1、2 TABLE OF CONTENTS Preface 1 Logical dynamics, agency, and inteligent interaction 2 Epistemic logic and semantic information 3 Dynamic logic of public observation 4 Multi-agent dynamic-epistemic logic 5 Dynamics of inference and awarenes 6 Questions and isue management 7 Soft information, correctio
2、n, and belief change 8 An encounter with probability 9 Preference statics and dynamics 10 Decisions, actions, and games 11 Proceses over time 12 Epistemic group structure and collective agency 13 Logical dynamics in philosophy 14 Computation as conversation 15 Rational dynamics in game theory 16 Met
3、ing cognitive realities 17 Conclusion Bibliography 3 To Arthur and Lucas 4 PREFACE This book is about Logical Dynamics, a theme that first gripped me in the late 1980s. The idea had many sources, but what it amounted to was this: make actions of language use and inference first-clas citizens of logi
4、cal theory, instead of studying just their products or data, such as sentences or proofs. My program then became to explore the systematic repercussions of this dynamic turn. It makes its first appearance in my book Language in Action (1991), where categorial gramars are linked to procedures of ling
5、uistic analysis using relational algebra viewing natural language as a sort of cognitive programing language for transforming information. My next book Exploring Logical Dynamics (1996) continued with this perspective, linking it to modal logic and proces theories in computer science: in particular,
6、 dynamic logic of programs. This added new themes like proces invariances and definability, dynamic inference, and computational complexity of logics. In the meantime, my view of logical dynamics has evolved again. I now se it as a general theory of agents that produce, transform and convey informat
7、ion and in al this, their social interaction should be understood just as much as their individual powers. Just think of this: asking a question and giving an answer is just as logical as drawing a conclusion on your own. And likewise, I would se argumentation with diferent players as a key notion o
8、f logic, with proof just a single-agent projection. This stance is a radical break with current habits, and I hope it wil gradualy grow on the reader, the way it did on me. The book presents a unified acount of the resulting agenda, in terms of dynamic epistemic logic, a framework developed around 2
9、000 by several authors. Many of its originators are found in my references and acknowledgments, as are others who helped shape this book. In this seting, I develop a systematic way of describing actions and events that are crucial to agency, and show how it works uniformly for observation-based know
10、ledge update, inference, questions, belief revision, and preference change, al the way up to complex social scenarios over time, such as games. In doing so, I am not claiming that this approach solves al problems of agency, or that logic is the sole guardian of inteligent interaction. Philosophy, co
11、mputer science, probability theory, or game theory have important things to say as wel. But I do claim that logic has a long-standing art of choosing abstraction levels that are sparse and yet revealing. The perspective offered here is simple, iluminating, and a useful tool to have in your arsenal w
12、hen studying foundations of cognitive behaviour. Moreover, the logical view that we develop has a certain mathematical elegance that can be appreciated even when the grand perspective leaves you cold. And if that technical 5 appeal does not work either, I would already be happy if I could convey tha
13、t the dynamic stance throws fresh light on many old things, helps us se new ones and that it is fun! This book is based on lectures and papers since 1999, many co-authored. Chapter 1 explains the program, Chapter 2 gives background in epistemic logic, and Chapters 312 develop the logical theory of a
14、gency, with a base line for readers who just wish to se the general picture, and extra topics for those who want more. Chapters 1316, that can be read separately, explore repercussions of logical dynamics in other disciplines. Chapter 17 summarizes where we stand, and points at roads leading from he
15、re. In composing this story, I had to select, and the book does not cover every aley I have walked. Also, throughout, there are links to other areas of research, but I could not chart them al. Stil, I would be happy if the viewpoints and techniques offered here would change received ideas about the
16、scope of logic, and in particular, revitalize its interface with philosophy. Acknowledgment First of al, I want to thank my co-authors on papers that helped shape this book: Cdric Dgrmont, Jan van Eijck, Jele Gerbrandy, Patrick Girard, Tomohiro Hoshi, Daisuke Ikegami, Barteld Kooi, Fenrong Liu, Mari
17、carmen Martinez, Stefan Minica, Siewert van Oterloo, Eric Pacuit, Olivier Roy, Darko Sarenac, and Fernando Velzquez Quesada. I also thank the students that I have interacted with on topics close to this book: Marco Aielo, Guilaume Aucher, Harald Bastianse, Boudewijn de Bruin, Nina Gierasimczuk, Wes
18、Holliday, Thomas Icard, Lena Kurzen, Minghui Ma, Marc Pauly, Ben Rodenhuser, Floris Roelofsen, Ji Ruan, Joshua Sack, Tomasz Sadzik, Merlijn Sevenster, Josh Snyder, Yanjing Wang, Audrey Yap, Junhua Yu, and Jonathan Zvesper. Also, many colleagues gave comments, from occasional to extensive, that impro
19、ved the manuscript: Krzysztof Apt, Giacomo Bonanno, Davide Grossi, Andreas Herzig, Wiebe van der Hoek, Hans Kamp, Larry Moss, Bryan Renne, Gabriel Sandu, Sebastian Sequoiah-Grayson, Yoav Shoham, Sonja Smets, Rineke Verbrugge, and Tomoyuki Yamada. I also profited from the readers reports solicited by
20、 Cambridge University Pres, though my gratitude must necesarily remain de dicto. Finaly, I thank Hans van Ditmarsch and especialy Alexandru Baltag for years of contacts on dynamic epistemic logic and its many twists and turns. 6 Chapter 1 LOGICAL DYNAMICS, AGENCY, AND INTELLIGENT INTERACTION 1.1 Log
21、ical dynamics of information-driven agency Human life is a history of milions of actions flowing along with a stream of information. We plan our trip to the hardware store, decide on marriage, rationalize our foolish behaviour last night, or prove an occasional theorem, al on the basis of what we kn
22、ow or believe. Moreover, this activity takes place in constant interaction with others, and it has been claimed that what makes humans so unique in the animal kingdom is not our physical strength, nor our powers of deduction, but rather our planning skils in social interaction with the Mamoth hunt a
23、s an early example, and legal and political debate as a late manifestation. It is this intricate cognitive world that I take to be the domain of logic, as the study of the invariants underlying these informational proceses. In particular, my program of Logical Dynamics (van Benthem 1991, 1996, 2001)
24、 cals for identification of a wide array of informational proceses, and their explicit incorporation into logical theory, not as didactic background stories for the usual concepts and results, but as first-clas citizens. One of the starting points in that program was a pervasive ambiguity in our lan
25、guage betwen products and activities or proceses. “Dance” is an activity verb, but it also stands the product of the activity: a waltz or a mambo. “Argument” is a piece of a proof, but also an activity one can engage in, and so on. Logical systems as they stand are product-oriented, but Logical Dyna
26、mics says that both sides of the duality should be studied to get the complete picture. And this paradigm shift wil send ripples al through our standard notions. For instance, natural language wil now be, not a static description language for reality, but a dynamic programing language for changing c
27、ognitive states. Recent trends have enriched the thrust of this action-oriented program. Rational agency streses the transition from the paradigm of proof and computation performed by a single agent (or none at al) to agents with abilities, goals and preferences plotting a meaningful course through
28、life. This turn is also clear in computer science, which is no longer about lonely Turing Machines scribbling on tapes, but about complex inteligent communicating systems with goals and purposes. Another recent term, inteligent interaction, emphasizes what is perhaps the most striking feature here,
29、the role of others. Cognitive powers show at their best in many-mind, rather than single-mind setings just as physics only gets 7 interesting, not with single bodies searching for their Aristotelean natural place, but on the Newtonian view of many bodies influencing each other, from nearby and far.
30、1.2 The research program in a nutshel What phenomena should logic study in order to carry out this ambitious program? I wil first describe these tasks in general terms, and then go over them more leisurely with a sequence of examples. A useful point of entry here is the notion of rationality. Indeed
31、, the clasical view of humans as rational animals sems to refer to our reasoning powers: To be rational is to reason inteligently. These powers are often construed narrowly as deductive skils, making mathematical proof the paradigm of rationality. This book has no such bias. Our daily skils in the c
32、ommon sense world are just as admirable, and much richer than proof, including further varieties of reasoning such as justification, explanation, or planning. But even this variety is not yet what I am after. As our later examples wil show, the esence of a rational agent is the ability to use inform
33、ation from many sources, of which reasoning is only one. Equaly crucial information for our daily tasks comes from, in particular, observation and communication. I wil elaborate this theme later, but right now, I cannot improve on the admirable brevity of the Mohist logicians in China around 500 BC
34、(Zhang & Liu 2007): “Zhi: Wen, Shuo, Qin” 1 knowledge arises through hearing from others, inference, and observation. Thus, while I would subscribe to the above feature of rationality, its logic should be based on a study of al basic informational proceses as wel as their interplay. But there is mor
35、e to the notion of rationality as I understand it: To be rational is to act inteligently. We proces information for a purpose, and that purpose is usualy not contemplation, but action. And once we think of action for a purpose, another broad feature of rationality comes to light. We do not live in a
36、 bleak universe of information. Everything we do, say, or perceive is coloured by a second broad system of what may be caled evaluation, determining our preferences, goals, decisions, and actions. While this is often considered 1 Somewhat anachronisticaly, I use modern simplified Chinese characters.
37、 8 alien to logic, and closer to emotion and fashion, I would rather embrace it. Rational agents deal inteligently with both information and evaluation, and logic should get this straight. Finaly, there is one more crucial aspect to rational agency, informational and evaluational, that goes back to
38、the roots of logic in Antiquity: To be rational is to interact inteligently. Our powers unfold in communication, argumentation, or games: multi-agent activities over time. Thus, the rational quality of what we do resides also in how we interact with others: as rational as us, les, or more so. This,
39、too, sets a broader task for logic, and we find links with new fields such as interactive epistemology, or agent studies in computer science. I have now given rationality a very broad sense. If you object, I am happy to say instead that we are studying reasonable agents, a term that includes al of t
40、he above. Stil, there remains a sense in which mathematical deduction is crucial to the new research program. We want to describe our broader agenda of phenomena with logical systems, following the methods that have proven so succesful in the clasical foundational phase of the discipline. Thus, at a
41、 meta-level, in terms of modeling methodology, throughout this book, the reader wil encounter systems obeying the same technical standards as before. And meta-mathematical results are as relevant here as they have always been. That, to me, is in fact where the unity of the field lies: not in a restr
42、icted agenda of consequence, or some particular minimal laws to hang on to, but in its methodology and modus operandi. So much for grand aims. The following examples wil ilustrate what we are after, and each adds a detailed strand to our view of rational agency. We wil then summarize the resulting r
43、esearch program, followed by a brief description of the actual contents of this book. 1.3 Entanglement of logical tasks: inference, update, and information flow The Amsterdam Science Museum NEMO (http:/ww.nemo-amsterdam.nl/) organizes regular Kids Lectures on Science, for some 60 children aged aroun
44、d 8 in a smal amphitheatre. In February 2006, it was my turn to speak and my first question was this: The Restaurant “In a restaurant, your Father has ordered Fish, your Mother ordered Vegetarian, and you have Meat. Out of the kitchen comes some new person carrying the three plates. What wil happen?
45、” 9 The children got excited, many litle hands were raised, and one said: “He asks who has the Meat”. “Sure enough”, I said: “He asks, hears the answer, and puts the plate on the table. What happens next?” Children said: “He asks who has the Fish!” Then I asked once more what happens next? And now o
46、ne could se the Light of Reason suddenly start shining in those litle eyes. One girl shouted: “He does not ask!” Now, that is logic After that, we played a long string of scenarios, including card games, Master Mind, Sudoku, and even card magic, and we discussed what best questions to ask and conclu
47、sions to draw. Two logical tasks The Restaurant is about the simplest scenario of real information flow. And when the waiter puts that third plate without asking, you se a logical inference in action. The information in the two answers alows the waiter to infer (implicitly, in a flash of the minds e
48、ye) where the third plate must go. This can be expresed as a logical form A or B or C, not-A, not-B C. One can then tel the usual story about the power of valid inference in other setings. With this moral, the example goes back to Greek Antiquity. But the scenario is much richer. Let us look more cl
49、osely: perhaps, appropriately, with the eyes of a child. To me, the Restaurant cries out for a new look. There is a natural unity to the scenario. The waiter first obtains the right information by asking questions and understanding answers, acts of communication and perhaps observation, and once eno
50、ugh data have acumulated, he infers an explicit solution. Now on the traditional line, only the later step of deductive elucidation is logic proper, while the former are at best pragmatics. But in my view, both informational proceses are on a par, and both should be within the compas of logic. Askin
