Saturday, May 30, 2015

Relevant Logic Revisited

In 1992 I tried to read Anderson and Belnalp's book `Entailment, Vol. 1: The Logic of Relevance and Necessity' (1976) to help Maria Claudia Mere with her PhD thesis. 

She completed her work `Logicas Relevantes: formalismo e semantica'
in 1993, and I was a bit disappointed with relevant logics. I was hoping for prettier mathematics, cleaner proof-theory and clearer philosophical views. Now that my standards have changed a little, maybe I should re-read this work.
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5 comments:

  1. UnknownMay 30, 2015 at 7:05 PM

    There's been a lot of progress since E1, in all three areas you point to. I'd recommend either Dunn & Restall's survey article, Read's book Relevant Logic, or Bimbo's new book Proof Theory. (Sorry for no links; I'm on my phone.)

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  2. UnknownMay 30, 2015 at 7:05 PM

    There's been a lot of progress since E1, in all three areas you point to. I'd recommend either Dunn & Restall's survey article, Read's book Relevant Logic, or Bimbo's new book Proof Theory. (Sorry for no links; I'm on my phone.)

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  3. ValeriaMay 30, 2015 at 7:30 PM

    Thanks! I've looked at Read's book before. today I saw Bimbo's book, which I didn't know about before, will check it out.

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  4. Neel KrishnaswamiJune 2, 2015 at 9:05 AM

    I wonder if there is something domain-theoretic to be said about relevance logic. If you think of relevance logic as "intuitionistic linear logic plus contraction", then the category of pointed domains and strict continuous maps gives a model of this situation.

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  5. ValeriaJune 2, 2015 at 10:34 AM

    hi Neel, thanks for the comment! indeed, this (that relevance logic = ILL+ contraction) is what I was thinking at that time, so the thesis I mentioned has a section on adding a comonad for contraction to dialectica categories as models of LL. and clearly pointed domains do that too. the problem I have with this idea is that if the domains are pointed, they are always inhabited, so the easy way of thinking of falsity as lack of inhabitation is gone. Your logic collapses true and false, which is something that logics of domains do, but usually only when you add fixpoints, as I'm sure you know. So at that stage I didn't want to have these kinds of models (I went on to do work with Andrea Schalk on non-collapsing models of Linear Logic). But nowadays even more collapsing models (compact closed categories) are all the rage, right? so why not? maybe we should go back and investigate the pointed domains as
    models and see if they give us something extra.

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