Johan van Benthem A dynamic life in logic On the occasion of his retirement from the University of Amsterdam

Transcription

1 Johan van Benthem A dynamic life in logic On the occasion of his retirement from the University of Amsterdam

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3 The Institute for Logic, Language and Computation 3

4 4 History The history of the ILLC goes back to the late 1970s, when a group of younger researchers in mathematical logic, Philosophy of Language, and Theoretical Computer Science started cooperating on the shared theme of Montague grammar. The biannual Amsterdam Colloquium is a living testimony to this original cooperation: the year 2013 marks the 19th installment of the colloquium. As a formal organization the institute was created in 1986 by groups within the Faculty of Mathematics and Computer Science and the Faculty of Philosophy. In 1989 a Computational Linguistics group from the faculty of Humanities joined the institute, followed by the Programming Research group of the Faculty of Mathematics and Computer Science which participated from 1991 until The institute, which originally was named Instituut voor Taal, Logica en Informatie (ITLI), obtained its present name in 1991 when it became an official University Research Institute. Most of the original founders in the mean time had obtained professorships in the various departments. The ILLC has cooperated with several other groups during the course of its history. A loose association with the Applied Logic Lab in the Faculty of Social Science, which grew out of the Pioneer project granted to M. Masuch, was turned into a full membership in 1996 which was terminated in 2004 when this group was dissolved. Another important development was the granting of the Spinoza award to our first director Johan van Benthem; he used his award for building his program Logic in Action incorporating three subprograms, called Computational Logic, chaired by Maarten de Rijke, Logic and Communication chaired by Paul Dekker and Yde Venema, and Dissemination of Logic, chaired by Jan van Eijck. The group of Maarten de Rijke eventually became the Intelligent Systems Lab which was moved to the Institute of Informatics in 2004 when Maarten de Rijke became professor for Internet Technology in that institute. The ILLC started activities in the area of Cognitive Science already in 1993 with the Pionier project of Michiel van Lambalgen on Reasoning with Uncertainty. Later the institute became a participant in the activities of the Cognitive Science Center of the Universiteit van Amsterdam (CSCA) program. It was within the ILLC that the twist towards a dynamic interpretation of logics nowadays known as the Amsterdam style was developed. Also the

5 statistically based school of language parsing named Data Oriented Parsing grew out of our research, with applications in music, other forms of art, and biology. For many years the ILLC was the administrator of the national Graduate program in Logic for Ph.D. students. In 1995 the Master program in Logic was established as the first international Master program at the University of Amsterdam; it became part of the regular University program in The Institute also was the host for the Marie Curie Ph.D. program Gloriclass during During the 20 years of its existence the ILLC has produced close to 200 Ph.D. students and a comparable number of master students, all in the area of logic and related topics. Most of the original founders of the Institute (R. Bartsch, P. van Emde Boas, A. Troelstra and R. Scha) have retired. Johan van Benthem, the first director of the Institute, was promoted to the prestigious position of University professor in He retires from this position in September 2014, but keeps his positions at the University of Stanford in California and at Tsinghua University in Beijing. 5 Scientific Mission The scientific mission of the Institute for Logic, Language and Computation (ILLC) is to study formal properties of information, viz. the logical structure and algorithmic properties of processes of encoding, transmitting and comprehending information. The latter notion is to be viewed in its broadest sense, covering not only the mathematical and algorithmic properties of formal languages, but also the flow of information in natural language processing, and human cognitive activities such as reasoning and music cognition. The research aim is to develop theories, logical systems and computational models that can handle this rich variety of information, making use of insights across such disciplines as linguistics, computer science (including artificial intelligence), philosophy, mathematics (including statistics), and cognitive science. The resulting view of information science transcends traditional boundaries in the univer- sity and the wider academic world. In addition to its specific research goals the ILLC aims to overcome such boundaries between faculties

6 6 and disciplines and to serve as a rallying point for information scientists across computer science, linguistics, mathematics, philosophy, and the social sciences. In particular, the ILLC strives to build strong alliances with local, national and international organisations that share this view. An important part of the mission of the ILLC concerns the education and training of a new generation of researchers in the interdisciplinary area of Logic, Language and Computation. The institute is strongly committed to its graduate programme, at the level of both MSc and PhD studies. More generally, the ILLC is also dedicated to the dissemination of its results, not only through specialised academic publications but also into the broader world of academic and general education, industrial research and the public debate. The three programmes Three ILLC Programmes The research at the ILLC comprises three programmes, each of which covers a broad area of logic and adjacent areas: Logic and Language (LoLa) This is a research programme in philosophical logic and the phi- losophy of language, crossing the borders with linguistics and cognitive science. The group takes human reasoning and the interpretation of natural language as the major themes, and logical and philosophical analysis as the basic scientific method. Logic and Computation (LoCo) This group strives to gain a deeper understanding of the nature of information and the processes of reasoning and interaction. The research of this group covers classical areas of mathematical logic, theoretical computer science, and artificial intelligence, but also ventures into economics and physics. Language and Computation (LaCo) Members of this group focus on computational and cog- nitive models of human information processing, especially natural language processing, music cognition, and information retrieval. This research concerns computational lin- guistics, cognitive science, and information science. The individual programmes have no uniform, fixed structure, but each consists of a small core of permanent scientific personnel (full, associate and

7 assistant professors), and a large, varying component of temporary personnel (postdocs and PhD students) in projects that are largely financed by external (i.e., non-university) sources. The research activities and output of these three groups will be described separately in this self-evaluation. 7 Unifying ILLC Themes Various kinds of cooperation between the three programmes take place as well. While this is generally dynamic and spontaneous in nature, one can identify a few clear common lines of research shared by the programmes. During the evaluation period, the two most prominent themes were the following: Logic & Games In the study of information, the concept, the development, but also the exchange of information are major topics. In this view, game theory and social aspects of information naturally come into play. Most strikingly, this has led to crucial contacts between logic and game theory, bringing an entirely new set of disciplines into the scope of logic: viz., economics and the social sciences. One particular area where interaction is crucial to intelligent behaviour is natural language, where notions from (evolutionary) game theory are used to chart the actual use of language between different agents. In fact, game-theoretic research methods permeate most areas covered by ILLC research, while on the other hand, formal properties of games themselves are objects of study at the ILLC. Cognitive Modelling While much of the research at the ILLC is abstract and seemingly far removed from everyday practice, there is the reality of human performance. Nowadays, disciplines such as neurophysiology and cognitive psychology are increasingly concerned with human information processing and make great progress in unravelling its underlying psychophysical mechanisms. These results are of immediate relevance to logic in the broad sense as it is conceived within the ILLC. Conversely, insights from logic turn out to be important for cognitive science and neurosciences, providing high-level models for cognitive functions, and leading to new questions and insights that suggest new experimentation at the level of brain processes. Also, computational

8 8 work done at the ILLC has witnessed a cognitive turn. In the fields of computational linguistics and music cognition, for example, the focus is on the development of computational models of human information processing that are cognitively plausible as well as practically useful. Of the many other recurrent themes running through the ILLC research we mention Modal Logic, Complexity Theory, Dynamic-Epistemic Logic, and Quantum Computing and Information Flow. Collaboration projects Within the University of Amsterdam, the ILLC has several on- going collaboration projects with other institutes, in particular with the Informatics Institute and the Amsterdam Center for Language and Communication. An important and long- standing external partner is the CWI (Center for Mathematics and Computation), four of whose researchers hold part-time professor positions at the ILLC. More recently, the ILLC is at the centre of a collaboration project between the Faculty of Humanities with the KNAW (Royal Netherlands Academy of Arts and Sciences) and the VU (Vrije Universiteit) in the area of Digital Humanties.

9 The China Connection: Joint Research in Logic 9

10 10 Joint research center in logic After several years of successful cooperation, Tsinghua University and the University of Amsterdam have decided to stengthen their ties in the form of a joint research center for logic, the first of its kind between The Netherlands and China. The aim of the centre is to create an active interface between the ILLC and the community at Tsinghua and elsewhere to further a broad interdisciplinary conception of logic, and act as a bridge for contacts between China and the international community. Activities include collaborative research projects including joint publications, mutual visits, etc. exchanging teachers for concentrated courses and seminars, exchanging students. developing a joint Tsinghua UvA graduate program in logic. new publication initiatives. meetings, workshops, strategic international flagship events. new funding proposals for research projects, center infrastructure, outreach. Meantime, the center also acts as a hub for collaboration with individual logicians and groups in China, and a league of congenial research centers in Europe and the US. The two institutions have collaborated on many projects in the past years resulting in many joint publications, they have exchanged senior visitors with great frequency, and many Chinese students have spent time at the ILLC as part of their graduate studies. So far, more than five of these Chinese students from Beijing that spent time at the ILLC have obtained professorships at key universities in Beijing. Here are a few illustrations.

11 11 Figure 1: The directors sign Existing collaboration Co-organized seminars and workshops in Beijing. Logic, Language and Cognition (2008), Proofs, Reasons, and Games (2008), Logic, Language and Philosophy (2010, 2011), Modal Logic and Logical Dynamics (2011). (http: //fenrong.net/events/) KNAW joint research project Ways of Worldmaking ( ). (http: //dcc.nwo.nl/project;id=79;title=ways+of+worldmaking) Short-term visits for intensive seminars. Van Benthem, Van Emde Boas, De Jongh, Stokhof, Veltman, and Venema. Four-volume translation project Door to Logic. Science Press, Beijing, completed in (See Workshop Door to Logic, May 22 23, 2010.) International workshop series LORI. Logic, Rationality, and Intelligent Interaction ( initiated by the ILLC, Tsinghua, and other Chinese universities. East Asian Schools on Logic, Language and Computation. For the most

12 12 recent school, organized by Jouko Väänänen and international colleagues, the next one will be at Tsinghua. Joint research Computational foundations of epistemic logic. Alexandru Baltag (ILLC), Johan van Benthem (ILLC), Fenrong Liu (Tsinghua), Kaile Su (Griffith & PKU). Key publication: F. Liu and K. Su, eds., Special issue on Logic and AI in China, Minds and Machines (23):1, Upcoming activity: LORI Hangzhou ( Social agency and games. Fenrong Liu (Tsinghua), Sonja Smets (ILLC), Patrick Girard and Jeremy Seligman (Auckland), Davide Grossi (Liverpool), Vincent Hendricks (Copenhagen). Key publication: F. Liu, J. Seligman, and P. Girard, Logical Dynamics of Belief Change in the Community, to appear in Synthese. Upcoming activity: visit to Beijing by members of Sonja Smets ERC project The Logical Structure of Correlated Information Change ( History of logic in China. Johan van Benthem (ILLC), Peter van Emde Boas (ILLC), Fenrong Liu (Tsinghua), Christoph Harbsmeier (Oslo), Jeremy Seligman (Auckland), Jincheng Zhai (Nankai). Key publication: F. Liu, J. Seligman and J. van Benthem, eds, Stud. Log., Special Issue on the History of Logic in China (4):3, ILLC IIAS Workshop on History of Logic in China, Amsterdam Upcoming activity: Handbook of the History of Logic in China Philosophy and semantics of natural language. Martin Stokhof (ILLC), Frank Veltman (ILLC), Lu Wang (Tsinghua), Zou Chongli (CASS). Upcoming activity: Chinese translation of the GAMUT textbook Logic, Language and Meaning, written by ILLC members. Organisation Scientific Directors Johan van Benthem & Fenrong Liu Board Junren Wan, Lu Wang, Martin Stokhof & Yde Venema

13 Members Alexandru Baltag (ILLC), Harry Buhrman (ILLC), Peter van Emde Boas (ILLC), Minghu Jiang (Tsinghua), Robert van Rooij (ILLC), Sonja Smets (ILLC), Pingzhong Tang (Tsinghua), Jouko Väänänen (ILLC), Frank Veltman (ILLC), Cai Shushan (Tsinghua), Wei Wang (Tsinghua) & Yuncheng Zhou (Tsinghua). External associates [based on current cooperations] Thomas Ågotnes (Bergen), Natasha Alechina (Nottingham), Jianyin Cui and Minghui Xiong (Sun yatsen), Patrick Girard and Jeremy Seligman (Auckland), Davide Grossi (Liverpool), Jiahong Guo & Fengkui Ju (BNU), Meiyun Guo and Minghui Ma (South West), Vincent Hendricks (Copenhagen), Wesley Holliday (Berkeley), Thomas Icard (Stanford), Gabriel Sandu (Helsinki), Kaile Su (Griffith), Yanjing Wang (PKU), Dag Westerståhl (Stockholm), Cihua Xu (Zhejiang), Junwei Yu (Renmin), Jincheng Zhai (Nankai) & Chongli Zou (Chinese Academy of Social Sciences). Shared positions Johan van Benthem is a University Professor at UvA, and a National Expert and Changjiang Professor at Tsinghua. Fenrong Liu is a full professor at Tsinghua, and visiting professor at the ILLC. Martin Stokhof is a visiting professor at the department of philosophy, Tsinghua. 13

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17 The Amsterdam Tradition in Logic 17

18 A Strong Tradition in Logic The University of Amsterdam has a strong tradition in logic, with a number of eminent professors that deeply influenced the foundations of mathematics, and the perspective on logic and its relation to philosophy and the sciences. In the following pages, the reader will find short digests of life and works of Brouwer, Heyting, Beth, Löb, and Van Benthem. (Eg)bertus Brouwer L.E.J. Brouwer ( ; the initials stand for Luitzen Egbertus Jan) is well known for his mathematical philosophy of intuitionism, but he also worked in a variety of areas in mathematics, such as topology, set theory, measure theory and complex analysis. Brouwer s fixed point theorem is a key result in topology. It states, roughly, and in a much more general form, that if you carry a map with you on an expedition, and you put that map flat on a table, then there must always be a you are here point on the map that points exactly to where you are. Brouwer made his mark in topology, the mathematical theory of the properties of objects that remain preserved if you

19 distort those objects by bending and stretching, before he became famous for his philosophy of mathematics. His intuitionistic philosophy was developed in Amsterdam, after 1912, the year when Brouwer was appointed adjunct professor (buitengewoon hoogleraar) at the University of Amsterdam, although the germ of it was already in his dissertation of Brouwer s inaugural lecture was called Intuitionism and Formalism. A year later he was appointed as full professor (gewoon hoogleraar), as successor of the mathematician Diederik Korteweg, who decided to change places with Brouwer until his retirement in In 1908 already, Brouwer had rejected the principle of the excluded third, which states that mathematical conjectures are either true or false, with exclusion of a third possibility. The philosophy of intuitionism was put forward by Brouwer as a radical break with the formalist tradition represented by David Hilbert. It involved rejection of large parts of classical mathematics and a program of vigorous reconstruction. Brouwer planned nothing less than a revolution in mathematics, and the development of a radically new constructive mathematics that he called intuitionistic mathematics. Mathematics is presented by him as a constructive mental activity of an ideal mathematical subject. Brouwer enjoyed a good fight about proper foundations, but he was deeply disappointed when this foundational struggle took a nasty turn. He was kicked out of the editorial board of the Mathematische Annalen, in spite of the opposition to this from Albert Einstein. Brouwer had a compelling personality, and he deeply influenced those around him. His lectures were widely attended. Rumor has it that Ludwig Wittgenstein took up philosophy again after attending a lecture by Brouwer in Vienna, in Earlier, Wittgenstein had convinced himself that his Tractatus Logico-Philosophicus had said everything there is to say about how language relates to the world and about the limits of what philosophers can meaningfully say. Brouwer retired from the university in He died in a traffic accident when he crossed the road in front of his house in Blaricum, in In a paper summing up Brouwer s achievements, his biographer Dirk van Dalen remarks:

20 Looking back at the Grundlagenstreit and the turbulent twenties, the correctness of Brouwers position with respect to formalism is now universally recognized. [3] Arend Heyting Arend Heyting took up the program of formalizing the philosophy of intuitionism as a logical formalism, much against the wishes of his thesis adviser Brouwer, who felt formalization would kill his philosophy. Heytings s effort made intuitionism a respected (but modest) part of mathematical logic. Heyting got his Master title in mathematics in 1922, and took up a position as a mathematics teacher in Enschede. These were the days where Dutch secondary school teachers still had enough leasure time to be active in research. In 1925, Heyting defended his PhD thesis on Intuitionistic Axiomatics for Projective Geometry. In 1936 Heyting accepted a position at the University of Amsterdam, and in 1948 he became the successor of Mannoury as professor. Heyting retired from the university in 1968, but remained active. Among other things, he edited the first volume of Brouwer s collected works, which appeared in 1975.

21 Heyting viewed himself as a spokesman for intuitionism, and he considered it as his main task to clarify and spread Brouwers ideas. This did not prevent him to clash with his mentor, who was rather negative about Heyting s program of formalizing intuitionism. Among Heyting s students were Anne Troelstra and Dirk van Dalen, the later biographer of Brouwer. Arend Heyting Foundation The Arend Heyting Foundation was founded in 1981 by prof. dr. A.S. Troelstra, under the auspices of the The Royal Netherlands Academy of Arts and Sciences (KNAW) and has as goal to further the knowledge of mathematical logic, and Intuitionism in particular. The Arend Heyting Foundation tries to attain this goal by organising an Arend Heyting Lecture on the aforementioned field at least once every three years. Evert Willem Beth Evert Willem Beth ( ) was a logician with an unusually wide range of interests. He studied mathematics and physics, but also philosophy and

22 psychology, in Utrecht, Leiden and Brussels. His PhD thesis (1935) was in philosophy: Rede en Aanschouwing in de Wiskunde (Reason and Intuition in Mathematics). It deals with the relation between intuition in the Kantian sense of Anschauung and rational deduction in Euclidean geometry. In the thesis, Beth made a clear distinction between geometry as a natural science, geometry as a deductive theory, and geometry as intuitively given. He became professor of logic and the foundations of mathematics at the University of Amsterdam in This was the first academic position in the Netherlands for logic and the foundation of mathematics. Throughout his career, Beth was in close contact with Alfred Tarski: he visited Tarski several times in Berkeley, and even spent some time as a research assistant with him. Beth considered himself a philosopher first and foremost, but he also contributed to mathematical logic, where his Beth tableau method and his definability theorem are well known. In 1951 he clashed with Alonzo Church, as a result of which he resigned from the editorial board of the Journal of Symbolic Logic, where Church was editor-in-chief. Beth had perhaps a broader conception of logic and its relation to philosophy than Church. One of the lasting achievements of Beth is in science politics. He devoted much of his energy to the construction of national and international associations for logic and philosophy of science, such as the Dutch Association for Logic (Nederlandse Vereniging voor Logica), the Institute for Foundational Studies (Instituut voor Grondslagenonderzoek), and the Interfaculty of Philosophy and Sciences (Centrale Interfaculteit). In his scientific biography of Beth, Paul van Ulsen characterizes his subject as mathematician, philosopher, organizer [4]. Beth held a subtle position with respect to the relation between formal and informal reasoning and thought. Formal and informal logic, the formalized languages, and the specialized technical languages of human communication do not appear simply as separate and independent occupations: they complete each other and influence each other. [1] Beth had weak health and was a heavy smoker. When he died at the early

23 age of 55, Arend Heyting wrote the following about him in a memorial in the Notre Dame Journal of Formal Logic: Evert Willem Beth [... ] was one of the very few modern scholars who combined a wide field of deep and well-founded knowledge with meticulous research of details in fields as far apart as Aristotelian philosophy of science and mathematical logic. Though he is best known for his work on mathematical logic, he considered himself a philosopher and saw as his main task to prepare the first steps towards a philosophy that will be able to deal with modern science. There is no doubt that many of his ideas will be of great value in the development of such a philosophy. [2] Evert Willem Beth Foundation The Evert Willem Beth Foundation was established in 1978 by a legate from Mrs. Cornelia Beth-Pastoor. Since 2001 the Foundation funds the Evert Willem Beth Outstanding Dissertation Prize, a prize for outstanding Dissertations in Language, Logic and Computation. Martin Löb After Beth, the chair of mathematical logic at the University of Amsterdam was occupied by Martin Löb ( ), famous because of Löb s paradox and Löb s theorem, which allows the deduction of an arbitrary sentence from a self-referring sentence.

24 In the obituary at the ILLC website, Löb is described as follows: He was a man of strong intellect and great determination who, as a teenaged refugee from Nazi rule, had overcome the violent disruptions of wartime and against the odds, established a distinguished academic career. Löb s own research spanned proof theory, modal logic and computability theory. Throughout his life he thought deeply about difficult problems, making fundamental contributions to each of those areas, but it is Löb s Theorem (1955) for which he is best known. Gödel, in his celebrated Incompleteness Theorem of 1931, had constructed a self-referential statement of formal arithmetic asserting its own unprovability and shown, assuming consistency, that it has to be true. This prompted Henkin to ask about statements which assert their own provability, and Lb showed by a typically clever and succinct argument, that they also must be true. (Whereas Gödel s Theorem is essentially a formalised version of the Liar Paradox, Lb s Theorem formalises Löb s Paradox: the sentence if this sentence is true then the moon is made of green cheese is true(!) so the moon is indeed made of green cheese.) His work lies at the heart of much research, continuing to this day, on reflection principles and provability logics, and it will forever remain at the central core of Mathematical Logic.

25 Johan van Benthem Johan van Benthem (born 1949) is University Professor of pure and applied logic, University of Amsterdam, and Henry Waldgrave Stuart Professor of philosophy, Stanford University. In the 1990s, he was the founding director of the Institute for Logic, Language & Computation (ILLC) in Amsterdam, a joint venture of mathematics, computer science, philosophy, and linguistics, for studying the structure and flow of information. He was first chairman, and is honorary member of FoLLI, a European organization with similar broad aims. He is a recipient of the national Spinoza Award, project Logic in Action from 1997 to 2001 (LiA). Member of the Royal Dutch Academy of Arts and Sciences (KNAW), the Academia Europaea (AE), and the Institut International de Philosophie (IIP). Changjiang Professor, Chinese Ministry of Education, Tsinghua University, Beijing. Johan van Benthem was educated at the University of Amsterdam, where he got bachelor degrees in physics and mathematics, master degrees in mathematics and philosophy, and a PhD degree in mathematics. Topic of the PhD thesis is Modal Correspondence Theory, an investigation of modal axioms and their definability in first- and higher order logics. This research led to a theorem characterizing the language of modal logic as consisting of just those first-order formulas that are invariant for bisimulation. Although the term

26 bisimulation was coined later by theoretical computer scientists interested in process theory, the concept itself can be found in Van Benthem s PhD thesis. In 1977, before the actual defense of his PhD thesis, Van Benthem was appointed lecturer in logic at the University of Groningen, where he stayed until his appointment in Amsterdam in In Amsterdam, van Benthem holds the chair of Evert Willem Beth, created in Beth s broad view of logic in between philosophy, mathematics, computer science, linguistics, cognitive psychology, and even rational public debate, now lives on in the Institute for Logic, Language and Computation. Van Benthem s position at Stanford is at a similar interdisciplinary interface, against the ba ckdrop of the Center for the Study of Language and Information, pioneered by Jon Barwise and others in the early 1980s. Like his predecessor Beth, Van Benthem has a wide compass of interests, ranging over modal logic, epistemic logic, dynamic logic, logics of time and space, semantics of natural language: generalized quantifiers and categorial grammars, substructural proof theory, philosophical logic, logics of computation, information update and interaction, logic and games. Van Benthem s key interest since his Spinoza project Logic in Action ( ) is logical dynamics, making actions of inference, observation, information update, belief revision, or preference change first-class citizens. These come together in the study of rational agency using dynamic-epistemic logics.

27 Bibliography [1] E.W. Beth. Opmerkingen over analytische wijsbegeerte. Algemeen Nederlands Tijdschrift voor Wijsbegeerte, 53(5):1 5, [2] Arend Heyting. In memoriam Evert Willem Beth. Notre Dame Journal of Formal Logic, 7(4): , October [3] Dirk van Dalen. L.E.J. Brouwer: The foundations of topology and the topology of the foundations. Proceedings of the KNAW, 100:11 14, [4] Paul van Ulsen. Beth als logicus. PhD thesis, ILLC,