In a few recent papers and talks, I’ve been using *flow graphs* to display the flow of information in proofs. These are the kinds of things that are easy to draw, but they’re not so straightforward to typeset.

Here’s an example:

They’re not easy to typset, because they’re an overlay over a proof. The arrows indicate the flow of information inside a proof.

As an aside, I love the flow graph on this natural deduction proof because the “action at a distance” nature of the disjunction elimination step is called out by those two sweeping blue and green arcs—the \(q\) and \(r\) assumptions are discharged by the appeal to the disjunctive conclusion \(q\lor r\). These are the only non-local informational connections in the proof. Each other arc in the flow graph is local, from a premise to a conclusion.

Now, typesetting these things is not straightforward, because the locations of the arrows are defined by typesetting the underlying proof (here, the black text) and the coloured arcs are typeset on top. How do you do that? And how do you do that in an algorithmic and structural way, focussing on the structure and not hand positioning each of the lines?

Thankfully, the tools to typset flow graphs are readily available, at least if you use LaTeX. I’ve written up a little document explaining how to do this, and the document and source are now available on Github for you to use as you see fit. If you’ve got any questions, feedback or recommendations for how to extend the technique, please don’t hesitate to get in touch.

I hope it’s helpful.

← With Gratitude to Raymond Smullyan | News Archive | Conditionals in Closed Set Logic →

I’m *Greg Restall*, and this is my personal website. I teach philosophy and logic as Professor of Philosophy at the University of Melbourne. ¶ Start at the home page of this site—a compendium of recent additions around here—and go from there to learn more about who I am and what I do. ¶ This is my personal site on the web. Nothing here is *in any way* endorsed by the University of Melbourne.

- School of Historical and Philosophical Studies, The University of Melbourne, Parkville 3010, Australia.
- greg@consequently.org
- keybase.io/consequently, to sign or encrypt a message to send to me privately.
- @consequently on Twitter.
- @consequently on Instagram.

To receive updates from this site, you can subscribe to the RSS feed of all updates to the site in an RSS feed reader, or follow me on Twitter at @consequently, where I’ll update you if anything is posted.