I’m scheduled to teach a course on modal logic in the Fall. So I’ll have to think about a textbook choice pretty soon. Last time I’ve used Fitting and Mendelsohn’s First-order Modal Logic (Kluwer, 1999), which I quite like. It’s accessible, which is important, since many of the students will be philosophy majors with little formal background beyond an introductory logic course. Fitting and Mendelsohn include a bunch of philosophical material, and, as the title indicates, focus on first-order logics. So you get into a lot of interesting material about possibilism versus actualism, you get to discuss abstraction (which is important for intensional semantics), and also non-alethic logics (deontic, epistemic, time), although not in as much depth as I’d like. Proofs and metatheory are done via trees. But it’s not terribly interesting for computer science students, who also make up a good chunk of the audience. So something like Blackburn, de Rijke, and Venema’s Modal Logic (Cambridge, 2002) would be more interesting to them (and me, I guess), but is probably too technical. Chellas’s Modal Logic (Cambridge, 1980) is nice, but probably also too technical, a little outdated, and doesn’t cover first-order systems. Hughes and Cresswell’s New Introduction to Modal Logic (Routledge, 1996), like Chellas’s book, does everything Hilbert-style (my students might kill me if I make them do exercises in that), and doesn’t have a lot of discussion of applications (philosophical or computer science). Plus, I prefer boxes and diamonds to L and M. Beall and van Fraassen’s Possibilities and Paradox (Oxford, 2003) and Priest’s Introduction to Non-Classical Logic (Cambridge, 2001) don’t cover enough modal logic for my purposes (e.g., no first-order logic). Girle’s Modal Logic and Philosophy (McGill-Queens, 2000) might be interesting, but I haven’t looked at it. He does discuss many applications of modal logic in philosophy, but I don’t know how in-depth. Anyone used it? Other ideas?

UPDATE: Two more textbooks worth noting: Chagrov and Zakharyaschev’s Modal Logic, and Bell, DeVidi and Solomon, Logical Options. As I said in the comments, the former may be somewhat expensive. The latter is not only affordable, but covers non-standard logics more broadly (second order, modal, intuitionistic, and many-valued logics).

I’ve had reasonably good results by combining Blackburn et al with Hughes and Cresswell. The first few chapters of Blackburn et al aren’t too bad technically, and if you combine those with, say, the first four sections of chapter 4 (and leave out chapter 3 altogether), you get a nice coverage for a single-semester course with a lot of material on applications and a nice broad perspective on the field. Hughes and Cresswell then goes through some of the basics of the properties of modal systems more slowly than Blackburn, and also makes available discussions of quantified modal logic, if you want that. Posted by Josh Dever

I agree with your characterizations of Chellas book. But a question: why do you say that Fitting’s book won’t be terribly interesting to CS majors? Posted by Anonymous

I like Fitting and Mendelsohn’s text since it gives a lot of philosophical discussion. Also interesting is Mendelsohn’s implicit integration of free logic in the section concerning existence (i.e. Plato’s beard), a lot of which was initially covered in his Notre Dame Journal of Formal Logic article.Predicate abstraction, a major focus of the text, is useful for taking care of essentially all scope distinctions including Russell’s wide/narrow scope and the de re/de dicto distinctions.Their proofs of soundness for the various semantic tableaux systems are straightforward and very easy to follow. So are the completeness proofs. Good coverage of varying and fixed domain semantics and actualist and possibilist quantification (the latter occupying too much of the text however).I suppose Blackburn’s text is better suited for students interested in computability theory and is surprisingly not as technical as the contents would have it appear. But in my opinion it lacks much of the interesting philosophical discussion surrounding modal logics and their applications. It seems (pedagogically) easier to supplement a less technical text with technical papers than vice versa. Posted by Mike De

Well, Fitting/Mendelsohn (a) don’t discuss any applications of modal logic in CS (say, mu-calculus, or temporal logics for program verification, that sort of stuff), and (b) they don’t do much metatheory beyond soundnes/acompleteness of tableaux (e.g., no discussion of finite model property, decidability, bisimulations, etc). These metatheoretical methods are important for the study of systems that are applied in CS. Posted by Richard Zach

I’ve not taught modal logic in a classroom, but I’ve learnt modal logic through supervising two MSc theses on the proof theory of modal logic (a fun way to learn, in fact, at least since the first victim of my pedagogy had a very mature and rigorous approach to research). It sounds like Richard has a pretty clear idea as to what the advantages and disadvantages of the texts are and what his audience is. Some thoughts:(BdRV = Blackburn, de Rijke & Venema)1. BdRV is an exceptional research resource with a very narroiw conception of its field, namely developing the most powerful technical apparatus for analysing normal modal logics. If you think any of your students might do research in the mathematical logic of modal logic, this is, I think the best resource to be using to build a basis for approaching the research. The treatment of the Goldblatt-Thomason theorem is truly excellent. But the other students are not going to get much out of it if they don’t have any mathematical logic culture. I’m guessing it might be nice to have a couple of weeks marked strictly optional that present a map of this stuff…2. BdRV presents a sophisticted view of what modal logic is, what they call the view based on relational structures, which is where the heart of the research subject is, but apart from some applications in computer science, it’s not going to be why most students enrolled on the course. It might be nice to talk about two pictures of modal logic, the philosophical logic view, based on the analysis of mode as alethic / deontic / epistemic, etc. and contrast this fundamental and subject motivating view to the sophisticated and technical relational structures view. The slogans in BdRV are pretty accessible and might make a nice lead for a classroom discussion on “what is modal logic about?”. On a side note, I’ve been wanting to impose my picture of the best way to get a synoptic grasp of modal logic upon the world by means of a series of wikipedia articles…3. One thing BdRV doesn’t even touch, and which no text covers well, is the proof theory of modal logic. The most widely recommended text is Fitting’s automated theorem proving text, but where it leaves the topic is in a not very inspiring place. The state of the texts really reflects the poor state of order in the research field: lots of little piecemeal results, with three more powerful but imperfectly understood technologies (labelled deduction/tableau, display logic, and Alex Simpson’s graph-labelled sequents). I’m hoping to change that, and Phinki’s MSc dissertation is as good an introduction to the topic as you will find…4. Nice, accesible, thought-provoking, and not-too-technical things to cover: Fitch’s paradox of knowability, Kaplan’s knower paradox and Beall’s linking of these: the literature is knee-deep in technicalities of semantic anti-realism, but you don’t need these technicalities to appreciate the paradoxes.5. Oh, and do install in your students the importance of the distinction between Kripke semantics and possible worlds semantics… Posted by Charles Stewart

I thought the terms “Kripke semantics” and “possible world semantics” are pretty much interchangable. Could you briefly explain the distinction or point to a document that does? Thanks a lot. Posted by Postmodernist

Tableaux are a nice method for modal logics, since they are so closely linked to the semantics. Raj Gore’s chapter on the topic from the handbook of tableau methods is available here . Bits of this chapter could fit into your course nicely, Richard, since it is interesting to computer scientists too. Pietro Abate has developed a system “the tableaux Workbench” specifically for people with little programming skills. You just need to plug in your tableaux rules and out pops a theorem prover for that logic.BdRV probably needs to be supplemented in any case. Even if teaching a mathematical modal logic course, it would be nice to include something on the lattice of normal modal logics, which is not covered in BdRV. Chagrov and Zakharyaschev cover this in their book. They also cover proof theoretic results such as interpolation. Posted by Jon

Charles: Display calculus is quite well understood in the context of modal logic. Kracht proved that an axiomatic extension of Hilbert-style modal logic can be properly displayed iff it is axiomatisable by a set of primitive modal axioms. See “Power and Weakness of the Modal Display Calculus” in Wansing’s Proof Theory of Modal Logic. Posted by Jon

Postmodernist: Possible world semantics assumes we are talking about necessity and alethic modality, and probably has the connotation of modal realism. Kripke semantics does not, but does carry the baggage of an accessibility relation.Check out the Wikipedia possible worlds article , although it’s far from what it should be (FYI, I edit wikipedia, but not with great enthusiasm, two other well-informed people are interested in getting that article in shape, but it has not happened yet; since I am on the topic: Richard, you used to edit a few wikipedia articles, what happened?).There’s no doubt that it is common to confuse the two, even by teachers at decent schools, but it is most definitely a mistake.Jon: I’m well aware of Kracht’s result, it’s one of the key results establishing the success of display logic so far as it goes. No, display logic is not well understood, in the sense I intend. Read my critique of display logic in my joint-with-Phiniki AiML paper to know why I maintain this. Posted by Charles Stewart

Jon, the Fitting/Mendelsohn text does everything based on Raj’s tableaux systems. Posted by Richard Zach

I suppose for completeness I should link to Chagrov and Zakharyaschev’s Modal Logic (which Jon mentioned already). At a list proce of US$195, it’s unfortunately out of the question to use it as a required text. Posted by Richard Zach

I used logical options since David DeVidi was my professor at the University of Waterloo where he still teaches.I don’t think it’s suitable for a modal logic course since it provides mostly a brief introduction to the topic. And all of the results pertinent to computer science you’re seeking aren’t covered.It also uses tableaux methods and proves the basic metalogical theorems. A dash of multi-modal and provability logic are covered. There’s stuff on fuzzy logic, lattices, boolean algebra, 2nd-order logic, term-forming operators, and free logic.Check out Sally Popkorn’s “First Steps in Modal Logic”. A little more expensive (but still affordable) but it covers bisimulations, finite model property, and has tons of good exercises. Posted by Mike De

I was hoping someone could recommend a few expository books or even papers on the subject of multi-dimensional logics. I’m not too worried about a philosophical exposition, but just an introduction to multi-dimensional Kripke semantics for a few common logics. I was able to find only two very very very dense books (“Handbook of Modal Logic” and “Multidimensional Modal Logic”) — I was looking for something lighter. Maybe a few good papers. Does anyone have suggestions? I have no problems with books that assume knowledge of ordinary prop calculus (modal and classical) and of tableaux. They just can’t make the “rocket scientist” assumption that books like Handbook of MDMD make :)Thanks. Posted by Postmodernist

Chagrov’s book is available online free of charge. Not sure if that helps, as a hard copy might still be necessary. Posted by S.B.

S.B. : Could you provide a link for the Chagrov book? Thank you. Posted by J. M.