In Semester 2, which starts on July 31, I’ll be teaching an honours seminar 161-438 Logic and Philosophy, in which we cover proof theory and its applications to semantics.

Now that my undergraduate teaching is done for the semester, I can devote more time to research. I’m going to use this place to post some material from my proof theory project. My goal is to present some key ideas in an accessible way. Today’s idea is the duality between proofs and counterexamples. Proofs: You can think of a valid argument as...

When the team are 0–1 down at the eighty-fourth minute, you don’t think they’ll win 3–1. Update: I’m glad I don’t have to detail the match, and can point you to this excellent piece of writing instead. It’s a reflection on the match by Jeremy, a first-year Arts/Engineering student here at the University of Melbourne. He’s one of the contributors...

Today is the Queen’s birthday public holiday in Australia. In Sydney the weather is freezing and the surf is huge. All this means I’ve finally got my SMIL work to compile against the trunk again. Now to get it working again!

This afternoon I was interviewed by Lisa Mitchell from The Age about academic blogging. She’s writing an article for the education supplement (published on Mondays). It’s a piece with a long lead time. I wonder if I’ll recognise anything I said in the article, and if she’ll quote me. (I blabbed on for 25 minutes. I hope there was some useful raw...

We’ve finished lectures for the semester, and I’m officially recovering. It was fun teaching Logic and Non-Classical Logic, but it was also a hard slog. Next semester I have a light teaching load, with my honours logic seminar. The highlight last week was Richard Zach’s visit. He gave two nice talks. One on vagueness and logic – setting out...

Here’s a silly puzzle for you. Regret seems like a factive emotion. You can’t truly regret that you forgot to feed the cat today if, indeed, you did feed the cat. If you did feed the cat and you forgot that you did, then it seems to you like you’re regretting not feeding the cat, but you’re as mistaken about your regret as you are about feeding...

Have you ever waited for a tradesperson to come to your place? Alan Hájek uses this example in an article entitled “The Cable Guy Paradox.” The issue is straightforward. You and I are waiting for the cable guy who has given you a window between 8am and 4pm for his arrival. He will arrive after 8am, and before 4pm. We while away our time with a...

As I mentioned before, I’ve been thinking about Vincent Hendricks and John Symons’ five questions about Formal Philosophy. This seems like as good a place as any to answer them. So, today, I’ll have a crack at the most autobiographical of the questions: Why were you initially drawn to formal methods? I suppose the natural way to interpret this...

Happy fifth birthday, Z! Today it’s unwrapping presents, a quiet family breakfast and lego-making, talking to grand-dad on the telephone, a little practice on the new bike, some school, and dinner together with more fiddling around with the new presents. The Party is on Saturday. (Wish us luck. We’ve not hosted a fifth birthday party before.)

Sometimes technologies can be use for purposes the inventors didn’t really intend. I’m sure that when the designers of the iTunes music store set the thing up, they didn’t expect that you’d be able to use it to download esoteric papers in philosophical logic. But you can. All I had to do was submit the RSS feed of my papers to the iTunes store on...

Su Rogerson has brought to my attention a lovely rendition of Curry’s paradox, due to Peter Geach, in his Reason and Argument (Blackwell, 1976), pages 93–95. The discussion takes place at a car yard. I’ll quote the discussion, interspersed with some commentary. (I’m quoting from a draft of Su Rogerson’s thesis, and not from the text. I’ll check...

I’ve finally added enclosures to my RSS feed of papers. This means that if you subscribe to my papers page using that feed, and you’re using an RSS reader that handles enclosures (this feature is primarily used for podcasts), then you can get it to download my papers automatically. This has the side effect that you can subscribe to me in iTunes:...

I’m trying to neaten up this place a bit, and I need your help and advice. Have a look here and let me know what you think of it. I’m trying to make it easier to see what’s new, what’s changed, etc. In particular, you look down to find links to other new stuff on the site. This opens up the sidebars for four things. The most recent picture, my...

This morning I uploaded a few new papers to the Australasian Journal of Logic, one of the projects I (mostly!) enjoy working on. It’s an open access, fully refereed, online journal in logic. If you’ve not seen it before, browse around and check it out. Let me know what you think. One thing that an online journals make possible is the freedom from...

Today in Logic I talked about vagueness and the sorites paradox. Then when I get back to the office, I find that this Saturday, Alan Saunders on The Philosopher’s Zone has a program on – you guessed it – the sorites paradox. Is that a spooky coincidence or what? No, it’s not spooky. It’s just a coincidence. Anyway, from the little outline, it’s...

I forgot to mention that I have written another paper recently. It’s a proof theory paper, putting down some thoughts on modal proof theory that I formulated when giving the S5 paper around and about in the last six months or so. In “Comparing Modal Sequent Systems” I look at different ways to understand modal deduction. In particular, I argue...

I’m sorry, I truly am. Back in the period 1990-1992, I wrote a couple of papers on the semantics of relevant logics. I thought they were pretty nifty, and I submitted them to a prestigious journal. They got accepted. The first of these papers is “Simplified Semantics for Relevant Logics (and some of their rivals).” Unfortunatley, there’s a hole...

This little spot called Melbourne Is the city of my birth It’s not as hot as Brisbane or as far away as Perth, It’s not as small as Adelaide, Compared to Canberra, it’s bliss, And if you’ve been to Melbourne, You can give Sydney a miss… As the world gets scarier, It’s a pretty decent area Melbourne The envy of the world. I think that was a...

Z and I – together with around 80,000 other people – filled the MCG to watch the track and field portion of Day 9 of the Commonwealth Games here. Some highlights: The completed renovations at the MCG make the huge stadium very easy to navigate. We got there early, so had no long queues to deal with (once we were at the ground itself – it was...

Z and I went in to the city to have a look at the Women’s and Men’s Marathon held here for the 2006 Commonwealth Games. The city was buzzing, the crowds friendly, and it was great to get a glimpse of the lead runners: especially Kerryn McCann and Hellen Cherono Koskei who raced neck-and-neck right into the stadium. No matter how you cut it, 42+...

It’s a happy day for us logicians at Melbourne. Greg Hjorth is going to be joining the Department of Mathematics and Statistics later in the year, taking up a five-year, professorial fellowship. He’s a super-smart set theorist and model theorist, and I’m looking forward to having him around on campus.

The paper reviews a number of approaches for handling restricted quantification in relevant logic, and proposes a novel one. This proceeds by introducing a novel kind of enthymematic conditional.

An historical essay, sketching the development of relevant and substructural logics throughout the 20th Century and into the 21st.

My entry in a book of interviews of philosophers who work on the more formal side of the discipline. It gives an account of how I got into this area, what I think logic is good for – when it comes to philosophy – and where I think we should head.

The notion of that information is relative to a context is important in many different ways. The idea that the context is small – that is, not necessarily a consistent and complete possible world – plays a role not only in situation theory, but it is also an enlightening perspective from which to view other areas, such as modal logics, relevant...

Vincent Hendricks and John Symons are working on a sequel to their book Formal Philosophy, in which philosophers who use “formal methods” talked about their work, their motivations, and their take on the state of philosophy. For the sequel, they are opening things up for others to take an “interview” with five questions, to appear in the next...

Toby Ord (a former student of mine, now taking Oxford by storm), has written up a nice short essay on degrees of truth and degrees of falsity. It shows how you can get a very nice little algebra if you extend the usual non-classical idea of a 4-valued logic in which truth and falsity are somewhat independent with the “fuzzy” idea of degrees of...

I’ve finally joined the ranks of the zombies with white earbuds. My trusty 2GB black iPod nano was acquired on the way home from our Sabbatical, in a duty free store at Changi Airport. I’ve had a little while to experiment with it, and so far, it’s been working better than I’d expected. I take it with me on my early morning walks, sometimes...

Today is the first day of the new phase of our lives – Zachary Luke Parker Restall had his first day of school today. Well done, Zachary!

I’ve published the report I wrote for regarding my project implementing SMIL Animation in Mozilla. At 147 pages and ~700kb it’s fairly detailed but I hope it will be of interest to some. Thanks to all who helped. Here it is: https://birtles.blog/smil/report/report.pdf

This morning found Z and me in the grocery store, doing yet more re-stocking of the pantry. Here are some hastily selected observations. Organic and fairtrade food has significantly higher market presence in the UK than in Australia. Our nearest Sainsbury’s had many more organic products than can be found in either of the two major chains here in...

I’m back in the teaching saddle for 2006. In Semester 1, I teach two undergraduate courses. 161-115: Logic and 161-212: Non-Classical Logic.

Happy New Year, my readers! We’ve landed in Melbourne (to a hot 8pm at around 42 degrees Celcius), and are slowly reconstructing our household bit by bit. The internet connection seems to work at least. We’ve managed to change lightbulbs, unpack bags, look at a bit of our large pile of mail, get the boy to bed (and even to sleep) and have some...

This is our manifesto on logical pluralism. We argue that the notion of logical consequence doesn’t pin down one deductive consequence relation, but rather, there are many of them. In particular, we argue that broadly classical, intuitionistic and relevant accounts of deductive logic are genuine logical consequence relations. We should not search...

This is an introductory textbook in logic, in the series Fundamentals of Philosophy, published by Routledge. I use the text in my Introduction to Formal Logic class at Melbourne. It’s available at Amazon UK and Amazon US. The book was translated into Chinese in 2024. The book has a dedicated website at http://consequently.org/logic.

We’re in the middle of packing up our Oxford home, to start the short trip back. We land in Melbourne on New Year’s Eve, after some stops in Köln (for the Christmas Markets), Augsburg (for Christmas with friends), Frankfurt Airport (to get on the plane), Singapore (to break the journey, and give us some summer in close proximity to air...

A good argument is one whose conclusions follow from its premises; its conclusions are consequences of its premises. But in what sense do conclusions follow from premises? What is it for a conclusion to be a consequence of premises? Those questions, in many respects, are at the heart of logic (as a philosophical discipline).

I’ve given my two talks here in St. Andrews, with really useful discussion in both of the talks. In the philosophy talk, questions ranged from matters of meaning theory, metaphysics and epistemology of possibility and necessity. Thanks especially to Daniel Nolan, Carrie Jenkins, Marcus Rossberg, Ole Thomassen Hjortland, Crispin Wright, Stephen...

… you’re on sabbatical. I’m now in St. Andrews visiting Arché for what can only be described as “November Madness.” I’m giving a seminar this afternoon in Arché/Philosophy (in the wonderful Edgecliffe building) and then tomorrow, I’m giving a seminar in computer science tomorrow. This means I’ll miss the Vagueness Seminar and a Philosophy...

G’day! I’ve produced a new patch to provide SMIL Animation for SVG. Since last time I’ve added: keySplines keyTimes accumulate restart min, max ElementTimeControl DOM interface

Here’s an updated patch with my latest changes including: Optimised performance—a lot of unnecessary rendering has been filtered out and the profiling I was able to perform suggests this has made a significant difference, especially when the animation is frozen. Animation now pauses and resets when the page is cached in the bfcache. Better thread...

We’re now in the second day of “week 1” of Michaelmas, here in Oxford, and the philosophy faculty library is considerably busier than it was in week 0, let alone the negative weeks. It’s just as well that I’ve got some writing done already. Today I’m heading off to Nottingham to give two talks. The Philosophy Department will get the first outing...

Aided by flat surf but hampered by perfect weather I’ve spent most of the last week tidying up my code and updating the documentation on the wiki. The latest patch is hopefully much better, or at least not quite as hideous as it was in some parts.

Additive animation appears to be working. The test case I mentioned in the last post works even the nasty tree re-ordering cases. I’ve also extended the additive test case a little to test a bit more of the dynamic behaviour.

This post is a change of scene for those of you that have come to expect gentle meditations on matters personal. I’m going to experiment with posting some of my work scribblings as an irregular record of thoughts I’m having while working on sabbatical. It may well confirm the impression that you might have that I’m crazy, but hey, I have tenure,...

I’ve done most of the work required for additive animation. The remaining part is to correctly order animations in the animation sandwich after changes to the document structure.

I’ve begun work on implementing compositing. This will take some time. Also I’m no longer sure I’ll be able to deliver syncbase timing this year as instead I may need to focus on integration issues, performance, documentation, thread-safety and so on. Hopefully all this will mean it has a better chance of getting checked in sooner though.

Here’s the second part of my reflections on our week on Iona. If you’re interested in that kind of news, read on. I haven’t mentioned the most significant thing about our time on Iona – the week was tempered by an event just before we left for the island. The story started on the Friday before we left Edinburgh on Saturday. It was my last day...

I’ve added a basic implementation of repeating. This doesn’t include accumulating or repeat-based timing but this test and a whole lot of other tests seem to work. Also, I’ve added a couple more tests.

I’ve implemented handling for multiple begin and end values including calculating the active duration, selecting the correct interval etc.

This is an extended post reflecting on the week in Iona. Read on if you want to find out what we did for a week on a small Hebridean island. It’s not immediately straightforward to get to Iona, when you start from our B&B in North Queensferry. Our day’s journey started early with a taxi ride to Edinburgh Waverley, and then a train to Glasgow...

The paper examines what its title says. Constant domain modal frames seem to be the natural semantics for quantified relevant logics and their cousins. Kit Fine has shown us that things are not that simple, as the natural proof theory is not complete for the natural semantics. In this paper I explore the somewhat simpler case of one-place modal...

Phew! We’re back in Oxford, and arrived in our house today. We’re in a cute little 2 bedroom house in the northern outskirts of Oxford, a quick busride down Banbury Road into Wolfson or the centre of town. I’m currently dealing with some of the backlog of email in a Starbucks (of all places!) with a wireless network. The week at Iona was great....

I thought I’d post this patch which contains my work so far. This patch contains most of the classes I outlined in my design. It will do very simple animation of lengths using a very limited subset of timing specifiers.

Too many things are happening for me to spend any time posting here until the whirl of activity settles down. Still, people have been wondering what’s going on, so here’s a bit of a run-down. After Logic Colloquium, I went back to Denmark to rejoin the family, to have a holiday in Blokhus with close friends. Much fun was had, involving sand...

Just a quick update in case anyone someone actually reads this page. I’ve implemented most of what I intended to cover in the first iteration and now some very basic animations work.

I hacked my last iPod Color using AlterPod so that I get the Prince of All Cosmos instead of the standard no entry sign. The iPod was later stolen, returning the little Prince to live amongst the stars!

Today is Day 4 of the colloquium. Yesterday was a day of rest, which for me involved a visit to the Byzantine and Christian Museum, in the morning, a lazy afternoon restructuring the order things in my ESSLLI course while staying in the shade, and visiting the Herakleidon Museum which featured an exhibit of Escher prints (the detail in some of...

It’s another busy day with lots of things to learn. Here’s my impressions so far, updated through the day. 9:20: Phokion Kolaitis is giving his second lecture — he’s good, and it’s been interesting to learn about dichotomy theorems in CSPs. Schaefer’s dichotomy results cast in terms of constraint satisfaction problems, are really interesting. The...