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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

2008).

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.

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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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