http://www.golori.org/teaching/

一门本科生的“一阶逻辑”， 一门研究生的“人工智能中的逻辑”。

如果选课的人数达到最低要求，我会在本学期开设这两门课。

转眼间，暑假已经结束，新的学期已经悄然来临。校园里渐渐多起来的学生、还有刚刚看到的课程时间安排都在告诉我，开学了！

这个学期，我准备开两门课：本科生的“一阶逻辑”，主要是给哲学系的学生上，所以，在讲授内容方面我还是考虑了很多。年初在荷兰的时候，对本科阶段的逻辑教育我曾经做过一些调查研究，收获颇多。我正在跟范本特姆（van Benthem）教授合写一本新的英文教材，适合哲学本科。计划我在清华、他在斯坦福和阿姆斯特丹大学试教，逐渐完善。

另一门是研究生课程“人工智能中的逻辑”，主要是希望研究生在学习了一阶逻辑和模态逻辑这些基础课程之后，能够接触更多的逻辑分支，特别是在计算机领域应用比较多的逻辑。一方面开阔视野，另一方面，学习其中的方法，为自己的研究或论文写作奠定基础。我一直觉得“研究生”应当用“研究”的态度来学习，寻找自己感兴趣的逻辑，钻进去，做自己喜欢做的工作。希望这门课程可以帮助他们发现自己的兴趣点。

教学其实是一个享受的过程，当你看到学生在作业中使用十分巧妙的办法证明了一个定理的时候，那种高兴的心情是很难用言语描述的。

Question by Junwei Yu: This is a general question, but I still would like to take this chance to ask. I sometimes wonder why we logicians bother to use formal languages, somehow in an extreme way. In contrast, many mathematicians only use partly formal language. How to understand such a difference? Could you please explain some historical background?

Answer: This is very perceptive, and it strikes a chord! I am a logician, I design and study formal systems in the standard style you describe. And nevertheless, I feel uneasy about it. It is definitely true that nobody uses formal systems with completely formal languages in some absolute sense. Even mathematicians use natural language, enriched with formal notations when they feel the need for it. And this mismatch strikes when you explain the importance of logical results to others, since the formal languages and formal systems are an impenetrable barrier. Say, Gödel’s results are about the incompleteness of formal systems of (first-order) arithmetic, whereas ordinary people, including mathematicians, thinks of ‘Arithmetic’ as an open practice – and it is much less clear what the logical results say about the latter. Likewise, traditional logic was about broad phenomena in reasoning, such as ‘negation’ or ‘quantification’, rather than what we now teach: the ladder of formal systems, from propositional logic via modal logic to first-order logic and beyond. Fortunately, logicians do not notice this problem, since they can publish formal systems and meta-theorems about them, without ever applying them to anything or explaining them to a broader audience. This ‘closed world’ can give you tenure and respect, so why worry?

Nevertheless, I am worried by what I call the ‘system imprisonment’ of modern logic. It clutters up the philosophy of logic and mathematics, replacing real issues by system-generated ones, and it isolates us from the surrounding world. I do think that formal languages and formal systems are important, and at some extreme level, they are also useful, e.g., in using computers for theorem proving or natural language processing. But I think there is a whole further area that we need to understand, viz. the interaction between formal systems and natural practice. Take mathematics itself. In the course of history, it has become a dynamic mixture of natural language and natural reasoning with formal additions: notations, proof patterns, and so on. Practizing mathematicians have recognized this, and developed hybrids of formal systems and natural language, such as De Bruyn’s ‘mathematical vernacular’, or Peter Koepke’s project on proof structure in Bonn today. More generally, philosophers like Frits Staal have emphasized the crucial role of ever new notations and their successful incorporation into existing scientific practice, in both Western and Asian traditions.

As a logician, I see an intriguing dynamics here. Mathematicians invent new notations and proof styles under pressure to become more precise, in scientific communication and face-to-face debate. Thus, more formal language enters natural language. But this happens in tandem with a reverse process. Good mathematicians are also able to step back from formalisms, and give a higher-level description of a proof in more natural language. We all feel we only really understand a proof when we can describe it at a variety of such levels. Indeed, I think that the mutual dynamics of precisation and paraphrase is an exciting form of ‘generalized proof theory’ whose study might be of benefit to everyone! And much more generally, the continual ‘successful insertion’ of cultural artefacts: notations, logical inferences, algorithms, new games, and so on is the hallmark of human behaviour. This is where logic meets reality. Even cognitive science in general would do well to understand this mixed practice.

Question by Yizhao Hu: I also have a very general question. I guess many logic students would appreciate your answer to this question. What is the best way to understand the theoretical value versus the practical value of logics? More specifically, for instance, why is completeness important to us?

Answer: I think one should pursue academic subjects because one likes them – and perhaps liking is not even enough, but there should be real love. There is the famous anecdote of Euclid who once, when asked by someone in the street for the practical value of mathematics, asked his slave to give that person some money, since he felt pity for people who go for practical value in life. How about that for an answer?

I see the main value of logic as theoretical. It is a wonderful style of thinking that provides foundations for many other sciences, and a discipline of proven value for abstract conceptual analysis. Moreover, logic is a unifying force in a fast-splintering Academia: climbing its mountains (as Fenrong once put it in a piece here in Holland) helps us see broad patterns and new connections between disciplines all across the university. That is why my own Institute for Logic, Language and Computation is the only university-wide research institute in Amsterdam. Logic works! In addition, and this has to do with falling in love, intellectually just as much as physically, logic can be beautiful, not always, but definitely in the right light at the right time of day…

Of course, and here your last example is to the point, this beauty sometimes resides in the ‘uselss’ results. Take the completeness theorem. For practical purposes, soundness is usually enough: we need to know that the inferences which we perform ar correct, so that our reasoning does not go badly astray. The reverse question, whether our system really captures all valid styles of inference, is much more a theoretical concern in the distance. But even so, what a nice concern, and what beautiful consequences, ever since Gödel’s dissertation proved completeness for first-order logic!

Now, many colleagues will give you equally strong answers on the practical applied side. It has been claimed by leading authorities that ‘logic is the calculus of computer science’, meaning that the ability to work with logical systems and methods makes you a successful engineer in information technology, software engineering, agent systems, and so on. I am sure that such uses exist, and logicians do work in industry and beyond. Likewise, it has been claimed that logic helps in computational semantics of natural language, legal reasoning, general argumentation analysis, and maybe even, that it helps you become a better public debater. (I have not noticed this phenomenon with myself yet, but there is still time…) And even police and military forces in some countries have found it useful to teach logical techniques of reasoning.

I do not want to put all this down, but for myself, I will give another answer here. It arises because people often ask me to justify why I have taught logic to generations of students. This cannot be just in order to train future research logicians, since we do not need huge amounts of these. But what I see myself as doing is this. I teach students to think in a certain abstract logical way, not as the only way they have in their repertoire, but as an ‘insertion’ in the earlier sense, or an ‘enhancement’ to what they are already able to do. This style is abstract and formal, but when used well, it can also be used to setp away from existing reality and see new patterns and options. Good logicians are creative, flexible, and can think outside of existing patterns. To me, then, ‘theory is the best investment in practice’! People with logic training can do any profession afterwards, but they do it ‘with an extra’. And this is not just self-serving speculation. I once organized a meeting on hiring students with entrepreneurs from Silicon Valley. And what they all said was this. “We want well-trained people in fundamental scientific thinking, not applied people educated to fit our current production line.” And the reason was clear. Firms today do not even know what they will be producing in some years from now, but they do know that the only invariant in this fast-changing world is theoretical insight and power of abstraction.

Question by Jiahong Guo: I have a small but very concrete question on an issue of translation. In your paper 'dynamic logic of preference upgrade', you discussed a very interesting notion, “regret”. You defined it as something that you would prefer but you know it is not the case. In Chinese, there are two possible words, “hou hui” and “yi han” to express the same meaning. Interestingly, the former term involves temporal elements. Namely one feels regretful after something happened in a way that was not expected. Inspired by this, can we add the temporal understanding into the explanation of “regret” in English? What do you think?

Answer: Finally we get to the delicate issues of translation! Indeed, in that dynamics paper, ‘regret’ was taken in an a-temporal sense in the paper you mention. That sense occurs, like in when I say I regret that, due to the Second Law of Thermodynamics, there is no never-ending energy supply. But I agree with you that many sense of regret in English are temporal, having to do with either the past (I regret the effects of my foolishness) or the future (I regret that I will have to die). Of course, in the paper, our main purpose was another one, namely to point out that regret can apply to situations that we know cannot occur – at least for people who are not out-and-out realists. Apart from ‘regret’, there must be many more cases in your translation experiences with my papers. Junwei mentioned my favourite term ‘fine-structure’, which in English means ‘detailed stucture’, but with a slight extra connotation of being ‘delicate’ and ‘good’. He said Chinese had no word with this same combination. I also enjoyed other examples in our email correspondence; these mismatches are not at all a nuisance, but rather little pleasures of comparing our two situations!

I hope we will also have a chance once to discuss your translation experiences more broadly. I realize that logic papers are special, in that they involve a lot of technical terms with fixed meanings, plus general intellectual style and jargon which is the same everywhere on the planet. But still, it would be intriguing to me to see just how logic terms translate into Chinese, and which obstacles one encounters. It has been claimed that modern logical systems are not ‘neutral’, in that they follow the subject-predicate structure of specific human languages, often Indo-European ones. On the other hand, I have never found that Chinese logic students have special difficulties with understanding modern logic, so one would want to see the abstraction level at which we communicate. (I remember this was my topic of conversation with the first student from mainland China that I ever encountered in my life, viz. Victor Guo in Stanford in 1983.) I wish I were a better expert in Chinese, so that I would get more out of this. Maybe in some years from now, I should try to translate your papers!

Question by Fenrong Liu: Jiahong’s question reminds me of the many emails exchanged between you and us translators from last October till now. We very much appreciated your patience and your kind explanations. But we have to admit that it is not an easy job to translate your work into Chinese. The general difficulty lies in the fact that it is rather a translation between two cultures than between two languages. Of course, we also have some difficulties in understanding logics. What is your impression of our questions?

Answer: Fenrong, now you raise all the hard questions. Do people really understand each other? Does language presuppose, or even determine culture, and vice versa? Is Whorf’s Thesis correct, and are we mentally locked into our language? This interview could get very long if we delved into all this! Of course,we are are not the first to raise these issues: they have been debated forever, in the case of Chinese and Western traditions, through all the centuries since our cultures first got into first-hand contacts. Frankly, I would be more interested in your own experiences as translators, and as students and researchers at the interface of Chinese and Western cultural than in my own views as a colleague and visitor from a distance.

But since you ask, maybe I will say this. I do think language, reasoning, and culture are deeply tied up. But many discussions about it seem fruitless to me, since one does not acknowledge some facts, and make some practical distinctions. First, given the relatively short period since our shared ancestors walked out of Africa, I would expect no very deep biological difference in neural-cognitive structure – though cultural artefacts like alphabet versus character script will no doubt influence some short-term processing facts. Now of course, culture provides a context where these basic skills are exercised, and clearly, when social life and educational organization are different, tendencies of interpretation and behaviour may well be different. But then I would say that all cultures face the same problems of arranging a just society and a reasonable life, so how much variation do we expect in stable solutions? I am often amazed at how similar situations are when you look at the invariances, rather than the accidental coding of behaviour. Chinese are supposed to be obsessed with ‘face’, but I can assure you the same is true in the West: it is just coded differently. Also, terms like ‘culture’ are so uniform that hey hide the enormous diversity between classes. Compare a Dutch intellectual to a Chinese farmer, and you will see worlds apart. But my guess is the same is true when you compare that farmer to a Chinese intellectual. Next, Chinese and Western intellectuals also share worldwide identities which make their personality no longer ‘mono-cultural’. Well, no conclusion here.

Personally, I am most struck by a simple empirical observation. All through world history, cultures have had contacts, mixed, taken over ideas, and so on. Good ideas – and alas, also bad ones – cross almost without effort, even though it sometimes may involve 'creative misunderstanding' (but that also happens between people inside the same culture). On a more specific note: consider the LORI lecture by Professor Zhang and Fenrong on Mohist Logic. I was struck by the amazing similarities with the Greek tradition, minds so far apart geographically seemed to have run on parallel tracks.

Once again, this is not an answer. I should learn from you, not the other way around.

Question by Jiahong Guo: Maybe this is a question that many of us want to ask, but I am saying it now. We have talked a lot so far on modal logic, but your research is not only on modal logic. Just to name a few, you have many works on spatial logic, logic of time, logic and cognition, and so on. Can you say something on the trend of logic in general in the 21st century?

Answer: My own interests are indeed much broader than Modal Logic, and over the years I have worked in several other areas. This is hard to avoid when you get older! Modal logic is my favourite methodology, though I do not see it as exclusive: I have also worked with first-order logic, and even type theory. And indeed, I have spent ten years of my life in the syntax and semantics of natural language, and other large chunks of time on methodology of science, connections with cognitive science, and recently, logic and games. I hope our translation Book series will eventually also show the full spectrum of these activities.

You ask for more general views on logic. I find it hard to repeat these here, since I feel I have produced a stream of programmatic papers and interviews on these, addressed to many different audiences. Maybe far too many already! My most recent lecture for the DMLPS Congress in Beijing will give you a fair impression. Another reason for a little modesty is that my views keep evolving, so one year’s truth can be another year’s falsity. For instance, our institute ILLC is a very different place today from when we founded it, and I cannot say that I foresaw or planned all of this.

So let me stick to just one slogan, which has already been mentioned several times in this interview. I think that modern logic may be on the threshold of changing its traditional agenda to become a broad theory of intelligent interaction, at the interface of the humanities, exact sciences, and social sciences, and I see my work as helping history along a little bit here – in a gentle non-violent persuasive mode.

Question by Fenrong Liu: I just got a notification that the Science Press, a prestigious Chinese publisher in Beijing, is willing to publish our book. The book will be titled as “A Door to Logic: Selected Works by Johan van Benthem-- Modal Logic”, this is the first Volume, as we planned. The publisher is also happy to publish two further volumes, namely “Logic and Natural Language” (volume 2) and “Logic and Philosophy” (volume 3). You have done much work already, especially for Volume 1, writing a preface for the book, and more importantly, new introductions to each section. I believe that readers will benefit a lot from these new additions. Would you like to take this chance to say a few words to your future Chinese readers?

Answer: So the wish in the previous answer has been granted already. China is really a place where dreams come true very fast! My word to readers is just this.

I hope that my papers indeed open a ‘Door to Logic’, an old discipline dating bach some 2500 years to Ancient Greece and India, but also a vibrant and diverse modern area with many great minds, lots of different opinions, and great panoramic points of view on scientific life. I think you might appreciate learning what my discipline has to offer, but equally well, logic will no doubt benefit from joining forces with Chinese readers, and increasingly also, original Chinese contributors to the field, who will bring their own insights and add new themes. I also think that such contacts are important in shaping a common intellectual universe where we can all participate as equals, and agree and disagree in a civilized and productive manner. The benefits of that, of course, go far beyond any special academic discipline.

On the other hand, a project like this also offers the special thrill of contacts between different cultures. There are all sorts of subtle differences in style and ' taste' that may arise in the process of opening the door to logic – but maybe that will add the delights of savouring 'different cuisines', which Chinese people are such experts in. I can say for myself that I find it a privilege that these contacts are taking place right now, where I can contribute my little share. Against this background, I do not see our project as one-way traffic from West to East.

Since this is an interview about Translations, let me end with a small linguistic point in this connection. Not many people realize that the Western word for getting clear on something is 'orientation', i.e., a term which contains the Latin word for the East! I once again thank my translators team for having put an intriguing process of orientation into motion.

Question by Fenrong Liu: Today we celebrate our successfully finishing the translation work by having this small workshop, so that we can talk face to face. The translated works are 13 papers of yours on modal logic. You have divided them into four sections by themes, namely, basic theory, modal logic and computation, modal logic and information, and modal logic and games. The publishing span of the papers runs from 1970s to now. Moreover, I noticed that those papers are cited very often in the literature. Can you briefly explain the development of your ideas over the years on modal logic? What were the biggest challenging questions over time?

Answer: Let me first thank you all for this initiative! ‘A Door to Logic’ is a great opportunity to work closely with clever nice young people, a chance to reach a new audience for logic in China, and a welcome opportunity to reflect on where my own work and my field is going. I hope this interview will show a bit of all of these things.

Let me start with my own development. What were the main lines and challenges? Life goes so fast that much is not so well-planned and rational. I often still think of myself as a young student who just started, and then realize to my own surprise that I have become an ’authority’. The good thing about that is that I can sympathize with the Chinese students which I met at our Workshop and other events in Beijing. How to find your way into the world of research? In my case, I had a joint interest in philosophy and mathematics, and modal logic was an excellent compromise between the two. (This was my own choice: my professors were not all that happy with it.) The origins of modal logic are philosophical, in the study of necessity, possibility, time, and causality. Frege and Russell had thrown these intensional notions out of their modern logic, rejecting Kant’s Table of Categories – but they came back through the work of philosophical logicians in the early 20^th century, and have stayed since then. But also, in my student days, a new movement was starting. Much philosophical logic had become a ‘cottage industry’, away from the logical mainstream, while it occurred to me and others that modal logics were really a special kind of classical systems which could be studied by standard techniques. This led to a mathematical theory of modal logic in the 1970s by my generation, and I still remember the excitement of those days. Major questions for me were exact correspondences between the expressive power of modal languages over relational models and classical, first-order and higher-order, languages describing the same. Others were more into axiomatic completeness, an art I have also practiced, but less often. In the process, a modal model theory was created, as well as systematic connections with universal algebra.

In the 1980s, I spent most of my time on logic and natural language, then a highly exciting new interface, and I lived ‘another life’ studying generalized quantifiers, categorial grammars, and natural logic. But around 1990, I returned to modal logic, partly because some very good students insisted it was my duty to supervise them in areas where I had once been active myself. One’s past always catches up! I found how much things had changed, with computer science becoming a major influence in addition to philosophy and mathematics. In particular, my dissertation work on what is now called bisimulation had been rediscovered in computational process theories, while people were also creating new systems in between modal and classical logic, with a delicate balance between expressive power and computational complexity. (There is a wonderful survey of three independent discoveries of bisimulation in a new LICS paper by Davide SanGiorgi from Pisa.) Through the 1990s, I then worked on understanding this balance of expressive power and complexity, which seems crucial to me in understanding what logical systems are and do. One discovery worth mentioning is the ‘Guarded Fragment’, a very large decidable system in between modal logic and first-order logic whose existence had remained unknown until then.

Right now, most of my work with modal logic is about informational processes and games for rational agents, since I have come to believe that ‘intelligent interaction’ is the heart of logic. This is connected with the spread of logical games for evaluation and bisimulation. And more importantly, this line of research goes back to the original philosophical motivation for modal logic as conceptual analysis of key structures in human cognition. But that is a larger story, which I will not spell out here.

That is it, in a nutshell. There is more about topics and challenges in the introductions which I wrote for this Translations book. If you want to read still more, try the Introduction to the “Handbook of Modal Logic”, written with Patrick Blackburn and Frank Wolter to give a fair impression of the many faces of the field today, and the major interdisciplinary connections influencing it. It may still be a bit in ‘Amsterdam style’, while there are other stories to tell about modal logic, e.g., with more emphasis on algebraic methods. Modal logic is not one unified country. But you can enter it with one story, and once inside, appreciate the other stories of the field.

But really, many challenges in one’s research are just due to chance encounters with students or colleagues who ask unexpected questions, and they also arise through collaborations with people that you respect and, very importantly: like!

Question by Jiangjie Qiu: This is a follow-up to Fenrong’s question. One can talk about the future once one knows about the history. You have been involved in the development of modal logic. Could you tell us what you think of the future of modal logic?

Answer: Jiangjie, I guess you mean that, when meeting one’s mother-in-law for the first time, one’s future suddenly becomes crystal-clear from seeing the past. I am not sure how true this is, but here are some thoughts that your question raises to me.

It has often been said that modal logic had no future, being about to die. When I first came to Stanford in 1983, Situation Theory was the new paradigm, which had won major battles against modal logic, and all that remained to be done were a few mopping-up operations against the last pockets of resistance. But nothing like that has happened! Modal Logic is about patterns of expression and reasoning which are so ubiquitous that they come up in new guises all the time. Ever since it was proposed around 1920, it has kept finding new uses. Some of the latest are ‘description logics’ in knowledge representation around 1990, grammar logics for sentence structure around 1995, and even web languages like XML from around 2000 turn out to have a modal logic core. Moreover, new connections with philosophy are still coming up, witness recent work on logics of freedom and social choice, and the same is true for mathematics, where just last year, new modal results became available about sheaves. I see no signs that this applicability of modal logic is diminishing at all. Indeed, and victory is sweet here, the best mathematical treatises on Situation Theory in the 1990s by Barwise and others turned out to revolve around, essentially, modal techniques!

In particular, I expect that modal logic will play an important role in creating a new theory of ‘intelligent interaction’ with broad sweep and impact. The most elegant systems of information flow and communication today are dynamic and epistemic logics, and also current connections between logic and game theory often run via modal logic. As I said already, this trend continues philosophical logic, and I expect a re-invigorated return to classical questions about modality, predication, and attitudes.

One deep issue are the future mathematical foundations of modal logic. Here I am not so sure what to predict. Modal model theory and algebra is still alive and kicking, witness the new Lindström theorems of my recent work with Balder ten Cate and Jouko Väänänen. But there is also another possible future history for the field, with a paradigm shift (though bisimulation is still there). This is the spectacular work on co-algebra, infinite streams, automata theory, and category theory in recent years. But then, co-algebra also links up with modal fixed-point logics such as the mu-calculus, which are a central theme also in the model-theoretic tradition. Time will tell!

Question by Meiyun Guo: As we can see from our translation project, modal logic has many applications in computer science. In particular, I noticed that in the recently appeared Handbook of Modal Logic, many chapter authors are computer scientists; does this mean that it is getting hard for philosophers to contribute in the study of modal logic? What are the remaining questions that the philosophers still can contribute to? You might know that there are many logicians who work in the department of philosophy in China; can you give us some advice?

Answer: Meiyun, I would say: open the doors! Surely, most logic research today is in computer science, and some people even say that the most innovative logic of today comes from there. But let’s get straight on what this means, and does not mean.

‘Computer science’ today has far outgrown the narrower technical study of programs and machines. Indeed, it has been claimed that computer science is just philosophy ‘continued by other means’. Just go to a conference on Knowledge Representation or on Agents, and you will find that there is some truth to this! I think that philosophers should be allies of computer scientists: at least, of the broad-minded visionary ones. And it is a small scandal that philosophy in the 20^th century has largely ignored the most striking intellectual revolution of all, viz. the tandem of information technology in society and the computational paradigm in Academia. Only now, ‘Philosophy of Information’ is coming to the fore, witness the Handbook on this topic co-edited with my colleague Pieter Adriaans, a classical philosopher who became a successful IT entrepreneur, and afterwards, a professor of learning systems in computer science. Boundaries do not mean all that much today, and philosophers can thrive anywhere!

Now about what you can do as a philosopher. Do not try to be a small mathematican proing the ‘easy theorems’ left over by technical logicians. Of course, it is good to do some technical work to get first-hand inside experience with mathematical methods. And technical experience also helps see through impressive formulas and theorems, and see the real ideas and abstractions. But the best contributions by philosophers use talents that they themselves are best at, such as conceptual analysis, new puzzles, and seeing new perspectives that plain ‘theorem provers’ need not be good at at all. For instance, in modern epistemology or philosophy of action, young philosophers are exploring an ‘open space’of notions with wonderful sensitivity to the subtleties of rational agency and intelligent interaction. Logicians benefit from this in their system construction, but the ideal is really a fruitful symbiosis between equal partners. Indeed, some of the main advances in Amsterdam were contributions by professors and students of philosophy. Think of ’dynamic semantics’ in the study of natural language, or the powerful update schemes of current dynamic-epistemic logic.

In other words, logic gives you a method and abstract iscipline, but do not compete with the mathematicians, and approach things with philosophical sensibility!

Question by Junwei Yu: I want to ask a more concrete question. I have translated your chapter “modal correspondence theory”, first published in the Handbook of Philosophical Logic. In that chapter your studied the relationship between modal logic and first order logic mainly, but what about the correspondence between modal logic and higher order logic?

Answer: Good question. I wrote a bit on this in my introduction to our translations Book. Also relevant is the Appendix in the Correspondence Chapter you translated. But let me try once more, as directly as I can – because you raise a subtle point.

Correspondence Theory is past of the general model theory of modal logic. Now that theory comes in two flavours: first-order over models, and second-order over frames. The first style is the 'standard story' of bisimulation invariance, expressive power vs. computational complexity, and fine-structure of first-order logic, which I mentioned in my answer to Fenrong, and which is also the main line of the “Handbook of Modal Logic”. By now we know a lot about it. The second style, and the main thrust of my book "Modal Logic and Classical Logic", is the fine-structure of (monadic) second-order logic, viewing modal formulas as defining special frame properties. I see this area of as under-developed, partly because classical model-theoretic methods are not available – and Correspondence Theory has not yet blossomed the way I originally hoped for. We have some old landmark results, of course, and Balder ten Cate solved some open problems in his recent ILLC thesis, which won the Ackermann Award of the European Association for Theoretical Computer Science. And there is much other work, for instance, on modal logics over topological spaces, which looks relevant to me. But we do not yet have a good sense of ‘modal fragments’ of second-order logic, partly because we do not know the relevant 'hierarchies'.

Nevertheless, I am also somewhat optimistic. Only recently, I published two papers which showed that there is a genuine hierarchy ‘first-order’, ‘fixed-point-definable’, ‘essentially higher-order’ among modal frame properties, and this throws new light on old correspondence-theoretic questions. In particular, there are lots of questions to ask about fixed-point extensions of the earlier Correspondence Theory. As a by-product of independent interest, Albert Visser and I found that, when viewed in this way, the two major modal-style fixed-point logics, mu-calculus and provability logic, are really very closely related. I think a lot more is waiting to be discovered here!

Question by Xinwen Liu: There is another thing I want to raise, though I am not sure whether my observation is correct or not. When I read papers in modal logic, the issue of complexity is always important. This is different from earlier logic research, which did not pay much attention to complexity. Is this related to the application of modal logics? As there are many such systems, do we need to compare them in terms of complexity?

Answer: Yes, complexity was not on the radar in my youth. We already felt quite virtuous when a logic was decidable in principle! You might think that this new theme is purely practical, but I do not think so. Complexity Theory has made us sensitive to the mathematical fine-structure of decidability, extending Recursion Theory which is mainly about undecidable processes, with its own natural levels and deep questions. In particular, it is a fundamental issue to understand the balance between semantic and algorithmic aspects of any logical system, i.e., the earlier-mentioned expressive power versus computational ‘difficulty’. I would even say that philosophers should pay much more attention to these notions, since complexity is an important notion all across cognitive tasks, interaction, and even organization. Developing huge formal systems without thinking about how they might work seems to do only half the job.

I myself was influenced a lot by our student Edith Spaan who wrote a dissertation in 1993 on complexity of modal logics. Instead of the usual business of results for one system after another, she proved very general theorems analyzing which features of a modal language determine its computational behaviour. That, of course, is what we should be aiming for – and especially, understanding the factors that lead to jumps in complexity from one system to another. Let me be a little bit more precise here. Any logical system has a ‘complexity profile’ for its three core tasks: model checking, satisfiability testing, and model comparison (testing elementary equivalence on finite models). For first-order logic, that profile is, in that task order: ‘Pspace-complete, Undecidable, NP’. For propositional logic, the profile runs: ‘Ptime, NP-complete, and Ptime’. Basic modal logic lies in between, it has less expressive power than first-order logic, but in return, its profile is nicer: ‘Ptime, Pspace-complete, Ptime’. To me, these facts seem a natural companion to expressive power, bisimulation, and other semantic themes. Moreover, they are intertwined. seeing why model-checking modal formulas is not exponential in the modal operator depth, unlike with first-order quantifiers, really gives you an important additional insight in how a modal language works.

Computational complexity is still a new topic, missing in standard logic textbooks. I have been experimenting with introducing it into basic logic courses. E.g., I want to make students see that propositional logic, instead of being just a stepping stone, is itself a rich theory of computation, once you understand the reductions betweenmodel checking and Ptime problems, and satisfiability and NP-problems, as explained in the great textbook by Papadimitriou. And I want them to understand the ‘balance’ and ‘complexity jumps’. But so far, it has not been easy. Maybe you can help!

Question by Meiyun Guo: In recent years you have been analyzing social phenomena by using modal logical tools. But I sometimes feel a little bit worried, since notions like preference, beliefs, expectation, and intention are subjective, does logic really helps us here, and how?

Answer: Aha, ‘soft facts, weak theory’? Or ‘real life, no logic’? Well, I am not guaranteeing success, just claiming that the time is ripe for more ambitious endeavours. And in this, I am not advocating anything idiosyncratic. The move from a focus on mathematical proof and machine computation to describing rational agency in social settings seems quite natural to me. It has been happening in many areas, and the recent convergences between computer science, logic, and game theory show that there is formal substance here. Moreover, I see this research as totally in line with traditional philosophical logic, which has always tried to analyze human-style notions like knowledge, belief, intention, duty, etc. These may be subjective notions, but their theory can be quite precise, witness the work of Hintikka, Kripke, Lewis, Stalnaker, and others. Likewise, even though agents preferences may be totally subjective, the logical theory of those preferences can be very objective! Moreover, studying agency seems a natural continuation of the traditional ‘core agenda’ of logic, as arising out of the study of political debate and legal procedure: both highly interactive social processes. I have argued for this view in a number of programmatic papers, a few of which have appeared or will appear in China, including my lecture at the DLMPS Congress in Beijing, August of this year. In particular, the logical systems describing this social dynamics still conform to all standards of precision that we know.

But your question is also: ‘What good does logic do when applied to human reality’? Well, at a fundamental level, it gives us models for thinking about human behaviour, and bringing out key features. Of course, these models do not capture every part of that behaviour: if you see a person in tears agonizing about a personal decision, decision, theory, logic, and game theory are surely not the whole story. Maybe a poet would do a better job at capturing the essence of that situation. But like game theory, logic offers at least some vantage points from which to understand what is happening, and as such, it adds to our repertoire for seeing us as what we are. Practically, I would even say that this style of analysis might help us improve our styles of behaviour and organization, in line with the ‘social software’ ideas of Rohit Parikh. But these are all words. The proof of ‘fit’ is in looking at what logical analysis actually does! Jan van Eijck and Rineke Verbrugge are editing a book with “Dialogues” following a project on logic and social software at the Netherlands Institute for Advanced Studies in 2006, with many illustrations. You can be the judge of their quality for yourself.

余俊伟问：这是一个一般的问题，可是我还是想利用这个机会问您，有时候，我在想为什么逻辑学家要自讨苦吃以一种极端的方式使用形式语言。相反，数学家只使用部分的形式语言。如何理解这里的区别？您能否解释一些历史背景知识？

范本特姆答：这是一个颇具洞察力的问题。我是一个逻辑学家，我设计并且研究形式系统，用向你所描述的标准方式。不管怎么说，我对形式系统还是觉得不舒服。肯定没有人在绝对意义上使用完全的形式语言，使用形式系统。即使数学家也使用自然语言，只是增加一些他们需要的形式记号。当你试图向别人解释某些逻辑结果的重要性的时候，这一现象就凸现出来了，因为形式语言和形式系统是一个难以渗透的屏障。譬如，哥德尔的结果是关于（一阶）算术形式系统的不完全性，而一般的人，包括数学家在内，认为“算术”是一个永远开放的实践领域——很难清楚地说明哥德尔的逻辑结果如何描述算术系统的。同样，传统逻辑是研究推理这一更广泛的现象的，例如，研究“否定”和“量化”，而不是像我们现在所讲授的那样：是形式系统的一个阶段，从命题逻辑通过模态逻辑到达一阶逻辑，甚至超越它。幸运的是，逻辑学家们并没有注意到这个问题，因为他们可以建立形式系统，证明关于这些系统的元定理，而不必考虑它们的实际应用或把它们解释给更广大的听众。这个研究的“闭世界”能够给你提供职位和尊重，为什么还要担忧？

不过，我对我称之为现代逻辑的“系统禁锢”很担心。它把逻辑哲学和数学混在一起，用系统-生成的问题代替了真正的问题，把我们与周围的世界完全割裂开。我认为形式语言和形式系统本身并不重要。在某种极端的层次上它们也是有用的，例如，在使用计算机进行定理证明或自然语言处理中。但是，我认为我们需要理解整个领域，即形式系统和自然实践之间的联系。就拿数学来说，在历史上，它曾经是自然语言和自然推理加上一些形式的记号、证明模式等的动态的混合物。从事数学研究的数学家们意识到这一点，发展了混合的形式系统和自然语言，譬如，德·布朗（De Bruyn） 的 “数学术语”，或在波恩的科普克（P. Koepke）正在做的关于证明结构的项目。更一般而言，哲学家斯塔尔（F. Staal）十分强调新记号和它们成功融入到现存科学实践中的关键作用，这一现象不管在西方，还是在亚洲的传统中都存在。

作为一个逻辑学家，我看到的是一个有趣的动态现象。出于想要在科学交流和面对面的讨论中更为精确的压力考虑，数学家们发现了新记号和证明模式。因此，更形式化的语言进入了自然语言。但是，这一过程的逆向也在同时进行。好的数学家也能够从形式主义中后退一步，用自然语言为证明做更高层次的描述。我们都有这样的感觉，当我们能够在不同的层次上描述一个证明的时候，我们觉得我们真正理解了那个证明。事实上，这种精确化和解释的互动是一个激动人心的“广义证明论”形式，对它的研究也许会让大家都受益。一般而言，文化产品，如记号、逻辑推理、算法、新博弈等的连续不断的“成功融入”也是人类行为的一大特点。这是逻辑与现实交汇的地方。一般的认知科学也在设法理解这种混合的实践。

胡义昭问：我想问一个问题，我想很多学习逻辑的学生会对这个问题和您的回答感兴趣的。如何正确理解逻辑的理论价值和实际价值？具体来说，譬如，为什么完全性对我们来说很重要？

范本特姆答：我认为一个人研究某些问题是因为他喜欢那些问题——也许喜欢不能说明问题的全部，应该是真正的爱。让我先讲一个关于欧几里德的故事，当有人在街上问他数学的实际价值是什么的时候，他让他的随从给了那个人一些钱，因为他觉得追寻数学的实际价值的人很可怜。你怎样看待他这样的回答？

我认为逻辑的价值在于其理论价值。逻辑是一种思维方式，为其他许多科学提供基础，我们已经证明了它对抽象概念分析的价值。而且，在快速-分裂的学术界，逻辑似乎是一支统一的力量：攀登逻辑的山峰可以帮助我们看到更广的模式，看清不同学科之间的联系（像刘奋荣曾经在一个小文章中提到的那样）。这就是为什么逻辑、语言和计算研究所（ILLC）是阿姆斯特丹唯一跨大学各系的一个研究所。逻辑在起作用！而且，这也与爱上逻辑有极大的关系，知性的爱同感性的爱是同样的道理，逻辑可以非常漂亮，但并不是总是漂亮，但在一天的适当时候在适当的光线条件下的确是这样……

你最后的说明切中要害，有时候漂亮在于那些“无用”的结果。譬如完全性定理的证明。对于实际的应用，可靠性通常就够了：我们需要知道我们进行的推理是正确的。我们的系统能否真正把所有有效的推理模式都刻画了，这是一个更理论性的思考。但是，这是一个多么美妙的问题，哥德尔的论文证明了一阶逻辑的完全性，这又是一个多么漂亮的结果！

如今，也许会有很多同事能够向你说明逻辑的实际应用价值。一些重要的权威曾经宣称“逻辑是计算机科学的演算”，意思是说，若你有能力做形式系统和方法，你就能成为一个在信息技术、软件工程、主体系统等方面成功的工程师。我相信这种应用是存在的，有逻辑学家们在工业界和其他领域工作。同样，有人认为逻辑在自然语言语义、法律推理、一般的论辩分析等方面非常有帮助，甚至逻辑能帮助你成为一个好的社会辩论家。（我还没有在我自己身上发现这些功效，但是，我似乎还有时间提高……）。甚至有些国家的警察和军事领域也发现了逻辑推理技巧的用处。

我不想就此结束，这里是又一个回答。因为我教逻辑已经很多年了，很多人曾经问过我类似的问题。我不能只说，教逻辑是为了培养未来的逻辑学家，因为显然不需要那么多的逻辑学家。我是这样看待教授学生逻辑这件事情本身的。我觉得我可以教学生用某种抽象的逻辑方式进行思考，而不是用他们以前习惯的方式。这是对他们已经具有的做事能力的一种“强化”，这是在我们所说的“融入”的意义上而言的。这种方式是抽象的和形式化的，但是如果你用得好，可以在远离现实的范围内使用，发现新的推理模式和选择的自由。好的逻辑学家是有创造力的、灵活的、能够思考现存模式之外的问题。对我而言，“理论是在现实中最好的投资”！获得了逻辑训练的人能够做好任何事情，因为当他们做其他事情的时候，是带着逻辑“这个额外产品”的。这不是一种自我满足的认识。我曾经同硅谷的企业家们一起组织过招聘学生的会议。他们都说，“我们希望雇到在基础科学方面受过严格训练的学生，而不是适用于目前生产线需要的应用型人才”。原因很简单，现在的公司不知道几年后他们会生产什么，但是他们知道，在快速发展的社会中有一些东西是不变的，那就是理论的洞见和抽象的能力。

郭佳宏问：我有一个涉及翻译的小问题。在您的论文“偏好改变的动态逻辑”中，您讨论了一个非常有趣的概念叫“regret”。您把它定义为下面的情况，你知道p不可能得到，但是你更喜欢得到p。在汉语中，对这样的情况有两个可能的翻译“后悔”和“遗憾”，它们有相似的含义。有意思的是，前者包含一些时态的要素。即，当有什么事情发生过，不像某人期望的那样，他会感到后悔。受这一解释的启发，我的问题的是，我们能否给英语中的“遗憾”添加时态的因素？

范本特姆答：结果我们还是遭遇关于翻译的棘手问题！的确，在那篇动态逻辑的文章中，“遗憾”是在你提到的非-时态的意义上解释的。对于这一解释，我们经常可以看到。譬如，我会说，很遗憾，由于热力学第二定律，没有无止尽的能源供应。但是我也同意你的观点，英语中遗憾的很多意义与时态有关，跟过去时有一定的关系（我觉得很遗憾由于我的愚蠢造成的后果），也跟将来时（很遗憾我总有死）有一定关系。当然，在那篇论文中，我们的主要目标有所不同，我们想指出遗憾适用于那些我们知道不会发生的情境——至少对于那些并非彻头彻尾的现实主义者。除了“遗憾”这个词，在你翻译我的其他论文时一定还碰到更多的例子。余俊伟曾经提到我喜欢用的一个词“fine-structure”，它在英语中意思是“微细结构”，具有“精致的”和“好的”这样的含义。他说在汉语中没有这样的词语与之相对应。我很喜欢我们在电子邮件中讨论过的其他例子；这些关于适当性的讨论并不是什么坏事，相反，我觉得这样的比较非常有趣！

我希望我们会再有机会更广泛地讨论你的翻译经历。我意识到，逻辑论文是非常特殊的，因为它们包括很多技术术语，这些术语具有固定的意义，再加上一般的学术方式和术语在世界各地都通用。但是，我对逻辑术语如何被翻译成汉语，障碍在哪里等问题很感兴趣。大家一般认为，现代的逻辑系统不是“中性的”，因为它们是沿着具体的人类语言（常常是印欧语系）的主谓结构发展而来的。另一方面，我自己从来没有看到，中国学生在理解现代逻辑时有什么困难。因此，我们希望找到那个抽象的层次可以进行交流。（我记得1983年在斯坦福首次跟从中国大陆来的第一个学生郭维德见面时，这就是我们讨论的话题）。我真希望我自己是汉语的专家，从而可以从我们的讨论中学到更多的东西。也许再过几年，我应该试着翻译你的论文！

刘奋荣问：郭佳宏的问题让我想起从去年10月到现在我们在翻译过程中交换的很多邮件。我们非常感谢您的耐心解释。我们不得不承认，翻译您的作品并不是件容易的事情。也许难题在于这是文化之间的一种翻译，而不仅仅是两种语言之间的翻译。您是如何看待这个问题的？

范本特姆答：刘奋荣，这个问题很难回答。换句话说，人们是否真的理解对方？语言是否预设或甚至决定文化，反之亦然？沃尔夫假设是否正确，我们是否被自己的语言所束缚？如果我们要谈论所有的这些问题，这个访谈可以更长！当然，我们不是第一个提出这样的问题：这些问题一直在讨论。譬如很多世纪以来，从我们的文化开始进行接触，大家就在讨论中国和西方的传统。坦白地说，我对你自己作为一个译者、一个学生、一个研究者，站在中西方文化的交汇处的经历很感兴趣，而不是我自己作为站在远处的一个同事和访问者的观点。

既然你问到这个问题，也许我应该说点什么。我认为语言、推理和文化是紧密联系在一起的。然而，很多关于这些问题的讨论看起来毫无成果，因为人们通常不愿意承认一些事实，不做实际的区分。首先，我们祖先从非洲走出来到现在，时间相对来说还是很短暂，我并不期待在神经-认知结构方面有很大的生理差别——尽管毫无疑问，文化产品，像字母表和字符会影响我们短期的处理事实的能力。当然，文化提供了一个背景，这些基本的技巧可以被操练。显然，当社会生活和教育结构不同时，解释和行为的倾向性会有所不同。我想说的是，所有的文化都面临同样的问题，如何建造一个公正合理的社会生活，在稳定的解决方案中我们到底希望有多少变化？当你看到那些不变的东西而不仅仅注意对行为的偶然解释时，我常常会惊讶，情况会如此惊人地相似。中国人很注重“面子”，我可以向你保证，同样的情况也在西方存在：只不过解释方式不同而已。而且，“文化”一词是如此的相似，它隐藏了阶层之间的巨大差异。你比较荷兰的一位学者和中国的一个农民，你会觉得这个世界是如此的不同。同样，如果你对荷兰的一个农民和中国的一位学者进行比较，恐怕也会得到同样的结论。而中国和西方的学者则具有很多共通的特性，使得他们不再属于“单个-文化”。不过，这里没有多少结论。

我自己被一些简单的经验观察所震撼。纵观世界历史，文化之间不断碰撞，混杂，一个战胜另一个，等等。好的想法，同样，坏的想法——互相渗透，即使这样的过程有时包含着“新的误解”（但是这也发生在同一种文化下的不同人群之间）。这里有一个具体的例子：在逻辑、理性和互动的会议上，张家龙教授做了关于墨家逻辑的报告。我很惊讶地发现，这与希腊的传统有着惊人的相似性，千里之遥的人类智力似乎在平行的轨道上运行。

这不是一个答案。在这个方面，我应当向你学习，而不是你向我学习。

郭佳宏问：我们已经讨论了这么多关于模态逻辑的问题，但是您自己的研究不仅仅局限于模态逻辑。只提及几个，您有很多工作是在空间逻辑，时间逻辑，逻辑和认知等领域中进行的。您能否对21世纪的逻辑趋势说点什么？

范本特姆答：我自己的兴趣的确比模态逻辑本身要广。这些年来，我的研究涉及其他很多领域。一旦你变老，很难避免这一点！模态逻辑是我最喜欢的方法，尽管我并不认为这是唯一的方法：我也研究一阶逻辑，甚至类型论。而且，我还花了10年的时间研究自然语言的语法和语义，其他很多时间研究科学方法论、与认知科学的联系等。最近，我还在研究逻辑和博弈。我希望我们的翻译系列会最终把我的这些活动全面展现给读者。

你在问我对逻辑的更一般的观点。我不想在这里再重复说明，因为针对不同的听众，我自己写了很多论文、访谈。也许实在是太多了！看看我最近在第13届方法论、逻辑和科学哲学会议上做的特邀报告，你会得到一些公正的印象。另外，我的观念也在不断进化，某一年的真实想法可能会变成下一年的错误认识。例如，我们的研究所ILLC的现在就与它刚刚建立的时候有很大的不同，很难说，我在多少年前已经预见到或计划到目前这样的情况。

我还是坚持我的那个口号，我在这个访谈中多次提到。我认为，在人文学科、精确性学科和社会学科的交汇处，现代逻辑或许开始由传统的议程转到更广泛的智能互动，我认为我的工作正在帮助这样的历史发展——以一种温和非暴力的劝说方式。

刘奋荣问：我刚刚收到通知，具有很高威望的科学出版社乐意出版我们的《逻辑之门》系列丛书。继第一卷模态逻辑之后，我们将会翻译出版第二卷《语言逻辑》和第三卷《逻辑哲学》。您为第一卷做了很多工作，除了回答译者的问题，您还为此书的出版写了新的序。特别是，您为每一部分撰写了新的导引。我相信，这会对广大的读者很有极大的帮助。您想不想借此机会对未来的读者说点什么？

范本特姆答：看来，上面的回答的中的很多期望已经有保证了。中国是一个能够很快实现你梦想的地方！我想对读者们说：

我希望我的论文的确开启了一扇“逻辑之门”。逻辑一个古老的学科，它的历史可以追溯到2500年之前的希腊和印度，而且逻辑也是一个充满活力的丰富多彩的现代领域，有很多大师，有很多不同的观点，有关于科学生活的全景透视。也许，你已经很高兴能够学习逻辑提供给你的东西，而同样重要的是，毫无疑问，逻辑会因为有了中国的读者和学者的加盟而受益匪浅。你们会给逻辑学带来自己的洞见和新的研究主题。我也认为这样的接触在塑造一个共同的知识分子群体方面有很重要的意义。在这里，我们大家可以平等地参与，对文明和生产方式表示同意或异议。这些好处远远超出了任何具体的学科。

另外，这个翻译项目也给不同的文化之间提供了接触的机会。在打开逻辑之门的过程中，我们会发现有很多在方式或“品位”方面的细微差别——但是这也许会增加我们品尝“不同菜肴”的喜悦，而在这方面中国人无疑是专家。对我而言，我觉得这样的接触发生在现在有很多优势，因为我自己还可以为此做一点事情。既然是“逻辑之门”，那么我们可以进来，也可以出去。

这是关于翻译的一个访谈，我想用一个小的语言典故来结束这里的对话。很少有人意识到，表示确定某物方位的词语在西方是“orientation”，它包含了“向东方”的拉丁语！最后，我想再次感谢所有的译者，把如此迷人的确定方位的过程付诸行动。

余俊伟问：我想问一个更为具体的问题。我翻译的是“模态对应理论”那一章，它最初出版在《哲学逻辑手册》。在那一章中，您主要关注的是模态逻辑和一阶逻辑之间的关系，那么模态逻辑和高阶逻辑之间的对应关系又是怎样的？

范本特姆答：问得好，这个问题涉及一个敏感的问题。我在《逻辑之门：模态逻辑》一书的导论中写了关于这个问题的一些想法。在你翻译的对应理论那一章的附录中也可以找到相关的内容。但是，我想再次试图在这里解释这个问题。

对应理论是模态逻辑一般模型论的一段历史。现在出现对应理论的两个方面：针对模型的一阶对应，和针对框架的二阶对应。第一种方式是关于互模拟不变性的“典型故事”，表达力对抗计算复杂性，研究一阶逻辑的微细结构。在我对刘奋荣的回答中也提到过，这是《模态逻辑手册》的主线。到目前为止，我们对此已经有很多认识。第二种方式，是我的专著《模态逻辑和经典逻辑》所研究的主要问题，是关于二阶逻辑微细结构的研究，把模态逻辑公式定义看作是用来定义框架的具体属性。我认为，这个研究领域还不够发达，部分原因是经典的模型论方法没有被使用——对应理论没有像我曾经希望的那样开花结果。当然，这一方面，我们已经有一些老的重要的技术结果，腾卡特在他的博士论文中解决了一些开放的问题，因此获得了欧洲理论计算机协会颁发的阿克曼奖。同时，还有许多其他的工作，例如，拓扑空间的模态逻辑看起来与这一方面的研究十分相关。但是，我们还没有对二阶逻辑的“模态片段”有很充分的认识，部分原因是我们不知道有关的“结构布局”。

不管怎么说，我总是持乐观态度。最近我发表了两篇论文，表明在模态框架属性中存在一个真正的结构布局：“一阶的”、“不动点可定义的”和“基本高阶的”，这为老的对应理论的问题带来了一丝曙光。特别是，关于早期对应理论的不动点扩展有许多问题值得研究。作为其他出于独立兴趣的研究的副产品，我和维施尔（A. Visser）发现，当我们这样思考问题的时候，两个主要的模态不动点逻辑，模态μ-演算和可证性逻辑紧密相连。我觉得，这里有很多问题有待进一步研究发现！

刘新文问：我想问另一个问题，尽管我不太确信我自己的观察是否正确。当我阅读模态逻辑的论文时，发现有很多关于复杂性问题的讨论。这似乎与早期的逻辑研究有所不同，那时候，大家不怎么考虑复杂性的问题。这一现象是否与模态逻辑的应用有关？是不是因为有太多的模态逻辑系统，我们需要比较它们的复杂性？

范本特姆答：是的，在我年轻的时候，复杂性并不在大家关注的视野之内。当我们知道一个逻辑在原则上是可判定的就已经觉得它很好了！你也许认为这个新方面纯粹是出于实际应用考虑的，但是我并不这样认为。复杂性理论扩展了研究不可判定进程的递归论，使我们能够对可判定性的数学精细结构有更清楚的认识，而且，复杂性理论本身具有十分自然的层次结构和其特有的深奥的问题。特别地，理解任何逻辑系统的语义和算法之间的平衡（即，前面提到的表达力对抗计算“难度”）是一个基本的问题。我想说，哲学家应当更多关注这些概念，因为复杂性是贯穿于认知任务、互动甚至组织结构中的一个重要概念。构造庞大的形式系统而不考虑它们如何运作似乎只是做了工作的一半。

我自己深受我的学生斯庞（E. Spaan）的影响，她在1993年写了关于模态逻辑复杂性的博士论文。她的论文不是像通常那样，为一个又一个的逻辑系统证明一些技术结果。相反，她证明了非常一般的定理，来分析模态语言的哪些特征能决定其计算行为。当然，那是我们应当努力的方向，特别是，理解什么因素导致一个系统的复杂性到另一个系统的复杂性有大的跳跃。我想在对此稍作更为精确的解释。相对于下面的三个核心任务：模型检测，可满足性测试和模型比较（测试有穷模型的初等等价性）， 任何逻辑系统都有一个“复杂性轮廓”。对一阶逻辑而言， 这个概图是：“P-空间完全的（Pspace-complete）, 不可判定的（Undecidable）, NP”。对命题逻辑而言，它们是：“P-时间的（Ptime）, NP-完全的（NP-complete）, 和P时间的（Ptime）”。基本的模态逻辑介于二者之间，它具有比一阶逻辑弱的表达力，但是，作为回报，它具有较好的复杂性概图：“P-时间的（Ptime），P-空间完全的（Pspace-complete）, P-时间的（Ptime）”。对我来说，这些事实是对表达力、互模拟和其他语义问题的一个自然补充。而且，它们互相交织在一起。理解为什么模态公式的模型检测在模态算子度中不是幂指数复杂的（这与一阶量词公式不同），的确给你对理解模态语言如何运作一个新的重要洞见。

计算复杂性仍然是一个新的研究课题，在经典的逻辑教科书中通常看不到有关它的阐述。我曾经试着把这一内容引入基本的逻辑课程中。譬如，我试图让学生明白命题逻辑不仅仅是一块踏脚石，一旦你理解模型检测和P时间可解的问题之间的规约，可满足性和NP-问题之间的规约，像在帕帕蒂米翠斯（C. Papadimitriou）写的教科书中解释的那样，你就会意识到命题逻辑本身是一个极为丰富的计算理论。我也希望学生能够理解所谓的“平衡”和“复杂性跳跃”等现象。但是到现在为止，这似乎并不容易做到。也许你可以帮忙做到！

郭美云问：近年来您在试图利用模态逻辑这一工具分析一些社会现象。我有一点担心，因为很多概念像偏好、信念、预期以及意图都具有主观性，逻辑能否在这里真的帮助我们？它在那些方面可以帮我们？

范本特姆答：啊哈，你在说“软的事实，弱的理论”？或者“真实的生活，没有逻辑”？好吧，我不能保证这些努力一定会成功，我只能说，现在的时机已经成熟，我们可以多尝试做一些新的尝试。我不是在提倡某种特异的东西。从对数学证明和机器计算的研究到对理性主体的描述的转变对我来说是一件十分自然的事情。在很多领域这样的事情已经发生。最近，计算机、逻辑和博弈论的汇合表明了这里有某种形式的东西存在。而且，我认为，这一研究完全跟传统的哲学逻辑研究相一致，哲学逻辑试图分析关于主体的一些概念，如知识、信念、意图、责任等。这些概念本身可能是主观的，但是，关于它们的理论则可以是非常精确的。像我们在辛梯卡（J. Hintikka），克里普克（S. Kripke），路易斯 （D. Lewis），斯托内克尔（R. Stalnaker）和其他人的作品中感受到的那样。同样，即使主体的偏好是完全主观的，关于偏好的逻辑理论可以是客观的！而且，对主体的现象进行研究似乎是传统逻辑“核心议程”的一个自然延续，我们知道，这源于政治辩论和法律程序这两个高度互动的社会过程。我在很多论文中为这种观点做过论证，其中一些论文已经发表在中国。今年8月我在第13届国际逻辑、方法论和科学哲学会议上做关于这一主题的特邀报告，论文会在之后发表。特别是，那些描述社会动态性的逻辑系统仍然要符合我们熟悉的精确性的所有标准。

但是，你的问题也可以阐述为：“逻辑在人类的现实中到底可以起什么作用？”在最基本的层次上说，逻辑为我们提供一些模型，以便我们思考人类的行为，找到关键的特征。当然，这些特征不能刻画行为的所有方面：如果你看到一个人哭泣，他在为个人的选择而苦恼。显然，决策论、逻辑和博弈不能解决问题。也许一位诗人会在描述这样的情境时做得更好。但是，像博弈论一样，逻辑至少提供一个好的视角，从那里你可以理解正在发生什么样的事情，等等。它给我们的节目单增加了一项新议程，让我们能够看清楚自己的样子。从实际的角度说，我认为这种分析有助于提高我们的行为和组织方式，这与帕瑞克（R. Parikh）所倡导的“社会软件”的想法相吻合。但是，这些都是高谈阔论。“适当性”的证明要看逻辑分析实际上做的事情！在2006年荷兰高等研究所的项目“逻辑和社会软件”完成之后，范·埃克（J.van Eijck）和弗布茹荷（R. Verbrugge）在编一本书，由“对话”组成，另加很多解释说明。你可以对其质量的优劣做出你的判断。

刘新文问：我还有一个观察，现在大家似乎对逻辑的组合很感兴趣。例如，我们可以在认知逻辑中加入动态算子得到动态认知逻辑，加入时间，得到时态的动态认知逻辑，然后再加入策略，等等。这一过程似乎永无止境。我有时想，这样做的目的到底是什么。当我们做这样的事情的时候，应当考虑什么问题？

范本特姆答：你是在问，我们能否持续不断地构造越来越大的逻辑系统？首先我想提醒你，对形式模型做“有控制地扩张”是一项科学的核心事业，所以，这样做本身没有甚么错。当然，应当也有“侧面的”创造性活动，找到简单的新模型来解释迄今为止未被探索的现实的一些方面。实际上，关于理性主体的个别方面（行为、信念和偏好等）的模型早已存在很长一段时间了。这是通常的“分析”方法的一种体现。但是，一个新问题在很大程度上被忽略了：这些要素如何能否成功地在一个系统中运作？或在一个人的头脑中所有的这些事情同时进行？

在1990年代出现一个激动人心的新趋势，即，考察当逻辑系统被组合在一起时候会怎么样，大家对模态逻辑系统的各种组合进行“实验”。你可以把这看作是实际的需要，但是，我自己把它看作是关于“认知体系”的一个基本问题：不同的逻辑子系统如何能够交换信息在一起工作？随着时间的流逝，大家清楚地看到，这个问题很棘手。整个系统的复杂性由组成部件的复杂性所决定，而且也受组合方式所决定。例如，哈尔彭（J. Halpern） 和 瓦帝（M. Vardi） 发现了下面的结果：如果把单独的可判定的认知逻辑和时态逻辑放在一起，假设主体具有完美的记忆力，那么组合的认知时态逻辑就变得不再可判定了。

这里的问题是，为了描述更有意义的现象，我们需要复杂的系统，主体能够执行很多不同的任务。适当的方法论是首先在简单的逻辑系统中分析这些任务。之后，我们需要理解如果把这些系统放在一起，它们是如何运作的。对此我们还远没有一个较为一般的认识。我曾经与帕奎特（E. Pacuit）和赫布兰第（J. Gerbrandy）写论文讨论过把动态认知逻辑和时态逻辑组合在一起的问题，我们脑中的确在思考这样的一些一般性问题。大家并不是在提倡“盲目的”组合，大家的确意识到了其中涉及的复杂性的极限问题。我同意你的想法，我们不能不加限制地构造大的怪物，但是我希望你能看到这是一个激动人心的挑战。什么样的原则可以使得组合的逻辑简单？我们如何能够避免著名的“科学悖论”、即创造的理论比现实还要复杂？我们的目标应当是解释现实，设法简化现实。

这里有很多事情我尚不知晓。例如，下面是我喜欢的一个悖论。在人类实践中，同时做几件事情似乎是很有效率的。例如，消除自然语言的歧义可以借助语义的和语用的上下文，而这又依赖于我们用语言去完成的进一步的任务。但是，把语法、语义和语用理论组合在一起的逻辑系统会变得很复杂。如何才能避免这样的不协调？在组合方法中我们忽视了什么东西？也许应当多考虑一下关于系统组织的一些原则。说了这么多，我现在很乐意把这一事业交还给你完成！

逻辑之门：作者与译者的对话

——约翰·范本特姆教授访谈录

（作者：刘奋荣 刘新文 余俊伟）

范本特姆（J. van Benthem）教授是当今最著名的逻辑学家之一，他的学术研究涉及模态逻辑、语言逻辑以及逻辑哲学等领域。从1970年代到现在，他撰写了6部专著和约300 篇学术论文，主编了4部具有权威性的逻辑手册，其影响从学术界对他的著作的引用程度可见一斑。由荷兰阿姆斯特丹大学资助，2006年10月开始启动的“逻辑之门”项目旨在将范·本特姆的著作翻译成中文，使汉语地区的读者更好地了解他在逻辑方面的研究成果。《逻辑之门》第一卷收录了他在模态逻辑领域的13篇经典论文。根据主题的不同，这些论文进一步分为四个部分：模态逻辑的基本理论、模态逻辑和计算、模态逻辑和信息、以及模态逻辑和博弈。2007年8月1日，项目第一期顺利完成；由北京市逻辑学会和阿姆斯特丹大学资助，翻译小组在中国人民大学举办了“Modality on the Move”的学术会议，范·本特姆教授应邀做了关于模态逻辑发展及现状的主题发言，译者们结合自己的研究和所译的论文分别做了学术报告。会议最后是著译者之间的一个互动，这一交流自由而广泛，涉及了模态逻辑的历史、现状和未来，翻译过程中遇到的种种问题，各自的研究兴趣和面临的困惑，等等。我们现将作者和译者之间的对话翻译整理如下，与广大读者共享。

刘奋荣问：今天我们欢聚一堂，一方面庆祝翻译工作的顺利完成，另一方面想借此机会与您面对面交谈。我们所翻译的是您的13篇论文，它们都是关于模态逻辑的。这些论文的出版时间跨度从1970年代到现在。我注意到，所有的这些论文被引用的频率很高。您能否解释一下这些年来您自己对模态逻辑的认识和想法是如何发展的？最具挑战性的问题曾经有哪些？

范本特姆答：首先，我想借此机会感谢大家为翻译工作所做的贡献！对我而言，“逻辑之门”使我有机会与年轻而聪明的中国逻辑学家进行紧密接触，也使我有机会在中国认识更多的新的逻辑工作者。同时，这也是一个很好的机会让我重新反思自己的研究以及这些研究领域何去何从的问题。我希望这个访谈能够在这些方面给读者提供有用的信息。

我想先谈谈自己的研究在这些年来的发展，即，什么是发展的主线和挑战？时间过得太快了，生活中的很多事情不能按照预先的计划进行。我经常把自己想成当年那个年轻的学生，刚刚步入研究领域。接着，我意识到自己已经变成了所谓的“权威”。对此我自己也觉得十分惊讶。这种心态倒是让我很容易能够跟在本次会议或其他场合遇到的中国年轻学者们产生共鸣。如何在一个研究领域找到你自己的路？当年，我对哲学和数学都感兴趣。显然，模态逻辑是二者最好的折衷（这是我自己的选择：我的教授对此不是十分满意）。 模态逻辑起源于哲学，它最初是对必然性、可能性、时间和因果联系等概念的研究。弗雷格和罗素曾经把这些内涵概念从现代逻辑中剔除出去，他们反对康德的范畴表——但是这些概念在20世纪初借着哲学逻辑学家们的著作得以回归，并从此逗留。很多哲学逻辑已经成为一个“家庭产业”，远离逻辑的主流。然而，我和其他人都认为，模态逻辑是经典逻辑系统的一个特殊的类，能够用经典的技巧对其进行研究。这导致了1970年代模态逻辑数学理论的产生，这是我们那一代人主要做的工作。当时的激动心情我至今仍记忆犹新。我当时思考的主要问题是，当我们讨论关系模型时，模态语言的表达力和经典一阶语言和高阶语言的表达力之间精确的对应关系到底是什么。当时，其他人更多关注公理系统的完全性。对此我也有过研究，但相对要少一些。在这一研究过程中，模态模型论产生了，跟泛代数的联系也被发现了。

在1980年代，我把大部分时间花在研究逻辑和自然语言上，那是一个十分激动人心的新领域。我们研究广义量词、范畴语法和自然逻辑，那是“另外一种生活”。在1990左右，我重新回到模态逻辑研究上来，部分原因是有一些优秀的学生坚持认为，我有责任在我自己曾经活跃的领域指导他们的研究工作。一个人总是逃脱不了自己的过去！于是，我发现模态逻辑的研究状况发生了巨大的变化。除了哲学和数学，计算机对其正发生着重要的影响。特别是，我的博士论文所研究的、现在被称为互模拟的概念，在计算机的进程理论中被重新发现。而人们也在构造一些介于模态逻辑和经典逻辑之间的新系统，从而可以在表达力和计算复杂性之间找到微妙的平衡。（在计算机科学中的逻辑2007年会议论文集中有一篇很好的综述论文介绍了历史上关于互模拟的三个独立的发现，作者是比萨的桑格亚格（D. Sangiorgi）。整个1990年代，我设法理解表达力和复杂性之间的平衡，这对于理解逻辑系统是什么或能够做什么似乎是至关重要的。值得一提的的发现是“安保片段”。它是一个很大的可判定的系统，介于模态逻辑和一阶逻辑之间。是我们首次发现了这个系统的存在。

目前，我在模态逻辑的大部分研究工作是关于信息处理和理性主体的博弈，因为我逐渐认为“智能的互动”是逻辑研究的核心。这与赋值逻辑博弈和互模拟逻辑博弈的推广有密切关系。更为重要的是，这一研究线索可以追溯到模态逻辑最初的哲学动机，即，模态逻辑是用来对人类认知的主要结构做抽象的观念分析。但是，这个故事太长，我不准备在这里详细说明。

以上我主要阐述了模态逻辑的核心内容。当然，还存在许多的课题和挑战，在即将出版的《逻辑之门：模态逻辑》一书的引论中我提到一些。如果你还希望看到更多这方面的内容，可以参考我与白磊本（P. Blackburn）和沃特尔（F. Wolter）为《模态逻辑手册》合写的引论。我们试图给模态逻辑领域的很多方面以及对其产生影响的跨学科联系做一个公正的描述。也许，那个引论带有一点“阿姆斯特丹风格”，不过，还有其他故事也讲述模态逻辑，譬如，强调代数的方法。模态逻辑不是一个完全统一的国家。你可以通过某一个故事进入这个领域。一旦你身居其中，你一定会欣赏这个领域的其他故事。

还有，一个人的研究会面临很多挑战是因为你有机会与一些学生或同事接触，他们会问你所预料不到的问题；而且，你有机会与你所尊重的人、你喜欢的人进行合作研究，在这样的过程中挑战会不断出现。

裘江杰问：上面，您主要谈了关于模态逻辑的发展历史。我们常常说，一旦一个人熟悉历史，他就可以预见未来。能否请您谈谈模态逻辑的未来？

范本特姆答：江杰，我想你的意思是，当一个人第一次见到他的丈母娘的时候，他未来的人生就变得很清晰了。我不太确信这在多大程度上是真的，但是你的问题的确引发了我的一些思考。

有人曾经说过，模态逻辑没有未来，会很快灭亡的。当我在1983年第一次到斯坦福的时候，情境理论是当时新的研究范例，已经赢得了对模态逻辑的主要战役，只剩下一些扫尾工作来结束模态逻辑最后的抵抗。但是，这种事情终究没有发生！我们知道，模态逻辑是研究表达式和推理模式的，而这些东西无处不在，总是不断以新的伪装重新出现。模态逻辑从1920年代被首次提出之后，它的新功用被不断发现。例如，1990年左右知识表示领域里出现的“描述逻辑”，1995年左右为研究句子结构提出的语法逻辑，甚至大约2000年之后的网络语言，譬如XML，都具有模态逻辑的内核。而且，模态逻辑与哲学的新联系不断出现，例如，新近发展起来的关于自由和社会选择的逻辑。与数学的联系同样如此，去年就出现了关于层（sheaves）的新的模态结果。至少我没有看到任何迹象表明模态逻辑的应用会越来越小。事实上，这种胜利结果非常喜人，在1990年代由巴威思（J. Barwise）和其他人撰写的关于情境理论的最好的数学论文都在使用模态的技巧。

特别是，我希望在开创“智能互动”的新理论方面模态逻辑会在广度和影响力方面发挥重要的作用。当今，关于信息流和交流最为精致的系统是动态和认知逻辑，模态逻辑也常常帮助建立逻辑和博弈之间的联系。正如我已经说过的，这一趋势在哲学逻辑中得到继续，我期待一个对譬如模态、论断和态度等的经典问题研究的复兴。

这里，一个较为深入的问题是模态逻辑未来的数学基础。对此，我不知道该如何预测。模态模型论和代数仍然生机勃勃，参见我最近与腾卡特（B. ten Cate）和外纳能（J. Vaananen）合作提出的新的林斯特龙（Lindström）定理。但是，随着范式的转换（尽管互模拟仍旧会在那里），也可能会有另一个未来的发展历史。近年来出现了的对余代数、无穷串、自动机理论和范畴论的研究，这些也是模型论传统的中心议题。最终时间会证明一切！

郭美云问：从我们的翻译项目可以看到，模态逻辑在计算机科学有很多应用。特别是，我注意到，在最近出版的《模态逻辑手册》中，很多章节的作者都是来自于计算机科学领域。这是否意味着哲学家对模态逻辑做贡献越来越难了？还有没有什么问题哲学家们可以试图解决的？您也许知道，在中国不少逻辑学家在哲学系工作，您能否给我们一些忠告？

范本特姆答：美云，我想对你说：打开那些门！确实是这样，如今的很多逻辑研究是在计算机科学领域。有人甚至说，大多数具有创新意义的逻辑都来自于计算机领域。但是，让我们先搞清楚这是什么意思。

“计算机科学”现在已经超越了只研究程序和机器的那个狭窄领域。事实上，有人宣称，计算机就是哲学，只不过是“由其他手段继续”进行的哲学。如果你去参加一个关于知识表示和理性主体的学术会议，你会发现这句话的确有几分道理！我认为哲学家应当成为计算机科学家的同盟军：至少在更广泛的理想意义上而言。有人说，20世纪的哲学在很大程度上忽略了最著名的人类智能革命，即，信息技术在社会中和计算范式在学术界的并驾齐驱。只有现在，“信息哲学”才真正站到我们面前，参见我和同事安德里昂（P. Adriaans）合编的《信息哲学手册》。安德里昂从一个经典的哲学家变成一个成功的IT企业家，然后，成为学习系统理论的教授。学术的界限并没有太大的意义，哲学家可以在任何地方繁荣发展！

现在我来回答你关于哲学家可以做什么的问题。请不要当小数学家，试图证明其他技术派逻辑学家剩下的“简单定理”。当然，做一些技术工作以便获得关于数学方法的直接经验是很有益处的。并且，技术的经验也帮助我们从公式和定理中看清楚背后的真正想法和如何得到抽象的。但是，哲学家们最大的任务是要充分利用他们的天赋，例如观念的分析、发现新难题、发现新视角，这些都是一般的“定理证明者”所不擅长的工作。例如，在现代的认识论或行动哲学中，年轻的哲学家们正在以他们对理性主体和智能互动的独特敏感度探寻一个观念的“开放领域”。逻辑学家们从他们的系统构造中受益匪浅，然而，最理想的状态是建立一种富有成效的、同等的互利合作的伙伴关系。实际上，在阿姆斯特丹一些主要的技术进步是由哲学系的教授和学生所做出的。例如，自然语言研究的“动态语义”或现在流行的动态认知逻辑的更新机制。

换句话说，逻辑是一门抽象的学科，给你提供方法，它并不跟数学家们竞争，逻辑学家凭借哲学的敏感度来研究事物！

郭佳宏问：我们已经讨论了这么多关于模态逻辑的问题，但是您自己的研究不仅仅局限于模态逻辑。只提及几个，您有很多工作是在空间逻辑，时间逻辑，逻辑和认知等领域中进行的。您能否对21世纪的逻辑趋势说点什么？

范本特姆答：我自己的兴趣的确比模态逻辑本身要广。这些年来，我的研究涉及其他很多领域。一旦你变老，很难避免这一点！模态逻辑是我最喜欢的方法，尽管我并不认为这是唯一的方法：我也研究一阶逻辑，甚至类型论。而且，我还花了10年的时间研究自然语言的语法和语义，其他很多时间研究科学方法论、与认知科学的联系等。最近，我还在研究逻辑和博弈。我希望我们的翻译系列会最终把我的这些活动全面展现给读者。

你在问我对逻辑的更一般的观点。我不想在这里再重复说明，因为针对不同的听众，我自己写了很多论文、访谈。也许实在是太多了！看看我最近在第13届方法论、逻辑和科学哲学会议上做的特邀报告，你会得到一些公正的印象。另外，我的观念也在不断进化，某一年的真实想法可能会变成下一年的错误认识。例如，我们的研究所ILLC的现在就与它刚刚建立的时候有很大的不同，很难说，我在多少年前已经预见到或计划到目前这样的情况。

我还是坚持我的那个口号，我在这个访谈中多次提到。我认为，在人文学科、精确性学科和社会学科的交汇处，现代逻辑或许开始由传统的议程转到更广泛的智能互动，我认为我的工作正在帮助这样的历史发展——以一种温和非暴力的劝说方式

刘奋荣问：佳宏的问题让我想起从去年10月到现在我们在翻译过程中交换的很多邮件。我们非常感谢您的耐心解释。我们不得不承认，翻译您的作品并不是件容易的事情。也许难题在于这是文化之间的一种翻译，而不仅仅是两种语言之间的翻译。您是如何看待这个问题的？

范本特姆答：这个问题很难回答。换句话说，人们是否真的理解对方？语言是否预设或甚至决定文化，反之亦然？沃尔夫假设是否正确，我们是否被自己的语言所束缚？如果我们要谈论所有的这些问题，这个访谈可以更长！当然，我们不是第一个提出这样的问题：这些问题一直在讨论。譬如很多世纪以来，从我们的文化开始进行接触，大家就在讨论中国和西方的传统。坦白地说，我对你自己作为一个译者、一个学生、一个研究者，站在中西方文化的交汇处的经历很感兴趣，而不是我自己作为站在远处的一个同事和访问者的观点。

既然你问到这个问题，也许我应该说点什么。我认为语言、推理和文化是紧密联系在一起的。然而，很多关于这些问题的讨论看起来毫无成果，因为人们通常不愿意承认一些事实，不做实际的区分。首先，我们祖先从非洲走出来到现在，时间相对来说还是很短暂，我并不期待在神经-认知结构方面有很大的生理差别——尽管毫无疑问，文化产品，像字母表和字符会影响我们短期的处理事实的能力。当然，文化提供了一个背景，这些基本的技巧可以被操练。显然，当社会生活和教育结构不同时，解释和行为的倾向性会有所不同。我想说的是，所有的文化都面临同样的问题，如何建造一个公正合理的社会生活，在稳定的解决方案中我们到底希望有多少变化？当你看到那些不变的东西而不仅仅注意对行为的偶然解释时，我常常会惊讶，情况会如此惊人地相似。中国人很注重“面子”，我可以向你保证，同样的情况也在西方存在：只不过解释方式不同而已。而且，“文化”一词是如此的相似，它隐藏了阶层之间的巨大差异。你比较荷兰的一位学者和中国的一个农民，你会觉得这个世界是如此的不同。同样，如果你对荷兰的一个农民和中国的一位学者进行比较，恐怕也会得到同样的结论。而中国和西方的学者则具有很多共通的特性，使得他们不再属于“单个-文化”。不过，这里没有多少结论。

我自己被一些简单的经验观察所震撼。纵观世界历史，文化之间不断碰撞，混杂，一个战胜另一个，等等。好的想法，同样，坏的想法——互相渗透，即使这样的过程有时包含着“新的误解”（但是这也发生在同一种文化下的不同人群之间）。这里有一个具体的例子：在逻辑、理性和互动的会议上，张家龙教授做了关于墨家逻辑的报告。我很惊讶地发现，这与希腊的传统有着惊人的相似性，千里之遥的人类智力似乎在平行的轨道上运行。

这不是一个答案。在这个方面，我应当向你学习，而不是你向我学习。

郭佳宏问：我有一个涉及翻译的小问题。在您的论文“偏好改变的动态逻辑”中，您讨论了一个非常有趣的概念叫“regret”。您把它定义为下面的情况，你知道p不可能得到，但是你更喜欢得到p。在汉语中，对这样的情况有两个可能的翻译“后悔”和“遗憾”，它们有相似的含义。有意思的是，前者包含一些时态的要素。即，当有什么事情发生过，不像某人期望的那样，他会感到后悔。受这一解释的启发，我的问题的是，我们能否给英语中的“遗憾”添加时态的因素？

范本特姆答：结果我们还是遭遇关于翻译的棘手问题！的确，在那篇动态逻辑的文章中，“遗憾”是在你提到的非-时态的意义上解释的。对于这一解释，我们经常可以看到。譬如，我会说，很遗憾，由于热力学第二定律，没有无止尽的能源供应。但是我也同意你的观点，英语中遗憾的很多意义与时态有关，跟过去时有一定的关系（我觉得很遗憾由于我的愚蠢造成的后果），也跟将来时（很遗憾我总有死）有一定关系。当然，在那篇论文中，我们的主要目标有所不同，我们想指出遗憾适用于那些我们知道不会发生的情境——至少对于那些并非彻头彻尾的现实主义者。除了“遗憾”这个词，在你翻译我的其他论文时一定还碰到更多的例子。余俊伟曾经提到我喜欢用的一个词“fine-structure”，它在英语中意思是“微细结构”，具有“精致的”和“好的”这样的含义。他说在汉语中没有这样的词语与之相对应。我很喜欢我们在电子邮件中讨论过的其他例子；这些关于适当性的讨论并不是什么坏事，相反，我觉得这样的比较非常有趣！

我希望我们会再有机会更广泛地讨论你的翻译经历。我意识到，逻辑论文是非常特殊的，因为它们包括很多技术术语，这些术语具有固定的意义，再加上一般的学术方式和术语在世界各地都通用。但是，我对逻辑术语如何被翻译成汉语，障碍在哪里等问题很感兴趣。大家一般认为，现代的逻辑系统不是“中性的”，因为它们是沿着具体的人类语言（常常是印欧语系）的主谓结构发展而来的。另一方面，我自己从来没有看到，中国学生在理解现代逻辑时有什么困难。因此，我们希望找到那个抽象的层次可以进行交流。（我记得1983年在斯坦福首次跟从中国大陆来的第一个学生郭维德见面时，这就是我们讨论的话题）。我真希望我自己是汉语的专家，从而可以从我们的讨论中学到更多的东西。也许再过几年，我应该试着翻译你的论文！