Dov Gabbay: "I am a logic" (1999)

By Jelle Gerbrandy and Anne-Marie Mineur

Contact Information
Prof. Dov M Gabbay
Augustus De Morgan Professor of Logic
Group of Logic, Language and Computation
Department of Computer Science
King's College London

Visiting Professor
University of Luxembourg

Research Interests

Based on the assumption that the Almighty has created a coherent being, that He has sprinkled a little logic in our minds, Dov M. Gabbay is working hard on getting theories on language, logic and information to converge. With that in mind, he publishes handbooks on all kinds of logic, he is an editor of the Journal of Logic and Computation and he is involved in the International Society for Pure and applied Logic. When the roads come together, he wants to be on every one of them. "Like a roundabout, it will be Gabbay coming from this way, Gabbay coming from that way...". We had to follow him to the airport to have our interview, but then again, some people deserve the "Superstar approach". Gabbay is now working at Imperial College in London, though officially on sabbatical to study Labeled Deductive Systems.

Biography - "This is what I want to do."

"I was born in 1945, and I grew up in Israel. I started my university studies in '63, I studied mathematics and physics for the BSc, mathematics for the MSc,-I did my Master's on many-valued logics-and then I did my PhD on non-classical logics, in 1969.

"I went to an extremely religious school. Take for example the way they taught physics. The teacher came to class and said: 'When God created the world, He used these equations, and then He derived everything from that.' No experiments, nothing, it was all mathematics. They taught history only because it was necessary, teaching languages was good, and they taught (mathematically) some science. Humanities-Arts, Music-, they did not take seriously. And they taught us a lot of Bible. So I naturally became one-sided, not only in what I knew, but also in my attitude. The school attitude was: 'Here is the word of God, you concentrate on that. Don't be distracted by junk.' I don't believe that you have to follow the Bible in the same way, although I believe it is good to know some things about it. But the attitude of 'this is what I want to do, don't be distracted', that was ingrained in me.

"At that time, this was a good attitude. A lot of my fellow students did get distracted. I didn't go to discotheques or out dancing with the girls. I made a concentrated effort. Of course, I could have gone funny at the age of forty.

"A part of the religious teaching was for everyone to get married, have children, and so forth. I got married in 1970. My wife is an artist, and I learned a lot from her; the fact that I can talk about things, for instance. I remember I was going out with her, before we were married, and we were walking from one part of the university to another part. My objective was to get from A to B, she wanted to stop and look at the moon, because it looked very nice. And I thought: 'What the hell would I want to look at the moon for, when I want to go to B?' Now, of course, I will look at the moon at all times with her.

"Then I went to Stanford, from 1970 to 1974, 1975. In Stanford I took up Dana Scott's position. When I worked in Stanford, I wanted to become a professor as fast as possible. I thought that if I worked only in one subject, intuitionistic logic for example, a large part of the department in Stanford would not be interacting with me. Then I saw that there was Logic and Language, and I started working on language with Julius Moravcsik. And I loved it.

"At that time I also used to go to statistics seminars in the other faculty. Probably, scientifically it was right, because now we have uncertainty, probabilistic reasoning and so on, but from the effort point of view, it would have been too much to do. Then one day Kreisel came to me and said that Gödel wanted to talk to me: 'Come to my office on Sunday.' So I went to his office on Sunday, and Gödel talked to me through Kreisel. It was a very strange situation: Kreisel was sitting on the phone, talking to Gödel in German, Gödel would ask a question, Kreisel would repeat it to me in English, I would answer, or Kreisel would answer for me. This is how I talked to Gödel. Basically, what Gödel said was: 'What is this young Gabbay doing? He is doing this, he is doing that, what is this? I knew what I was doing when I was sixteen.' And Kreisel said: 'Well, he's young, he's enthusiastic.' So I dropped statistics after that, but kept the language, because I was interested in that. I will get into statistics now, probably. ''After that, we decided to go back to Israel. So I resigned and went back to the Bar-Ilan University, and I stayed there until 1982. In that year I went for a year to Imperial College, to work with Bob Kowalski, and to see what was all this talk about logic programming and applications of logic in computer science and so on. I had never taken this subject seriously before. I had done some things with computer science when I was in Israel, I used to work a lot with Amir Pnueli, who developed temporal logic for computer science. We had a joint seminar. But I never took it seriously in the sense that there is a lot to be learned there. It just didn't hit me. I was thinking more in terms of expressive power and so on. Some of the results I was getting were useful to computer science, but I never thought of them in that way. At Imperial it suddenly did hit me. So I stayed there.

The handbooks - A legacy to the next century

"Imperial College is very big. Had I gone back to Israel, I would have had to read more, but at Imperial, if you want to know something, you grab someone. That saves a lot of time. The flow of information there is from logic to computer science: you show me the problem, I will solve it. The bottleneck is in understanding the problem. So at that time I decided that the best way to learn is to start the Handbook of Logic in Computer Science (Abramsky et al, 1992) and the Handbook of Logic in AI (Gabbay et al, 1993) . I started this in 1984 with some of my Imperial College colleagues, as a method of learning it myself and so that I would be forced to see what was happening. That is how those handbooks started.

"There are four volumes out of Logic and Computer Science, and two more volumes are ready. Then we have four volumes of Logic in AI, with another volume ready. Also, we have plans now with Kluwer for the Handbook of Practical Reasoning with Hans J\"urgen Ohlbach, which will be five volumes, the Handbook of Uncertainty, five volumes, the Handbook of Tableaux, one volume, and several volumes of the Handbook of Algebraic Logic. Then of course the second edition of the Handbook of Philosophical Logic (Gabbay et al, 1983) , which will probably be seven or eight volumes, and a new Handbook of Mathematical Logic with Jon Barwise.

"Also, we want to make a dictionary of logic. What we would like to do is make a big collection of material on logic. We want to put it on the network and allow people to log in, see the entries, maybe suggest new entries, and let it grow like this. After a while we'll have a proper dictionary, which then we will collect on a CD with all the handbooks. So, if you want to know about Hintikka, you get the dictionary, you look up Hintikka, you get references, short descriptions and so on. Then you click on those and you might go to the relevant chapters of the handbooks, you can browse around there... I think that will take seven years to do. We are starting it now, and we will see how it goes. And I think we will do it through the ISPL ( The International Society for Pure and applied Logic-JG).

"Why am I doing all these handbooks? We want to leave a legacy to the students of logic of the next century. It serves the community, you need these things, it helps bringing different areas together, it helps clarifying concepts. Also, the field is moving fast: you have to read a lot of papers. A handbook is systematic: you write a chapter with a view, and it is coordinated with the other chapters. Therefore, you get an attitude. When a survey is written and coordinated with other authors, they agree on an attitude. And the attitude-a theme-is important for new problems. Sometimes you write a chapter to provide a coordinate system, so that others can relate to it. You see it in mathematics: you have several equivalent definitions of the same thing, but only one of them generalizes. That means that the others were not the right formulations of the concept.

"We had this problem with the chapter on non-monotonic logic: we did not put it in the handbook of philosophical logic, at that time. I think I was the only one who wanted to put it in, but all the others were against it. They said that it was not ready yet, that there was no field. But now we have a whole volume on it. So, would it have been the right move, to put such a chapter in? Maybe it would have given a view that all the AI people since then would have used or related to, maybe it would have misled them, I don't know. There was nothing on it, then. It's difficult, you could be wrong.

"With the handbooks, we tried to organize the area. And indeed, some of the chapters, like the chapter on topology, was completely new ( in the Handbook of Logic in Computer Science-JG), it was invented because there was a gap in how to describe the use of topology for computer science. Mike Smyth did very strong research: he simply discovered the whole thing. And there was new research generated by other questions.

"I want to be safe not to do things that will disappear after ten years. The best thing is to look for more than one reason for doing what you are doing, and also look at the principles involved. I think the dictionary and the handbooks are the things I leave for the next century.

God and logic - 'A strong image'

"When you do research, I think there are two ways you can go about choosing your work, and I think the choice has to do with one's character. Some people just home in onto something, others like to expand to see different points of view. So you can either choose something, like Situation Calculus, and work on it all the time and you can spend years and years doing that. And then if it is a hit, you have done something, and when it is not, you have gone out of history together with Situation Calculus, or whatever it was you were doing.

"On the other hand, you cannot do everything. You must have a model, a strong image. An image such as the Americans had when they said they wanted to put a man on the moon-that is a strong image. If you go towards it, you will develop all kinds of things, you will affect the economy, affect science. My strong image is this: God created the physical universe, with some rules, and we study them, describe them. Some admire the Almighty for this, some don't, that does not matter. In this universe, He put us, with practical reasoning in our minds. There's something there that you can study and model, just like the physical universe. Analyzing what goes on in our minds may be much more difficult than studying the physical universe. It is a sort of a joke: He put the more complex thing in us. Anything that has to do with this, I go after.

"You can immediately draw some conclusions from this. We are coherent, at least I think so. As practical reasoners-somebody who switches, in today's terms, from one logic to another, who takes actions, decisions-we are coherent. Then any major theory that legitimately can describe part of this activity must be connected to any other theory describing other parts of this activity.

"So I started looking around: what is common? You have substructural logics on the one hand, you have inheritance systems in artificial intelligence, you have categorial logics... There are those people who believe in syntax, in proof theory, people who don't want to look at semantics, there are people who believe in semantics and not in proof theory, and there are people who believe that classical logic is the only logic. And when you look around to see how logic is applied, you see you have different communities: you have temporal logic in software engineering, you have temporal logic in AI, you have different communities analyzing language, and so on.

"All these theories must be connected, because they are modelling the activity of the same human, but you need a theory that makes the connection. I try to work in these areas in such a way that when sooner or later the roads come together, like on a roundabout, it will be Gabbay coming from this way, Gabbay coming from that way... There is a lot to be done, and I feel the same excitement as somebody who is pointing the telescope looking for new stars.

"This is another reason for doing the Handbooks, The Journal of Logic and Computation and for the Interest Group in Pure and applied Logic: to bring these people together, to accelerate this process. All based on the assumption that the Almighty has created a coherent being, that He has sprinkled a little logic in our minds.

Logic and reality - 'Why was that sin?'

"Whether I am a sort of preacher? I am not saying that if you teach people more logic, they will behave more rationally. I do not think that. But I think that if you teach people more logic, at least they will not make mistakes in evaluating the situation. We have our vices, right? I may look at your wife and want her-I might even kill you. No amount of logic will change that: these are basic instincts, they will not change. But I may not realize that maybe I do not exactly want her, perhaps it is something else and I got my signals wrong. So if I can think more clearly, I can reason it out. It will not make me better or worse, but I will have better glasses to see reality as it is. And then I can be bad if I want to. So it will eliminate some of the problems. If I do not want to share my goodies with you, I will not. And you may not want to share your goodies with me. But maybe if we can think, we might realize that when we put a little bit together, and we watch each other without machine guns ready, we might make more money this way, and then we are cooperating. You have to reason it out.

"Me, I tend to keep my options open and try and reason things through. In other words, I want to know that from x1 I can go to x2 and from x2 I can go to x3, but I am not going to x3 because the Bible says: Don't do that-and I believe in the Bible. For example, if I have a bad colleague, I might find it nice to run him over with my car. I will not do it, because at the moment, I am not running people over with my car. But I want it clear, I don't want it fuzzy.

"What I find sometimes is that there is no reality. Reality is the way we perceive things, and a part of this is representation in our minds. You might be happy as you are now. I can make you unhappy in two ways: I can stand on your toe and it will hurt-that's real. But I can also say: 'Did you know that your neighbour is getting more?' I change the modelling in your mind, and suddenly then you are not happy. So what has happened? You changed reality. A lot of reality is how you see things, not everything is real. And that part of reality, logic can affect.

"Take the story of Adam and Eve and the snake. What was the big sin of the snake? What did he do? He talked. He just changed the point of view of Eve. He told her: 'Why are you not eating just because God said so?' Is that wrong? He just talked. He did not deny the facts, tell any lies, he just changed the point of view. So why was that sin? I think because points of view are very important. And point of view is representation, which is the area of logic.

"You have to be very careful. If you ask a colleague: 'Why isn't your wife supportive of you?' or 'Why isn't your husband coming?' this could have the same effect as knocking them on their heads. So you should be careful in what you say to other people, because you are affecting their model; in fact, you are changing reality.

LDS - 'Perhaps this was it'

"In the literature, there have been instances of where labels were used. You had, for example, Anderson and Belnap who used labels to compute relevance. But labels were used only as a side effect. It was a bit like moving all the furniture against the wall because you want to wash the floor. It is a side effect of washing the floor, not redesigning the room. So people used labels, but not as a general method.

"I tried to see what happens if you put labelling into the logic, and then I saw that diverse systems begin to look similar. I thought that perhaps this was it. I gave some lectures, checked more systems, and then applied to the SERC (Science and Engineering Research Council) for a five years' sabbatical, to do labelled deductive systems. I got some projects; a project on labelled tableaux, a project on consequence relations, and started working on it. The motivation was to connect all these roads in the roundabout. Fibering systems, why we move from one system to another... Because this is what we do. This is intelligence. If I say that she is a smart girl, I do not say that because she can do so many resolutions per second. I say that because she can move from one logic to another, one mode to another. It is not only power, but also the right adjustments; intelligence is a mixture of these things.

"I do not believe that there is a single logic, like classical logic. I look at how people reason, and that is the logic. In order to describe this logic you would have to have notations for action, notations for mechanisms. You should not look at a theory and what follows from it, but at a theory and how it develops. I think a logical system is really what AI people call agents. The whole matter comes into it, and that's a system: evolving, maybe continuously reacting systems. The way we are; I am a logic, each one of us is a logic (Gabbay, 1994) . Someone said: 'Each man is a world unto itself.' I say: 'Each man is a logic unto himself.'

"Perhaps LDS could be the framework to connect these different formalisms. LDS is a very flexible formalism. For example, if you take lambda calculus and you have an application area, then you have to translate the application area into lambda calculus formulas. With LDS, you look at the application, take some of the application area, name it and use it as labels. So you are bringing the semantics into the language, you help the natural logic in there. You can go with the application.

"LDS is not a single logic, it is a methodology, a framework in which you can bring things from the application area into whatever system you are doing. It means that you never necessarily have a clash between the formalism and the application. You do not have to bend the formalism to hack the application in. You don't have to do this, because you take from the application as labels and bring it in in that way.

"Consider Newtonian mechanics. It does not matter for Newtonian mechanics whether you invent relativistic mechanics before or after, because it is a limit case of relativity theory for low speeds. So if you get it before or after you know relativity, that does not matter. But if you take the steam engine: you don't want to look at a steam engine if you already have diesel. The question is whether LDS, or anything you put forward, is like a steam engine-when something better comes, you don't like it anymore-or it is like Newtonian mechanics, which is a limit case or part of something bigger. I believe that I am looking for some logical principles that people will use. I hope that some of the stuff that I isolated will be kept because I isolated the principles.

"I once followed a very strange course on meteorology. They had models of the atmosphere and stratosphere and how particles come from the sun and fall down again, all kinds of things like this. They had an ideal model, but they would show that it was wrong. Made a correction, and then made another correction... It looked like a suit with a lot of patches on it. And I always asked myself: 'Don't they have a new model?' But that was all there was: so-and-so's correction, and another guy's correction. Maybe we are doing the same for the time. Until we have better theories.

Computer science and logic - Honey through a pipe

"Many of the problems we want to solve are not different from what Aristotle wanted: you take the human, you see how the human interacts with his environment, you try to analyze it. A lot of that is logic. In those days, there was only philosophy, there wasn't pressure. Then when computer scientists came in and they wanted a machine to help or simulate a human, there came industrial interest, there was money in it. Also, because the Japanese started to put money into it and talked about a fifth generation, everybody started to get interested. Logic became a buzz-word, and that is in itself an important service.

"So there was a push to look into these problems. What happened first is that some people started building systems without thinking, just things that worked. Then other people migrated from philosophy departments and from mathematics into computer science, and they did start thinking. The interest in computer science forced the issue, and pushed logic more into the area of human activity, of human problems in thinking, and from that into processing, into theorem proving and verification systems, and so on. All these applications led to a lot of new developments.

"I see computer science as a rich area of applications, and if you work there, you get ideas. Take this example: suppose the city of Utrecht decided they wanted to put a big pipe and somehow push honey into the nearby villages. Now this is going to cause a lot of technical problems, possibly will lead to new equations, they might discover new mathematical spaces. And this is what's happening with logic and computer science. You may agree or disagree on putting honey through a pipe, but that does not matter. The rise of logic programming has importance in providing a computational tool for the logician. Even if logic programming as a computer language is not as important as some others, it did its service as a tool for logicians and by pushing logic up front. And now, fuzzy logic is new.

Linguistics - 'Mrs. Thatcher is thin'

"I think the study of language is important for logic, because a lot of our way of reasoning is reflected in the way we use language. I do not know exactly in what way logic and linguistics stand in relation to each other. There is a lot of logic in language. For example, if you say: 'John loves John', then that is ungrammatical. Let's say that is for a syntactical reason. If you say: 'John looked through the window, but he saw nothing', that is alright. But 'John looked through the window, but mrs. Thatcher is thin', that does not sound right. This is not because of the structure, but because of non-monotonic expectations of the language, so that part is logic. And I am sure that logic and linguistics interact in more complex ways. To parse a sentence, you may need a combination.

"A lot of the modelling methods used in the study of language come from logic. But language also influences logic: we developed new temporal logics that came from the study of language. Like two-dimensional or three-dimensional temporal logics. Or consider quantifiers: we have quantifiers now that we didn't have in logic before.

Fallacies-Bonzo: Easy to feed your children

"I think it is important to look at the phenomenon of fallacies and what the community of informal logic has to say about that. This is a very important subject, and I intend to work on it. I am planning a book, with John Woods and Andrew Irvine. A book on fallacies and informal reasoning. We are going to make a new edition and we agreed that I would participate: to analyze, using LDS, what's happening here (1).

"When we reason, it is much more effective to use all these fallacies than to use proper deduction. Say, you owe me one hundred pounds and you don't want to pay me back. It doesn't matter how I argue, that I say that you are a real jerk for not paying. But if I say that your wife won't like you, or your girlfriend won't like you, then that might be most effective. So real reasoning is very different from what is usual in logic. And I plan to move into it. I think it is important.

"I have some examples, of which I don't know what they illustrate. Suppose you take a taxi to Schiphol. It should cost 25 guilders. But you have a charter flight to America: if you miss it, you will loose a lot of money. And it is raining. Then the driver stops, and says: 'I want fifty guilders. And if you do not pay, you are going to miss your flight, even if you take another taxi.' But he will not say it like this, he'll say: 'Well, its raining, it's more difficult than I thought, you have five pieces of luggage, your children are screaming: it's fifty.' He'll feel the need to find some excuse. I think there is something there, some rules we play by. All we need is to keep on looking, communicate with practical reasoning people, psychologists...

"Let me do an experiment with you. I claim that if you give me a hundred guilders now, just this once, it will be a hundred guilders you will never use. Because I am sure you will have more than a hundred guilders, or else an overdraft with a hundred guilders more or less makes no difference. It is not a big order of magnitude. And on the day you die, you will have never used your last hundred guilders. It does not matter whether you give it to me or not. So if I have to buy a present for somebody, and it is a hundred guilders more, or if I lose a hundred guilders, I don't worry about it, because it does not matter.

"Another example of how people reason. In Israel, I was teaching logic to middle-aged people, managers, housewives, teachers, who take a year of university in the middle of their lives. There is this dog food called Bonzo. It is made of meat: little round dry pieces, just like rice crispies or whatever-dry round pieces. The way you feed it to your dog: you put it in a bowl and pour water over it. It is very healthy, and not only it is good meat, but it is even kosher. You get it in big bags, and it is very easy to feed your children. In the morning, you give them cornflakes, and when they come back from school, you can give them some Bonzo and pour water over it. So I said to the class: 'Fine, do you want to use it? Look, I brought a bag.' And there was a revolution, they went crazy. Some of the mothers said: 'I am not feeding my children dog food.' And I said: 'It is not, it is kosher, it is a safe meat. The substance is alright, it is just labeled 'dog food'.' I asked: 'If I take something from your fridge, and put a label on it that says 'dog food', would you then not eat it?' And they said: 'No, it is dog food now.' A lot of this kind of reasoning is not traditional logic.

Teamwork: Doing dishes

"I can't do what I do if I don't think about it all the time. My wife, Lydia Rivlin is very helpful as well, she takes care of things. So in that sense I think I am lucky, the home is taken care of, I have very good team work in the university, with my friend and colleague, Jane Spurr, doing the handbooks and such, and I also have very good research assistants. My policy is, as I put it, to get people who were born with a jet engine stuck to their backs. Very strong people. Some professors are afraid for very strong people, because if the guy is good, and you come up with some new theorem, he might come and say that it is rubbish. He or she will tell you that, if he or she is good. And if he or she is right, you must follow it.

"I always follow the truth. I want to follow the truth, so I like very good people. I have many projects, some of them are run by other people. It is much better, that way. You have to trust them, feel that they are competent in what they are doing to the extent that you don't have to worry. Whatever they do, you accept, even though it is not exactly, because it almost never is exactly, and you do not know that if you would have done it, you would have done it better. It is a partnership. I like teamwork. It is like painting the fence with the other kids.

"Usually, there are things you are better at, and there are things that are still important to whatever you are doing, but you are not as good at it. So if you team up with someone else who happens to be very well complemented, and you have similar ways of thinking, if you are compatible, one can make a terrific team this way. The best image I know of this is the following. At the beginning of this century the British were very good at building ships. They used teams of right handed persons and left handed persons. A right handed person hits with his hammer this way, a left handed person that way, and they stood next to each other, each hitting the nail, one, one, one... And if they are well-coordinated, they can hit nails in very quickly.

"There are things you do not want to do. I can do things very easily that other people find very difficult. For example, I don't mind adding numbers for hours and hours, I don't mind cleaning toilets, I don't mind washing dishes, I don't mind making tea, I don't mind xeroxing for hours and hours... Because it is automatic: I can think of something else. I am sure there are lots of people who hate doing this, even though they can. It would be perfect for me to share a flat with somebody who doesn't like doing this, but who does like to pay the bills, to check whether the amounts are correct, etcetera. That is something I hate doing. It requires thinking, and thinking I keep for logic."


(1) A second edition of the book by John Woods and Douglas Walton: Argument, the logic of the fallacies, which will be done by John Woods, Dov Gabbay and Andrew Irvine.


Abramsky, S. D. Gabbay and T.S.E. Maibaum (eds.). 1992. Handbook of Logic in Computer Science (Volume 1). Clarendon Press

Gabbay,, D., C.J. Hogger and J.A. Robinson (eds.) . 1993. Handbook of Logic in Artificial Intelligence and Logic Programming (Volume 1). Clarendon Press

Gabbay, D. and F. Guenther (eds.) . 1983. Handbook of Philosophical Logic (Volume 1). D. Reidel Publishing Company

Gabbay, D. 1994. 'What is a Logical System' in Dov Gabbay (ed) What is a Logical System?. Oxford University Press

60 Birthday: Dov M. Gabbay, 2005:

Sergei N. Artemov, Howard Barringer, Artur S. d'Avila Garcez, Luís C. Lamb, John Woods (Eds.): We Will Show Them! Essays in Honour of Dov Gabbay, Volume One. College Publications 2005, ISBN 1-904987-25-7

Samson Abramsky: A Cook's Tour of the Finitary Non-Well-Founded Sets. 1-18

Sergei N. Artemov: Existential Semantics for Modal Logic. 19-30

David Ahn, Sisay Fissaha Adafre, Maarten de Rijke: Recognizing and Interpreting Temporal Expressions in Open Domain Texts. 31-50

Atocha Aliseda: What is a Logical System? A Commentary. 51-56

Amihood Amir: Two Glass Balls and a Tower. 57-76

Carlos Areces, Patrick Blackburn: Reichenbach, Prior and Montague: A Semantic Get-together. 77-88

Wouter van Atteveldt, Stefan Schlobach: A Modal View on Polder Politics. 89-104

Arnon Avron: Logical Non-determinism as a Tool for Logical Modularity: An Introduction. 105-124

Matthias Baaz, Rosalie Iemhoff: On the Proof Theory of the Existence Predicate. 125-166

Sebastian Bader, Pascal Hitzler: Dimensions of Neural-symbolic Integration - A Structured Survey. 167-194

Howard Barringer, David E. Rydeheard: Modelling Evolvable Systems: A Temporal Logic View. 195-228

Johan van Benthem: Open Problems in Logic and Games. 229-264

Alexander Bochman: Nonmonotonic Reasoning. 265-308

Krysia Broda, Alessandra Russo: Compiled Labelled Deductive Systems for Access Control. 309-338

Peter Bruza, Richard J. Cole: Quantum Logic of Semantic Space: An Exploratory Investigation of Context Effects in Practical Reasoning. 339-362

Carlos Caleiro, Amílcar Sernadas, Cristina Sernadas: Fibring Logics: Past, Present and Future. 363-388

Walter Alexandre Carnielli, Marcelo E. Coniglio: Splitting Logics. 389-414

Ariel Cohen, Michael Kaminski, Johann A. Makowsky: Indistinguishability by Default. 415-428

Marcello D'Agostino: Classical Natural Deduction. 429-468

Artur S. d'Avila Garcez, Luís C. Lamb: Neural-Symbolic Systems and the Case for Non-Classical Reasoning. 469-488

Anuj Dawar: How Many First-order Variables are Needed on Finite Ordered Structures? 489-520

Jürgen Dix, Ugur Kuter, Dana S. Nau: Planning in Answer Set Programming using Ordered Task Decomposition. 521-576

Kosta Dosen, Zoran Petric: Negation and Involutive Adjunctions. 577-586

Luis Farintilde;as del Cerro, Olivier Gasquet, Andreas Herzig, Mohamad Sahade: Modal Tableaux: Completeness vs. Termination. 587-614

Paolo Ferraris, Vladimir Lifschitz: Mathematical Foundations of Answer Set Programming. 615-664

Melvin Fitting: A Mistake on My Part. 665-670

Marcelo Finger: DAG Sequents with Substitution. 671-686

Chris Fox, Shalom Lappin: Polymorphic Quantifiers and Underspecification in Natural Language. 687-700

Michael Gabbay, Murdoch Gabbay: Some Formal Considerations on Gabbay's Restart Rule in Natural Deduction and Goal-Directed Reasoning. 701-730

Murdoch Gabbay, Michael Gabbay: a-logic. 731-764

Sergei N. Artemov, Howard Barringer, Artur S. d'Avila Garcez, Luís C. Lamb, John Woods (Eds.): We Will Show Them! Essays in Honour of Dov Gabbay, Volume Two. College Publications 2005, ISBN 1-904987-26-5

Joseph A. Goguen, Kai Lin: Specifying, Programming and Verifying with Equational Logic. 1-38

John Grant, Sarit Kraus, Donald Perlis: Formal Approaches to Teamwork. 39-68

Wilfrid Hodges: Detecting the Logical Content: Burley's 'Purity of Logic'. 69-116

Ian M. Hodkinson, Mark Reynolds: Separation - Past, Present, and Future. 117-142

Dale Jacquette: Kripke's Modal Objection to the Description Theory of Reference. 143-168

Jan Willem Klop, Roel C. de Vrijer: Infinitary Normalization. 169-192

Agi Kurucz, Frank Wolter, Michael Zakharyaschev: Modal Logics for Metric Spaces: Open Problems. 193-108

Daniel Leivant: Partial Correctness Assertions Provable in Dynamic Logic. 209-224

Lorenzo Magnani: Abduction and Cognition in Organic and Logical Agents. 225-258

David Makinson: Friendliness for Logicians. 259-292

Larisa Maksimova: Interpolation and Joint Consistency. 293-306

George Metcalfe, Nicola Olivetti: Goal-Directed Methods for Fuzzy Logics. 307-330

Alice ter Meulen: Still. 331-340

Wilfried Meyer-Viol, Ruth Kempson: Sequence-Dominance Grammars. 341-370

Ben C. Moszkowski: A Hierarchical Analysis of Propositional Temporal Logic based on Intervals. 371-440

Rolf Nossum: Nesting Patterns in Fibred Logics of Context. 441-452

Hans Jürgen Ohlbach: Modelling Periodic Temporal Notions by Labelled Partitionings - The PartLib Library. 453-498

Anjolina Grisi de Oliveira, Ruy J. G. B. de Queiroz: A New Basic Set of Transformations between Proofs. 499-528

Gabriella Pigozzi: Should We Send Him to Prison? Paradoxes of Aggregation and Belief Merging. 529-542

Amir Pnueli: Verification of Procedural Programs. 543-590

Odinaldo Rodrigues: Iterated Revision and Automatic Similarity Generation. 591-614

Vladimir V. Rybakov: Inference in Temporal Next-Time Logic. 615-638

Erica Melis, Jörg H. Siekmann: e-Learning Logic and Mathematics: What We Have and What We Need. 639-662

Valentin B. Shehtman: On Neighbourhood Semantics 30 years later. 663-692

Patrick Suppes: Psychological Nature of Verification of Informal Mathematical Proofs. 693-712

Jon Williamson: Objective Bayesian Nets. 713-730

John Woods: Epistemic Bubbles. 731-774