# Logic Day

November 1, 2019
Logic Group, The University of Melbourne

461
Arts West
Parkville 3010
Australia

## Organisers:

University of Melbourne

## Details

There will be a Logic Day on 1 November in Arts West 461 North Wing. The presenters will be Greg Restall, Shawn Standefer, Dave Ripley, and Tomasz Kowalski. The abstracts and schedule are below.

Shawn Standefer (Melbourne) will present "A note about reduced frames".

Abstract: Routley-Meyer frames have been used to give a frame semantics for relevant logics. In this talk, I will provide a brief overview of what is known about reduced frames, Routley-Meyer frames with a single normal point, and then present an incompleteness result for them.

Greg Restall (Melbourne) will present "What's So Special About Logic: Practices, Rules, and Definitions".

Abstract: Over the last century or so, the discipline of logic has grown and transformed into a powerful set of tools and techniques that find their use in fields as far apart as philosophy, mathematics, computer science, electrical engineering and linguistics. Is there anything distinctive about logic and its results, or is it just another kind of abstract mathematics, or another kind of empirical scientific theory? In this talk I’ll explain why the distinctive subject matter of logical theory means that the tools of logic (proofs and models) can play a special role in our thought and in our talk. This explanation will turn crucially on our practices of assertion and denial, and how it can constrain those practices by using rules and definitions.

Dave Ripley (Monash) will present "Metainferences and the spirit of classicality".

Abstract: Sometimes I run around calling nontransitive things "consequence relations". And when I really want to stir the pot, I call nontransitive consequence relations "classical" when they extend the consequence relation of classical logic. As a referee once pointed out, this may be a way of holding to the letter of classical logic, but it does not keep to the spirit of the thing. (That, of course, is the intention.)   But what is the spirit of classical logic? Is it just a certain attitude some logicians take up, or can we give it a precise and nonarbitrary sense? In particular, is there anything about the consequence relation of classical logic itself (which is of course transitive) that could indicate a distinction between its transitive extensions and its nontransitive extensions? In 2013, Cobreros et al argued not: that any such distinction would have to be arbitrary. I now think we were mistaken, that there is a good (precise, nonarbitrary) sense to be made of the spirit of classical logic. In this talk, I'll draw on work by Humberstone and Teijeiro to give an overview of the situation and offer a candidate for the letter of the spirit.

Tomasz Kowalski (La Trobe) will present "Small varieties of total tense algebras and semiassociative relation algebras."

Abstract: A tense algebra is total if the relation of the underlying
general frame is total, i.e., xRy or yRx holds for any points x,y
(in particular, R is reflexive). There is precisely one minimal non-
trivial variety of total tense algebras, term-equivalent to the variety
of Boolean algebras. Jipsen, Kramer and Maddux showed that this variety
has at least countably many covers in the lattice of varieties of total
tense algebras. James Koussas and TK extended this result by showing
that there are continuum such covers. This also yields an analogous
result for varieties of semiassociative relation algebras.

Schedule

11-12:15: Shawn Standefer "A note on reduced frames"

12:15-1: Lunch

1-2:15: Tomasz Kowalski "Small varieties of total tense algebras and semiassociative relation algebras"

2:15-2:45 Coffee

2:45-4 Dave Ripley "Metainferences and the spirit of classicality"

4-5:15: Greg Restall "What's So Special About Logic: Practices, Rules, and Definitions"

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