# Logic Workshop 2015

We’re closing out the year with a two-day Logic Workshop, running December 10-11. Talks will be in Old Quad G14 and will start at 11 each day. The tentative schedule is below. Everyone is welcome.

Thursday Dec 10

11 – Daniel Murfet (Melbourne) — Complexity and linear logic

12 – Ross Brady (La Trobe) — On the Law of Excluded Middle

2 – Tomasz Kowalski (La Trobe) — NP-complete fragments of qualitative calculi

3 – Szabolcs Mikulás (Birkbeck) — Residuated semigroups and substructural logics

Friday Dec 11

11 – Jake Chandler (La Trobe) — The Irreducibility of Iterated to Single Revision (handout)

12 – Lloyd Humberstone (Monash) — Archetypal Rules — A Conjectured Result in Need of a Proof

2 – Greg Restall (Melbourne) — Generality and Existence 3: Identity and Substitution

3 – Shawn Standefer (Melbourne) — Instability, contraction, and truth

#### Abstracts

**Chandler**: (joint work with Richard Booth): After a number of decades of research into the dynamics of rational belief, the belief revision theory community remains split on the appropriate handling of sequences of changes in view, the issue of so-called iterated revision. It has long been suggested that the issue is at least partly settled by facts pertaining to the results of various single revisions of one’s initial state of belief. Recent work has pushed this thesis further, offering various strong principles that ultimately result in a wholesale reduction of iterated to one-shot revision. The present talk offers grounds to hold that these principles should be significantly weakened and that the reductionist thesis should ultimately be rejected. Furthermore, the considerations provided suggest a close connection between the logic of iterated belief change and the logic of evidential relevance.

**Kowalski**: A qualitative calculus can be seen as a certain algebra of binary relations, with a weak version of relational composition. Some relation algebras that are not representable in the standard Tarski sense, become representable with this weaker notion of composition. We call these algebras qualitatively representable. One such is the non-representable algebra on 4 atoms found by McKenzie.

Network satisfaction problem can be defined for qualitatively representable algebras in the usual way. I will present a sufficient condition for a network satisfaction problem over (a reduct of) a qualitatively representable algebra A to be NP-hard. It shows in particular that network satisfaction problem over McKenzie algebra is NP-complete.

**Restall**: In this talk, I extend a sequent proof system for free logic to include an identity predicate. Or rather, *two* different candidate identity predicates allowing for the substitution of a lesser or greater class of predications. I show that the resulting system is well-behaved proof theoretically (the Cut rule is admissible) and the identity predicates can be well motivated in terms of their defining rules.

**Standefer**: Non-contractive approaches to truth reject the structural rule of contraction. One philosophical justification based of rejecting contraction, offered by Zardini, is based on the idea of unstable states of affairs. I argue that when understood in terms of revision theory, this idea equally motivates rejecting other principles that non-contractive theorists want to maintain.

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