Smets, S.

van Benthem, J.

English

Johan van Benthem

Sonja Smets

Crossref

Synthese

New logical perspectives on physics

van Benthem, Johan

Smets, Sonja

University of Groningen Research Database

Proceedings - University of Groningen

   University of GroningenNew logical perspectives on physicsvan Benthem, Johan; Smets, SonjaPublished in:SyntheseDOI:10.1007/s11229-011-9911-yIMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2012Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):van Benthem, J., & Smets, S. (2012). New logical perspectives on physics. Synthese, 186(3), 615-617.https://doi.org/10.1007/s11229-011-9911-yCopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 31-10-2023Synthese (2012) 186:615–617DOI 10.1007/s11229-011-9911-yNew logical perspectives on physicsJohan van Benthem · Sonja SmetsReceived: 19 February 2011 / Accepted: 19 February 2011 / Published online: 22 April 2011© The Author(s) 2011. This article is published with open access at Springerlink.comThis special issue is situated at the interface between Logic and the Foundations ofPhysics. 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 generallogical structure of physical theories. In recent years, more themes have come to thefore, and we may be witnessing a revival. The papers presented here emanate from asymposium held at the University of Utrecht in January 2008 with the aim of chartingestablished as well as new connections between the two fields. One of the main ques-tions discussed was whether and how modern techniques coming from logic, computerscience and information theory might be combined with state-of-the-art insights in thephilosophy of physics to gain a better understanding of the main foundational issuesand open problems in modern physics. The success of this symposium has shown thatthere are several possible answers to this question. The invited papers in this issuepresent the reader with an overview of the main topics at play right now. A commonJ. van BenthemInstitute for Logic, Language & Computation (ILLC), University of Amsterdam,P.O. Box 94242, 1090 GE Amsterdam, The Netherlandse-mail: johan@science.uva.nlJ. van BenthemDepartment of Philosophy, Stanford University,Stanford, CA 94305, USAS. Smets (B)Department of Artificial Intelligence, University of Groningen,Postbus 407, 9700 AK Groningen, The Netherlandse-mail: S.J.L.Smets@rug.nlS. SmetsDepartment of Philosophy, University of Groningen,Postbus 407, 9700 AK Groningen, The Netherlands123616 Synthese (2012) 186:615–617feature is that all authors make essential use of logical and formal methods in physicsand point out new interesting connections between the two fields.Research in logic has made essential progress in the last decades, along manydimensions that seem relevant to the foundations of physics. One conspicuous strandconcerns mathematical depth. Much traditional research in the foundations of mathe-matics has now begun to blend with powerful more mainstream mathematical devel-opments in algebra, category theory and other fields, making logical techniques morewidely available in mathematics and, in principle also, mathematical physics. Anothernoticeable trend is an ever-growing amalgam of logic and formal theories of compu-tation and processes—perhaps the bulk of logic research as pursued today—rangingfrom modal logics (spatial logic, dynamic logic and temporal logic of actions) to proof-theory-inspired linear logic and other resource-sensitive logics, game logics, processalgebras, coalgebraic logics, etcetera. Finally, there has also been an extension ofdescriptive coverage in another direction, with what has been called a “dynamic turn”toward interaction and communication between intelligent agents, bringing logic intouch with artificial intelligence, game theory, social choice theory, linguistics, cog-nitive 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. Forinstance, modal and spatial logics can provide efficient formal tools to talk about thequalitative temporal and spatial evolution of dynamical systems. These logics canhandle a large variety of interactive properties of processes and they can also be usedto 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 someof these developments by highlighting new logical perspectives on spatial structures.This reflects the larger emerging area documented in the “Handbook of Spatial Log-ics”, edited by M. Aiello, J. van Benthem and I. Pratt-Hartmann (Springer, Dordrecht2008).Another current trend in logic of potential interest for physics and the philosophyof physics, is reflected in the paper by H. Andréka, J. Madarasz, I. Németi andG. Székely on “A Logic Road from Special Relativity to General Relativity”. Inspiredby the grand traditions of algebraic logic and classical model theory in the study ofgeometry, the authors present a detailed first-order analysis of the structure of bothSpecial and general relativity theory, throwing surprising new light on their not alwaysevident logical connections. This paper is at the same time a characteristic sample ofthe ‘Budapest School’ at the interface of logic, space-time geometry, and physics.Another recent trend in Logic combines the use of proof theory and categoricallogic with insights from the foundations of physics, as pursued in the Oxford projectsof S. Abramsky and B. Coecke. The paper of B. Coecke and R.W. Spekkens on “Pic-turing Classical and Quantum Bayesian Inference” takes this categorical line of workone step further into the direction of a graphical representation of Bayesian inferenceand quantum causal relations. Another topic in this line of research, is the paper byS. Abramsky on “Big Toy Models” in which the author shows how Chu spaces can beused to represent physical systems including both classical and quantum systems.A next trend of interest relates to intuitionistic logic and Heyting algebra, i.e., theconstructive foundations of mathematics, now brought to bear on the foundationsof quantum physics. The paper by C. Heunen, N.P. Landsman and B. Spitters on123Synthese (2012) 186:615–617 617“Bohrification of Operator Algebras and Quantum Logic” shows how an intuitionisticapproach can shed new light on the difficulties and problems of traditional quantumlogic. While traditional quantum logic has its merits, it also confronts us with deepquestions that touch upon the roots of logic itself. In particular the original workof Birkhoff and von Neumann has left both philosophers and logicians wonderingwhether empirical theories like quantum physics can really provide principled weak-ening of our classical logical principles.While the preceding paper opts for the intuitionistic approach of weakening clas-sical logic, the paper “The Dynamic Turn in Quantum Logic” by A. Baltag andS. Smets connects traditional quantum logic with the above-mentioned dynamic turn inlogic. It shows how the non-classical character of quantum logic can also be diagnosedquite differently, as the result of bringing dynamic actions of measurement on suitablequantum information systems explicitly into the logic. The result is a classical propo-sitional logic with explicit operators for quantum measurement actions by observingagents, creating one more interface between logic, physics and computation.Finally, the latter direction of work ties in nicely with the survey paper of J. vanBenthem on “The Logic of Empirical Theories Revisited”. The author first looks atthe interface of logic and philosophy of science as it has functioned over the lastcentury, and recalls some of its main trends. He then argues that bringing in agencyand informational action explicitly into logical systems leads to an overhaul of formalmodels in the philosophy of science, bringing it much closer to the actual dynamicsof observation, communication, and other activities that make up scientific inquiry.All logical methods in this volume reach beyond traditional styles of formalizingphysical 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 theyhave much more common ground than is often supposed. But we do not just see thisas a one-way street of importing ideas. While new logical methods may be of rele-vance to physics, we are also well aware that physical models of information flow andeven social behaviour may come to form a natural companion to existing logical andcomputational ones.These are just our editorial views: now the authors will take the stage, and we aregrateful for what they have provided so generously in the following pages. We alsotake this opportunity to thank all participants of the 2008 Symposium on Logic andPhysics held at Utrecht University. Special thanks go to our fellow members of theorganizing committee : Dennis Dieks, Anne Kox, and Albert Visser. Finally, we arehappy to mention the sponsors who made this Symposium possible: The Evert WillemBeth Stichting, The Heyting Stichting, and the Disciplinegroep Theoretische Filosofieat the University of Utrecht.Open Access This article is distributed under the terms of the Creative Commons Attribution Noncom-mercial License which permits any noncommercial use, distribution, and reproduction in any medium,provided the original author(s) and source are credited.123

Dissertations of the University of Groningen

   University of GroningenNew logical perspectives on physicsvan Benthem, Johan; Smets, SonjaPublished in:SyntheseDOI:10.1007/s11229-011-9911-yIMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2012Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):van Benthem, J., & Smets, S. (2012). New logical perspectives on physics. Synthese, 186(3), 615-617.https://doi.org/10.1007/s11229-011-9911-yCopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 29-12-2022Synthese (2012) 186:615–617DOI 10.1007/s11229-011-9911-yNew logical perspectives on physicsJohan van Benthem · Sonja SmetsReceived: 19 February 2011 / Accepted: 19 February 2011 / Published online: 22 April 2011© The Author(s) 2011. This article is published with open access at Springerlink.comThis special issue is situated at the interface between Logic and the Foundations ofPhysics. 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 generallogical structure of physical theories. In recent years, more themes have come to thefore, and we may be witnessing a revival. The papers presented here emanate from asymposium held at the University of Utrecht in January 2008 with the aim of chartingestablished as well as new connections between the two fields. One of the main ques-tions discussed was whether and how modern techniques coming from logic, computerscience and information theory might be combined with state-of-the-art insights in thephilosophy of physics to gain a better understanding of the main foundational issuesand open problems in modern physics. The success of this symposium has shown thatthere are several possible answers to this question. The invited papers in this issuepresent the reader with an overview of the main topics at play right now. A commonJ. van BenthemInstitute for Logic, Language & Computation (ILLC), University of Amsterdam,P.O. Box 94242, 1090 GE Amsterdam, The Netherlandse-mail: johan@science.uva.nlJ. van BenthemDepartment of Philosophy, Stanford University,Stanford, CA 94305, USAS. Smets (B)Department of Artificial Intelligence, University of Groningen,Postbus 407, 9700 AK Groningen, The Netherlandse-mail: S.J.L.Smets@rug.nlS. SmetsDepartment of Philosophy, University of Groningen,Postbus 407, 9700 AK Groningen, The Netherlands123616 Synthese (2012) 186:615–617feature is that all authors make essential use of logical and formal methods in physicsand point out new interesting connections between the two fields.Research in logic has made essential progress in the last decades, along manydimensions that seem relevant to the foundations of physics. One conspicuous strandconcerns mathematical depth. Much traditional research in the foundations of mathe-matics has now begun to blend with powerful more mainstream mathematical devel-opments in algebra, category theory and other fields, making logical techniques morewidely available in mathematics and, in principle also, mathematical physics. Anothernoticeable trend is an ever-growing amalgam of logic and formal theories of compu-tation and processes—perhaps the bulk of logic research as pursued today—rangingfrom modal logics (spatial logic, dynamic logic and temporal logic of actions) to proof-theory-inspired linear logic and other resource-sensitive logics, game logics, processalgebras, coalgebraic logics, etcetera. Finally, there has also been an extension ofdescriptive coverage in another direction, with what has been called a “dynamic turn”toward interaction and communication between intelligent agents, bringing logic intouch with artificial intelligence, game theory, social choice theory, linguistics, cog-nitive 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. Forinstance, modal and spatial logics can provide efficient formal tools to talk about thequalitative temporal and spatial evolution of dynamical systems. These logics canhandle a large variety of interactive properties of processes and they can also be usedto 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 someof these developments by highlighting new logical perspectives on spatial structures.This reflects the larger emerging area documented in the “Handbook of Spatial Log-ics”, edited by M. Aiello, J. van Benthem and I. Pratt-Hartmann (Springer, Dordrecht2008).Another current trend in logic of potential interest for physics and the philosophyof physics, is reflected in the paper by H. Andréka, J. Madarasz, I. Németi andG. Székely on “A Logic Road from Special Relativity to General Relativity”. Inspiredby the grand traditions of algebraic logic and classical model theory in the study ofgeometry, the authors present a detailed first-order analysis of the structure of bothSpecial and general relativity theory, throwing surprising new light on their not alwaysevident logical connections. This paper is at the same time a characteristic sample ofthe ‘Budapest School’ at the interface of logic, space-time geometry, and physics.Another recent trend in Logic combines the use of proof theory and categoricallogic with insights from the foundations of physics, as pursued in the Oxford projectsof S. Abramsky and B. Coecke. The paper of B. Coecke and R.W. Spekkens on “Pic-turing Classical and Quantum Bayesian Inference” takes this categorical line of workone step further into the direction of a graphical representation of Bayesian inferenceand quantum causal relations. Another topic in this line of research, is the paper byS. Abramsky on “Big Toy Models” in which the author shows how Chu spaces can beused to represent physical systems including both classical and quantum systems.A next trend of interest relates to intuitionistic logic and Heyting algebra, i.e., theconstructive foundations of mathematics, now brought to bear on the foundationsof quantum physics. The paper by C. Heunen, N.P. Landsman and B. Spitters on123Synthese (2012) 186:615–617 617“Bohrification of Operator Algebras and Quantum Logic” shows how an intuitionisticapproach can shed new light on the difficulties and problems of traditional quantumlogic. While traditional quantum logic has its merits, it also confronts us with deepquestions that touch upon the roots of logic itself. In particular the original workof Birkhoff and von Neumann has left both philosophers and logicians wonderingwhether empirical theories like quantum physics can really provide principled weak-ening of our classical logical principles.While the preceding paper opts for the intuitionistic approach of weakening clas-sical logic, the paper “The Dynamic Turn in Quantum Logic” by A. Baltag andS. Smets connects traditional quantum logic with the above-mentioned dynamic turn inlogic. It shows how the non-classical character of quantum logic can also be diagnosedquite differently, as the result of bringing dynamic actions of measurement on suitablequantum information systems explicitly into the logic. The result is a classical propo-sitional logic with explicit operators for quantum measurement actions by observingagents, creating one more interface between logic, physics and computation.Finally, the latter direction of work ties in nicely with the survey paper of J. vanBenthem on “The Logic of Empirical Theories Revisited”. The author first looks atthe interface of logic and philosophy of science as it has functioned over the lastcentury, and recalls some of its main trends. He then argues that bringing in agencyand informational action explicitly into logical systems leads to an overhaul of formalmodels in the philosophy of science, bringing it much closer to the actual dynamicsof observation, communication, and other activities that make up scientific inquiry.All logical methods in this volume reach beyond traditional styles of formalizingphysical 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 theyhave much more common ground than is often supposed. But we do not just see thisas a one-way street of importing ideas. While new logical methods may be of rele-vance to physics, we are also well aware that physical models of information flow andeven social behaviour may come to form a natural companion to existing logical andcomputational ones.These are just our editorial views: now the authors will take the stage, and we aregrateful for what they have provided so generously in the following pages. We alsotake this opportunity to thank all participants of the 2008 Symposium on Logic andPhysics held at Utrecht University. Special thanks go to our fellow members of theorganizing committee : Dennis Dieks, Anne Kox, and Albert Visser. Finally, we arehappy to mention the sponsors who made this Symposium possible: The Evert WillemBeth Stichting, The Heyting Stichting, and the Disciplinegroep Theoretische Filosofieat the University of Utrecht.Open Access This article is distributed under the terms of the Creative Commons Attribution Noncom-mercial License which permits any noncommercial use, distribution, and reproduction in any medium,provided the original author(s) and source are credited.123

   University of GroningenNew logical perspectives on physicsvan Benthem, Johan; Smets, SonjaPublished in:SyntheseDOI:10.1007/s11229-011-9911-yIMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2012Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):van Benthem, J., & Smets, S. (2012). New logical perspectives on physics. Synthese, 186(3), 615-617.https://doi.org/10.1007/s11229-011-9911-yCopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 09-09-2023Synthese (2012) 186:615–617DOI 10.1007/s11229-011-9911-yNew logical perspectives on physicsJohan van Benthem · Sonja SmetsReceived: 19 February 2011 / Accepted: 19 February 2011 / Published online: 22 April 2011© The Author(s) 2011. This article is published with open access at Springerlink.comThis special issue is situated at the interface between Logic and the Foundations ofPhysics. 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 generallogical structure of physical theories. In recent years, more themes have come to thefore, and we may be witnessing a revival. The papers presented here emanate from asymposium held at the University of Utrecht in January 2008 with the aim of chartingestablished as well as new connections between the two fields. One of the main ques-tions discussed was whether and how modern techniques coming from logic, computerscience and information theory might be combined with state-of-the-art insights in thephilosophy of physics to gain a better understanding of the main foundational issuesand open problems in modern physics. The success of this symposium has shown thatthere are several possible answers to this question. The invited papers in this issuepresent the reader with an overview of the main topics at play right now. A commonJ. van BenthemInstitute for Logic, Language & Computation (ILLC), University of Amsterdam,P.O. Box 94242, 1090 GE Amsterdam, The Netherlandse-mail: johan@science.uva.nlJ. van BenthemDepartment of Philosophy, Stanford University,Stanford, CA 94305, USAS. Smets (B)Department of Artificial Intelligence, University of Groningen,Postbus 407, 9700 AK Groningen, The Netherlandse-mail: S.J.L.Smets@rug.nlS. SmetsDepartment of Philosophy, University of Groningen,Postbus 407, 9700 AK Groningen, The Netherlands123616 Synthese (2012) 186:615–617feature is that all authors make essential use of logical and formal methods in physicsand point out new interesting connections between the two fields.Research in logic has made essential progress in the last decades, along manydimensions that seem relevant to the foundations of physics. One conspicuous strandconcerns mathematical depth. Much traditional research in the foundations of mathe-matics has now begun to blend with powerful more mainstream mathematical devel-opments in algebra, category theory and other fields, making logical techniques morewidely available in mathematics and, in principle also, mathematical physics. Anothernoticeable trend is an ever-growing amalgam of logic and formal theories of compu-tation and processes—perhaps the bulk of logic research as pursued today—rangingfrom modal logics (spatial logic, dynamic logic and temporal logic of actions) to proof-theory-inspired linear logic and other resource-sensitive logics, game logics, processalgebras, coalgebraic logics, etcetera. Finally, there has also been an extension ofdescriptive coverage in another direction, with what has been called a “dynamic turn”toward interaction and communication between intelligent agents, bringing logic intouch with artificial intelligence, game theory, social choice theory, linguistics, cog-nitive 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. Forinstance, modal and spatial logics can provide efficient formal tools to talk about thequalitative temporal and spatial evolution of dynamical systems. These logics canhandle a large variety of interactive properties of processes and they can also be usedto 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 someof these developments by highlighting new logical perspectives on spatial structures.This reflects the larger emerging area documented in the “Handbook of Spatial Log-ics”, edited by M. Aiello, J. van Benthem and I. Pratt-Hartmann (Springer, Dordrecht2008).Another current trend in logic of potential interest for physics and the philosophyof physics, is reflected in the paper by H. Andréka, J. Madarasz, I. Németi andG. Székely on “A Logic Road from Special Relativity to General Relativity”. Inspiredby the grand traditions of algebraic logic and classical model theory in the study ofgeometry, the authors present a detailed first-order analysis of the structure of bothSpecial and general relativity theory, throwing surprising new light on their not alwaysevident logical connections. This paper is at the same time a characteristic sample ofthe ‘Budapest School’ at the interface of logic, space-time geometry, and physics.Another recent trend in Logic combines the use of proof theory and categoricallogic with insights from the foundations of physics, as pursued in the Oxford projectsof S. Abramsky and B. Coecke. The paper of B. Coecke and R.W. Spekkens on “Pic-turing Classical and Quantum Bayesian Inference” takes this categorical line of workone step further into the direction of a graphical representation of Bayesian inferenceand quantum causal relations. Another topic in this line of research, is the paper byS. Abramsky on “Big Toy Models” in which the author shows how Chu spaces can beused to represent physical systems including both classical and quantum systems.A next trend of interest relates to intuitionistic logic and Heyting algebra, i.e., theconstructive foundations of mathematics, now brought to bear on the foundationsof quantum physics. The paper by C. Heunen, N.P. Landsman and B. Spitters on123Synthese (2012) 186:615–617 617“Bohrification of Operator Algebras and Quantum Logic” shows how an intuitionisticapproach can shed new light on the difficulties and problems of traditional quantumlogic. While traditional quantum logic has its merits, it also confronts us with deepquestions that touch upon the roots of logic itself. In particular the original workof Birkhoff and von Neumann has left both philosophers and logicians wonderingwhether empirical theories like quantum physics can really provide principled weak-ening of our classical logical principles.While the preceding paper opts for the intuitionistic approach of weakening clas-sical logic, the paper “The Dynamic Turn in Quantum Logic” by A. Baltag andS. Smets connects traditional quantum logic with the above-mentioned dynamic turn inlogic. It shows how the non-classical character of quantum logic can also be diagnosedquite differently, as the result of bringing dynamic actions of measurement on suitablequantum information systems explicitly into the logic. The result is a classical propo-sitional logic with explicit operators for quantum measurement actions by observingagents, creating one more interface between logic, physics and computation.Finally, the latter direction of work ties in nicely with the survey paper of J. vanBenthem on “The Logic of Empirical Theories Revisited”. The author first looks atthe interface of logic and philosophy of science as it has functioned over the lastcentury, and recalls some of its main trends. He then argues that bringing in agencyand informational action explicitly into logical systems leads to an overhaul of formalmodels in the philosophy of science, bringing it much closer to the actual dynamicsof observation, communication, and other activities that make up scientific inquiry.All logical methods in this volume reach beyond traditional styles of formalizingphysical 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 theyhave much more common ground than is often supposed. But we do not just see thisas a one-way street of importing ideas. While new logical methods may be of rele-vance to physics, we are also well aware that physical models of information flow andeven social behaviour may come to form a natural companion to existing logical andcomputational ones.These are just our editorial views: now the authors will take the stage, and we aregrateful for what they have provided so generously in the following pages. We alsotake this opportunity to thank all participants of the 2008 Symposium on Logic andPhysics held at Utrecht University. Special thanks go to our fellow members of theorganizing committee : Dennis Dieks, Anne Kox, and Albert Visser. Finally, we arehappy to mention the sponsors who made this Symposium possible: The Evert WillemBeth Stichting, The Heyting Stichting, and the Disciplinegroep Theoretische Filosofieat the University of Utrecht.Open Access This article is distributed under the terms of the Creative Commons Attribution Noncom-mercial License which permits any noncommercial use, distribution, and reproduction in any medium,provided the original author(s) and source are credited.123

International Migration, Integration and Social Cohesion online publications

UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl)UvA-DARE (Digital Academic Repository)New logical perspectives on physicsvan Benthem, J.; Smets, S.DOI10.1007/s11229-011-9911-yPublication date2012Document VersionFinal published versionPublished inSyntheseLink to publicationCitation for published version (APA):van Benthem, J., & Smets, S. (2012). New logical perspectives on physics. Synthese, 186(3),615-617. https://doi.org/10.1007/s11229-011-9911-yGeneral rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s)and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an opencontent license (like Creative Commons).Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, pleaselet the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the materialinaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letterto: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. Youwill be contacted as soon as possible.Download date:26 Jul 2022Synthese (2012) 186:615–617DOI 10.1007/s11229-011-9911-yNew logical perspectives on physicsJohan van Benthem · Sonja SmetsReceived: 19 February 2011 / Accepted: 19 February 2011 / Published online: 22 April 2011© The Author(s) 2011. This article is published with open access at Springerlink.comThis special issue is situated at the interface between Logic and the Foundations ofPhysics. 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 generallogical structure of physical theories. In recent years, more themes have come to thefore, and we may be witnessing a revival. The papers presented here emanate from asymposium held at the University of Utrecht in January 2008 with the aim of chartingestablished as well as new connections between the two fields. One of the main ques-tions discussed was whether and how modern techniques coming from logic, computerscience and information theory might be combined with state-of-the-art insights in thephilosophy of physics to gain a better understanding of the main foundational issuesand open problems in modern physics. The success of this symposium has shown thatthere are several possible answers to this question. The invited papers in this issuepresent the reader with an overview of the main topics at play right now. A commonJ. van BenthemInstitute for Logic, Language & Computation (ILLC), University of Amsterdam,P.O. Box 94242, 1090 GE Amsterdam, The Netherlandse-mail: johan@science.uva.nlJ. van BenthemDepartment of Philosophy, Stanford University,Stanford, CA 94305, USAS. Smets (B)Department of Artificial Intelligence, University of Groningen,Postbus 407, 9700 AK Groningen, The Netherlandse-mail: S.J.L.Smets@rug.nlS. SmetsDepartment of Philosophy, University of Groningen,Postbus 407, 9700 AK Groningen, The Netherlands123616 Synthese (2012) 186:615–617feature is that all authors make essential use of logical and formal methods in physicsand point out new interesting connections between the two fields.Research in logic has made essential progress in the last decades, along manydimensions that seem relevant to the foundations of physics. One conspicuous strandconcerns mathematical depth. Much traditional research in the foundations of mathe-matics has now begun to blend with powerful more mainstream mathematical devel-opments in algebra, category theory and other fields, making logical techniques morewidely available in mathematics and, in principle also, mathematical physics. Anothernoticeable trend is an ever-growing amalgam of logic and formal theories of compu-tation and processes—perhaps the bulk of logic research as pursued today—rangingfrom modal logics (spatial logic, dynamic logic and temporal logic of actions) to proof-theory-inspired linear logic and other resource-sensitive logics, game logics, processalgebras, coalgebraic logics, etcetera. Finally, there has also been an extension ofdescriptive coverage in another direction, with what has been called a “dynamic turn”toward interaction and communication between intelligent agents, bringing logic intouch with artificial intelligence, game theory, social choice theory, linguistics, cog-nitive 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. Forinstance, modal and spatial logics can provide efficient formal tools to talk about thequalitative temporal and spatial evolution of dynamical systems. These logics canhandle a large variety of interactive properties of processes and they can also be usedto 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 someof these developments by highlighting new logical perspectives on spatial structures.This reflects the larger emerging area documented in the “Handbook of Spatial Log-ics”, edited by M. Aiello, J. van Benthem and I. Pratt-Hartmann (Springer, Dordrecht2008).Another current trend in logic of potential interest for physics and the philosophyof physics, is reflected in the paper by H. Andréka, J. Madarasz, I. Németi andG. Székely on “A Logic Road from Special Relativity to General Relativity”. Inspiredby the grand traditions of algebraic logic and classical model theory in the study ofgeometry, the authors present a detailed first-order analysis of the structure of bothSpecial and general relativity theory, throwing surprising new light on their not alwaysevident logical connections. This paper is at the same time a characteristic sample ofthe ‘Budapest School’ at the interface of logic, space-time geometry, and physics.Another recent trend in Logic combines the use of proof theory and categoricallogic with insights from the foundations of physics, as pursued in the Oxford projectsof S. Abramsky and B. Coecke. The paper of B. Coecke and R.W. Spekkens on “Pic-turing Classical and Quantum Bayesian Inference” takes this categorical line of workone step further into the direction of a graphical representation of Bayesian inferenceand quantum causal relations. Another topic in this line of research, is the paper byS. Abramsky on “Big Toy Models” in which the author shows how Chu spaces can beused to represent physical systems including both classical and quantum systems.A next trend of interest relates to intuitionistic logic and Heyting algebra, i.e., theconstructive foundations of mathematics, now brought to bear on the foundationsof quantum physics. The paper by C. Heunen, N.P. Landsman and B. Spitters on123Synthese (2012) 186:615–617 617“Bohrification of Operator Algebras and Quantum Logic” shows how an intuitionisticapproach can shed new light on the difficulties and problems of traditional quantumlogic. While traditional quantum logic has its merits, it also confronts us with deepquestions that touch upon the roots of logic itself. In particular the original workof Birkhoff and von Neumann has left both philosophers and logicians wonderingwhether empirical theories like quantum physics can really provide principled weak-ening of our classical logical principles.While the preceding paper opts for the intuitionistic approach of weakening clas-sical logic, the paper “The Dynamic Turn in Quantum Logic” by A. Baltag andS. Smets connects traditional quantum logic with the above-mentioned dynamic turn inlogic. It shows how the non-classical character of quantum logic can also be diagnosedquite differently, as the result of bringing dynamic actions of measurement on suitablequantum information systems explicitly into the logic. The result is a classical propo-sitional logic with explicit operators for quantum measurement actions by observingagents, creating one more interface between logic, physics and computation.Finally, the latter direction of work ties in nicely with the survey paper of J. vanBenthem on “The Logic of Empirical Theories Revisited”. The author first looks atthe interface of logic and philosophy of science as it has functioned over the lastcentury, and recalls some of its main trends. He then argues that bringing in agencyand informational action explicitly into logical systems leads to an overhaul of formalmodels in the philosophy of science, bringing it much closer to the actual dynamicsof observation, communication, and other activities that make up scientific inquiry.All logical methods in this volume reach beyond traditional styles of formalizingphysical 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 theyhave much more common ground than is often supposed. But we do not just see thisas a one-way street of importing ideas. While new logical methods may be of rele-vance to physics, we are also well aware that physical models of information flow andeven social behaviour may come to form a natural companion to existing logical andcomputational ones.These are just our editorial views: now the authors will take the stage, and we aregrateful for what they have provided so generously in the following pages. We alsotake this opportunity to thank all participants of the 2008 Symposium on Logic andPhysics held at Utrecht University. Special thanks go to our fellow members of theorganizing committee : Dennis Dieks, Anne Kox, and Albert Visser. Finally, we arehappy to mention the sponsors who made this Symposium possible: The Evert WillemBeth Stichting, The Heyting Stichting, and the Disciplinegroep Theoretische Filosofieat the University of Utrecht.Open Access This article is distributed under the terms of the Creative Commons Attribution Noncom-mercial License which permits any noncommercial use, distribution, and reproduction in any medium,provided the original author(s) and source are credited.123

   University of GroningenNew logical perspectives on physicsvan Benthem, Johan; Smets, SonjaPublished in:SyntheseDOI:10.1007/s11229-011-9911-yIMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2012Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):van Benthem, J., & Smets, S. (2012). New logical perspectives on physics. Synthese, 186(3), 615-617.https://doi.org/10.1007/s11229-011-9911-yCopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 11-12-2022Synthese (2012) 186:615–617DOI 10.1007/s11229-011-9911-yNew logical perspectives on physicsJohan van Benthem · Sonja SmetsReceived: 19 February 2011 / Accepted: 19 February 2011 / Published online: 22 April 2011© The Author(s) 2011. This article is published with open access at Springerlink.comThis special issue is situated at the interface between Logic and the Foundations ofPhysics. 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 generallogical structure of physical theories. In recent years, more themes have come to thefore, and we may be witnessing a revival. The papers presented here emanate from asymposium held at the University of Utrecht in January 2008 with the aim of chartingestablished as well as new connections between the two fields. One of the main ques-tions discussed was whether and how modern techniques coming from logic, computerscience and information theory might be combined with state-of-the-art insights in thephilosophy of physics to gain a better understanding of the main foundational issuesand open problems in modern physics. The success of this symposium has shown thatthere are several possible answers to this question. The invited papers in this issuepresent the reader with an overview of the main topics at play right now. A commonJ. van BenthemInstitute for Logic, Language & Computation (ILLC), University of Amsterdam,P.O. Box 94242, 1090 GE Amsterdam, The Netherlandse-mail: johan@science.uva.nlJ. van BenthemDepartment of Philosophy, Stanford University,Stanford, CA 94305, USAS. Smets (B)Department of Artificial Intelligence, University of Groningen,Postbus 407, 9700 AK Groningen, The Netherlandse-mail: S.J.L.Smets@rug.nlS. SmetsDepartment of Philosophy, University of Groningen,Postbus 407, 9700 AK Groningen, The Netherlands123616 Synthese (2012) 186:615–617feature is that all authors make essential use of logical and formal methods in physicsand point out new interesting connections between the two fields.Research in logic has made essential progress in the last decades, along manydimensions that seem relevant to the foundations of physics. One conspicuous strandconcerns mathematical depth. Much traditional research in the foundations of mathe-matics has now begun to blend with powerful more mainstream mathematical devel-opments in algebra, category theory and other fields, making logical techniques morewidely available in mathematics and, in principle also, mathematical physics. Anothernoticeable trend is an ever-growing amalgam of logic and formal theories of compu-tation and processes—perhaps the bulk of logic research as pursued today—rangingfrom modal logics (spatial logic, dynamic logic and temporal logic of actions) to proof-theory-inspired linear logic and other resource-sensitive logics, game logics, processalgebras, coalgebraic logics, etcetera. Finally, there has also been an extension ofdescriptive coverage in another direction, with what has been called a “dynamic turn”toward interaction and communication between intelligent agents, bringing logic intouch with artificial intelligence, game theory, social choice theory, linguistics, cog-nitive 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. Forinstance, modal and spatial logics can provide efficient formal tools to talk about thequalitative temporal and spatial evolution of dynamical systems. These logics canhandle a large variety of interactive properties of processes and they can also be usedto 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 someof these developments by highlighting new logical perspectives on spatial structures.This reflects the larger emerging area documented in the “Handbook of Spatial Log-ics”, edited by M. Aiello, J. van Benthem and I. Pratt-Hartmann (Springer, Dordrecht2008).Another current trend in logic of potential interest for physics and the philosophyof physics, is reflected in the paper by H. Andréka, J. Madarasz, I. Németi andG. Székely on “A Logic Road from Special Relativity to General Relativity”. Inspiredby the grand traditions of algebraic logic and classical model theory in the study ofgeometry, the authors present a detailed first-order analysis of the structure of bothSpecial and general relativity theory, throwing surprising new light on their not alwaysevident logical connections. This paper is at the same time a characteristic sample ofthe ‘Budapest School’ at the interface of logic, space-time geometry, and physics.Another recent trend in Logic combines the use of proof theory and categoricallogic with insights from the foundations of physics, as pursued in the Oxford projectsof S. Abramsky and B. Coecke. The paper of B. Coecke and R.W. Spekkens on “Pic-turing Classical and Quantum Bayesian Inference” takes this categorical line of workone step further into the direction of a graphical representation of Bayesian inferenceand quantum causal relations. Another topic in this line of research, is the paper byS. Abramsky on “Big Toy Models” in which the author shows how Chu spaces can beused to represent physical systems including both classical and quantum systems.A next trend of interest relates to intuitionistic logic and Heyting algebra, i.e., theconstructive foundations of mathematics, now brought to bear on the foundationsof quantum physics. The paper by C. Heunen, N.P. Landsman and B. Spitters on123Synthese (2012) 186:615–617 617“Bohrification of Operator Algebras and Quantum Logic” shows how an intuitionisticapproach can shed new light on the difficulties and problems of traditional quantumlogic. While traditional quantum logic has its merits, it also confronts us with deepquestions that touch upon the roots of logic itself. In particular the original workof Birkhoff and von Neumann has left both philosophers and logicians wonderingwhether empirical theories like quantum physics can really provide principled weak-ening of our classical logical principles.While the preceding paper opts for the intuitionistic approach of weakening clas-sical logic, the paper “The Dynamic Turn in Quantum Logic” by A. Baltag andS. Smets connects traditional quantum logic with the above-mentioned dynamic turn inlogic. It shows how the non-classical character of quantum logic can also be diagnosedquite differently, as the result of bringing dynamic actions of measurement on suitablequantum information systems explicitly into the logic. The result is a classical propo-sitional logic with explicit operators for quantum measurement actions by observingagents, creating one more interface between logic, physics and computation.Finally, the latter direction of work ties in nicely with the survey paper of J. vanBenthem on “The Logic of Empirical Theories Revisited”. The author first looks atthe interface of logic and philosophy of science as it has functioned over the lastcentury, and recalls some of its main trends. He then argues that bringing in agencyand informational action explicitly into logical systems leads to an overhaul of formalmodels in the philosophy of science, bringing it much closer to the actual dynamicsof observation, communication, and other activities that make up scientific inquiry.All logical methods in this volume reach beyond traditional styles of formalizingphysical 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 theyhave much more common ground than is often supposed. But we do not just see thisas a one-way street of importing ideas. While new logical methods may be of rele-vance to physics, we are also well aware that physical models of information flow andeven social behaviour may come to form a natural companion to existing logical andcomputational ones.These are just our editorial views: now the authors will take the stage, and we aregrateful for what they have provided so generously in the following pages. We alsotake this opportunity to thank all participants of the 2008 Symposium on Logic andPhysics held at Utrecht University. Special thanks go to our fellow members of theorganizing committee : Dennis Dieks, Anne Kox, and Albert Visser. Finally, we arehappy to mention the sponsors who made this Symposium possible: The Evert WillemBeth Stichting, The Heyting Stichting, and the Disciplinegroep Theoretische Filosofieat the University of Utrecht.Open Access This article is distributed under the terms of the Creative Commons Attribution Noncom-mercial License which permits any noncommercial use, distribution, and reproduction in any medium,provided the original author(s) and source are credited.123

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