Friday, April 2, 2021

Spring has sprung


Spring has sprung and knocked me off badly. Had a horrible dental surgery, four hours plus on the dentist chair with billions of bad things happening. This was on Tuesday. Thought, oh dear, I guess I miscalculated how bad this was going to be, now, I will take my medicines and be back on my feet tomorrow. ho, ho, this was the good day. My body mounted a united front against the medication prescribed (medication that I had had several times before) and I got to feel really weak, as I kept being sick several times a day. 

Not good, not good at all. I'm finally better, touch wood, and  now I have read Terry Pratchett's Nation and I loved it. 

I was reminded of the many reasons why I love Pratchett's books: they do make you think about the important things in life in novel ways. My favorites are the Witches stories, I love all the witches, but Granny Weatherwax is a favorite: "If you want to amount to anything as a witch you got to learn three things. What’s real, what’s not real, and what’s the difference.” 

“We look to… the edges,' said Mistress Weatherwax. 'There’s a lot of edges, more than people know. Between life and death, this world and the next, night and day, right and wrong… an’ they need watchin’. We watch ‘em, we guard the sum of things.  

“You can‘t go around building a better world for people. Only people can build a better world for people. Otherwise it‘s just a cage.” 

Cage or no cage, it's time to go back to thinking about multiagent systems and what do we expect of them minimally. Well, if you have many agents, one expects that each one of them is a reasoning agent on its own and that its reasoning can be of the classical, constructive, linear  or modal variety. And similarly, when considering how they interact with each other, the same possibilities arrive. Thus it would make some sense to compare these kinds of reasoning agents. Something that we want to discuss next.

(when the internet is behaving a bit better and I can upload pictures!)

Sunday, February 21, 2021

Dialectica Categories as Matrices


The Topos Institute officially opened on the 4th January 2021. On the 4th February David Spivak gave the first  Topos Institute Colloquium on the category POLY. I have not decided, yet, what I want to talk about in the Colloquium: too many ideas.  But when Brendan Fong suggested that we had internal talks where we explain to our colleagues what we do, I was very pleased to do it. The idea was a short talk, with few or no slides and lots of discussion. Great, right?

I talked on Friday and the slides are already in slideshare. And the conversation was great, but we couldn't get to half of the material. Oh well, the discussion was that good. So I decided that writing a few blog posts about the various Dialectica categories and some of the work that ensued is a good thing. This is the first post. 


The Dialectica construction starts from a cartesian closed base category (with coproducts -- think of Sets!) and builds structure on top of that. 

So we have a new category Dial whose objects are triples (U, X, alpha), where U and X are sets and alpha is a relation. Now you can think of a relation alpha either as a subset of a product (alpha is contained in the product UxX) or as a map, from the product UxX to 2, taking a pair of elements (u,x) to alpha(u,x) which either holds (alpha(u,x)=1) or doesn't hold (alpha(u,x)=0). Here we will concentrate on the view of relations as maps to 2, instead of subsets. (OK, I do need to find a way of inserting LaTeX here, will do it soon!)

Now recently I became aware of a series of blog posts by Scott Garrabrant that describe how Chu spaces can be given an intuitive explanation in terms of a collection of agents interacting with an environment. Since Chu spaces and dialectica categories have (almost) the same objects, this same explanation works for dialectica categories too. So you can think of U as your (undercover) agents, and of  X as your unknown environments and alpha relates some agents to some unknown conditions in the environment.

One of the differences between Chu spaces and dialectica objects is that for Chu the set in which we evaluate the relation W does not have any structure: it's simply a set with elements {w, v, t,...}.  For dialectica we need an order on the elements of W to even construct the category.

Here's Scott's concrete example: Consider the case where there are two possible environments,  for rain, and  for sun. The agent independently chooses between two options,  for umbrella, and  for no umbrella, r for rain and s for sunny,  and . There are four possible worlds in . We interpret  as the world where the agent has an umbrella and it is raining, and similarly for the other worlds. The Chu  C space looks like a matrix 2x2, but nothing stops me from thinking of this as a dialectica object:

Vaughan Pratt has been trying to convince me that these matrices are lovely since before 2000, when we organized together a Workshop on Chu and Dialectica Spaces in Santa Barbara, that eventually became the TAC Special Volume. But while Vaughan has tried to tell me that the matrices are a good model of Linear Logic, Scott tells me that are a useful way of formalizing a community of agents.

I have been wanting to have a model of reasoning agents for a while. Dealing with multiagent systems (MAS) is what my friends Natasha and Brian do and I have always wanted to try to work more with them. So this is not it, yet, but I hope this thinking of dialectica categories as multiagent systems might turn out to be the bridge I need to work with Natasha again.

Saturday, January 30, 2021

Better reporting in 2021

 I am truly appalling at reporting the work I have done. So my new year's resolution is to improve (at least a little) on that. 


I have been working since 2015 in the Scholarship Committee of the ACM-W, when I was invited to join by Adriana Compagnoni. I have mixed feelings about the organization (I have mixed feelings about all the professional organization societies nowadays!) but I do believe that giving young students some money to attend computing conferences is a good thing.

Now work in the Scholarship Committee, like all other voluntary work, is heavier than it looks. So you join thinking, it's only some 2 hours times 6 a year, I can do that. But then the hours multiply themselves and things get to be much more work than you thought it would be and mostly it needs to happen (Murphy's Law) when you actually have a very hard time to do it! But this is life.

So I first worked for the Scholarship Committee as a judge of awards. But I hated the job, as the criteria are not so clear, there's an awful lot of scope for people gaming the system and I hated not doing a proper job. So I've asked to be only a writer for the committee and now I only describe what what people have judged. But  then the corona virus hit. And things got complicated. I think we need to take the opportunity to make things better, if we can. But who knows whether we can or not?

Meanwhile, this was my December 2020 note for the Scholarship, apart from the boilerplate that we have in every newsletter, of course.

   This month, almost nine months into the COVID-19 pandemic, with many conferences postponed, cancelled or transformed into online events, fewer people are submitting applications. Thus, we decided that this was a convenient time to write about our Scholarship Committee, some about our origins, and motivations, some about the people that keep it running. 

We first had short interviews with the Chairs of the Scholarship Committee, professors Elaine Weyuker and Viviana Bono, in previous editions of the newsletter. But it also seemed appropriate to ask the members of our committee about their personal histories. Of course, as you may have noticed yourself,  working from home has not made life easier for researchers and professors. Everyone who teaches  has had to adapt to the new conditions. For many, this has proved a very difficult journey to digital teaching, without any time for learning or preparation. Still, everyone in academia is l trying to cope with the new reality of the pandemic as best as they can, and we are not an exception.

This seems a good time to tell you a bit about why we run the Scholarship Committee the way we do and also a bit about the stories of the people behind the scenes. And we’re glad to start off with a  researcher who was an alumna of the program herself, only a few years back. Yelena Mejova is a Senior Research Scientist at the ISI Foundation in Turin, Italy, a part of the Digital Epidemiology Group. Her research concerns the use of social media in health informatics, as well as tracking political speech and other cultural phenomena. (To read the interview with Prof Mejova head to

The A

Thursday, January 21, 2021

Too many ideas, too little time

Last week we had our "Logica e Representatividade" (Logic and Representativeness) meeting on the 14th January 2021, the World Logic Day, almost a week ago  today. The meeting went very well! I was a bit concerned that we had only decided to do it around the 14th December and there was the festive period (between Christmas and New Year's)  in the middle of this month! of course sensible people don't do much during these holidays, so I worried that we would end up without speakers, without discussions and without an audience. and true to the old adage that when in doubt, just produce some slidedeck or two, I spent some lovely panic time doing exactly that.
Thank goodness I was wrong in all three accounts: all of our Invited Speakers did show up with some lovely videos, moving histories, clever positioning. The discussions flowed naturally and we had a decent audience on YouTube, I'm told. As I had said in December, the idea was to get the ball rolling, to start the discussions on all kinds of lack of representation in Logic, and we certainly did that. the difficulty will be the next step!
But meanwhile I have been thinking about Public Announcement logic (PAL). More precisely about intuitionistic  PAL, as described by Ma, Palmigiano and Sadrzadeh in "Algebraic semantics and model completeness for IntuitionisticPublic Announcement Logic" and by Balbiani and Galmiche's "About intuitionistic public announcement logic". 
The reason I've been thinking about it is that I wanted to complete some old work with Natasha Alechina, Michael Mendler and Eike Ritter in "Categorical and Kripke semantics for constructive S4 modal logic".
The issue I want to explore is the relationship between algebraic semantics and frame semantics. 

Monday, January 11, 2021

A quote for World Logic Day

My friends at the  Vienna Center for Logic and Algorithms at Vienna University of Technology (VCLA at TU Wien) invited me to be an Ambassador for Logic, in their celebrations of World Logic Day 2021.

At first, I was somewhat reticent, I am no good at slogans and epigrams (I wish I was!).

But then I got into the spirit, I think, and you can see my quote below:

When all is said and done, what's left, what stays, from being human, is Logic. Logic removes all the flesh and ornaments, and gives us the underlying bones of what we know. Whether it intends to do so or not, logic turns out to be a moral compass. We overlook it at our own peril, as Logic is even more inexorable than taxes and death.

 At least I think I can say with a clean conscience that I am a logician, not so sure about semanticist, computer scientist, AI researcher, mathematician, or philosopher. But I try.

But then the DIVISION OF LOGIC, METHODOLOGY AND PHILOSOPHY OF SCIENCE AND TECHNOLOGY asked some of its logicians for a short video about the importance of Logic. So I recorded a 2 min message  and this message end up in the Conseil International de Philosophie et des Sciences Humaines (CIPSH), cool! 

(yeah, I think I could get used to this idea of people asking me about my opinion! it does have a nice ring to it, I say, I say)

Sunday, January 10, 2021

Just so that I remember

I need to go over all the posts on the Women in Logic Facebook group and 'store' them somewhere safe, either adding them to blogs or at least keeping the information for future use. 

but of course, this takes an awful lot of effort and time, which I haven't got right now. 

So simply a quick cut-and-paste of one such:


some links H/T Bruno Lops

Saturday, January 2, 2021

Frege and his little monsters

This is NOT a serious post, in case this is not obvious. 

I don't like quantifiers, I call them Frege's little monsters.

I don't like the universal quantifier  because it brings infinity into models. Don't get me wrong, I love infinity as much as any other mathematician and I still get a twinge of pride when I explain Cantor's basic theorems (enumerability of the rationals and lack of such of the reals)  to anyone who hasn't seen them before, especially young ones. But I once attended a lecture by Phokion Kolaitis, who showed me that finite model theory is really very 'different' from model theory: nothing works the way models are supposed to work. It is not the case (as I thought before) that finite model theory is an easy (because finite and surveyable) instance of usual model theory. And one can do an awful lot without bringing infinite domains into our logic pictures.

Also universal quantification and especially vacuous quantification is horrible and very non-intuitive. The typical example of something that we feel forced to accept simply because, without it, the system is even worse.

But you have a duality, people might object. Maybe simply look at the existential quantifier and let the universal be simply its dual. Well,  this does not work for constructivists, who do not believe that 'for all' and 'there exists' are totally dual. But  also, if you chose the existential that is  not exactly dual to universal quantification, the one that has more content, the one which says which 'x' is that that makes "there exists x such that A(x)" true, well then you have a connective that has complicated binding rules, requires commuting conversions and it's not  proof-theoretically well-behaved.

Semantically it's very simple, right? If you say that there exists something such that the predicate A is true of that something, well, just show me the culprit! Call it 'a', because we have a long tradition of thinking of x's and y's as variables and thinking of a's and b's as constants and  then we know that "A(a)" is true. And that a model of this sentence should have 'a' in its domain. Seems simple and direct, but it is anything but simple.

So they are both little monsters, Frege's monstrinhos, and when we want to model them categorically not only do we need our triple adjunction, we also need the Beck-Chevelley condition (BCC), which everyone does its best not to explain. Of course the whole set-up of free and bound variables, predicates and functions, and how substitution works for them, has to be put in place and made to work, before you can add the little monsters.

Anyways I was about to post here a picture of  Frege by Renee Jorgensen Bolinger, in the style of van Gogh. Her pictures of philosophers are great and I really want to buy a few, you can see them at her site.
But she requires people to ask her for permission and I cannot be bothered, so you just need to go and look up her site!