem and I. Pratt-Hartmann (Springer, Dordrecht
Another current trend in logic of potential interest for physics and the philosophy
of physics, is reflected in the paper by H. Andréka, J. Madarasz, I. Németi and
G. Székely on “A Logic Road from Special Relativity to General Relativity”. Inspired
by the grand traditions of algebraic logic and classical model theory in the study of
geometry, the authors present a detailed first-order analysis of the structure of both
Special and general relativity theory, throwing surprising new light on their not always
evident logical connections. This paper is at the same time a characteristic sample of
the ‘Budapest School’ at the interface of logic, space-time geometry, and physics.
Another recent trend in Logic combines the use of proof theory and categorical
logic with insights from the foundations of physics, as pursued in the Oxford projects
of S. Abramsky and B. Coecke. The paper of B. Coecke and R.W. Spekkens on “Picturing
Classical and Quantum Bayesian Inference” takes this categorical line of work
one step further into the direction of a graphical representation of Bayesian inference
and quantum causal relations. Another topic in this line of research, is the paper by
S. Abramsky on “Big ToyModels” in which the author shows how Chu spaces can be
used to represent physical systems including both classical and quantum systems.
A next trend of interest relates to intuitionistic logic and Heyting algebra, i.e., the
constructive foundations of mathematics, now brought to bear on the foundations
of quantum physics. The paper by C. Heunen, N.P. Landsman and B. Spitters on

“Bohrification of Operator Algebras and Quantum Logic” shows how an intuitionistic
approach can shed new light on the difficulties and problems of traditional quantum
logic. While traditional quantum logic has its merits, it also confronts us with deep
questions that touch upon the roots of logic itself. In particular the original work
of Birkhoff and von Neumann has left both philosophers and logicians wondering
whether empirical theories like quantum physics can really provide principled weakening
of our classical logical principles.
While the preceding paper opts for the intuitionistic approach of weakening classical
logic, the paper “The Dynamic Turn in Quantum Logic” by A. Baltag and
S. Smets connects traditional quantum logicwith the above-mentioned dynamic turn in
logic. It shows how the non-classical character of quantum logic can also be diagnosed
quite differently, as the result of bringing dynamic actions of measurement on suitable
quantum information systems explicitly into the logic. The result is a classical propositional
logic with explicit operators for quantum measurement actions by observing
agents, creating one more interface between logic, physics and computation.
Finally, the latter direction of work ties in nicely with the survey paper of J. van
Benthem on “The Logic of Empirical Theories Revisited”. The author first looks at
the interface of logic and philosophy of science as it has functioned over the last
century, and recalls some of its main trends. He then argues that bringing in agency
and informational action explicitly into logical systems leads to an overhaul of formal
models in the philosophy of science, bringing it much closer to the actual dynamics
of observation, communication, and other activities that make up scientific inquiry.
All logical methods in this volume reach beyond traditional styles of formalizing
physical theories. It is our hope that by promoting work in this direction, physicists,
philosophers of physics and logicians can come closer together, and find that they
have much more common ground than is often supposed. But we do not just see this
as a one-way street of importing ideas. While new logical methods may be of relevance
to physics, we are also well aware that physical models of information flow and
even social behaviour may come to form a natural companion to existing logical and
computational ones.
These are just our editorial views: now the authors will take the stage, and we are
grateful for what they have provided so generously in the following pages. We also
take this opportunity to thank all participants of the 2008 Symposium on Logic and
Physics held at Utrecht University. Special thanks go to our fellow members of the
organizing committee : Dennis Dieks, Anne Kox, and Albert Visser. Finally, we are
happy tomention the sponsors who made this Symposium possible: The EvertWillem
Beth Stichting, The Heyting Stichting, and the Disciplinegroep Theoretische Filosofie
at the University of Utrecht.

1 comentario:

  1. Comparto el tema y la introducción del último numero de Synthese, que podríamos caractertizar como Lógica y los Fundametnos de la Física. Las dos entradas posteriores serán del mismo tema. Uno de los artículos es de Lógica Cuantica. Espero que los disfruten


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