Melbourne Logic Seminar - 21st/Sept Logic Workshop

10:00~11:00 Rohan French

Title:  Sequent Calculi for Urn Logic

Abstract:

Approximately speaking, an urn model for first-order logic is a model where the domain of quantification changes depending upon which objects have been `drawn from the domain'. In this talk I'll give a sequent calculus for urn logic using decorated formulas which can be read as saying that ``after o1, ..., on have been drawn, A''.

11:10~13:10 Fracesco Poali

Title: SEMANTIC MINIMALISM FOR LOGICAL CONSTANTS

Abstract:

In a 2003 paper, I defended a minimalist account of meaning for logical constants as a way to ward off Quine's meaning variance charge against deviant logics. Its key idea was that some deviant propositional logics share with classical logic the operational meanings of all their connectives, as encoded in their sequent calculus operational rules, yet validate different sequents than classical logic - therefore, we can have genuine rivalry between logics without meaning variance. Ole Hjortland levelled several objections at this view. The aim of this paper is to address these criticisms, highlighting at the same time the rôle played by logical consequence in this version of semantic minimalism.

13:10~14:00 Lunch

14:00~15:00 Lloyd Humberstone

Tiltle: Monotonic Logic

Abstract:

As a case study in the role of some of the structural rules, I would like to go through some material in the early sections of my paper 'Heterogeneous Logic' (Erkenntnis 29 (1988), 395--435) for the case in which the left-hand language of a heterogeneous logic coincides with its right-hand language.

15:10~16:10 Dave Ripley

Title: Some substructural arithmetic (joint work with Ole Hjortland)  

Abstract:

 Two distinct but overlapping research traditions pursue formal theories of a truth predicate: call them classical and nonclassical. This sometimes makes sense, but sometimes seems a shame; it would be good for these traditions to be more integrated than they are. One stumbling block to this integration is that classical theories of truth are often pursued with an eye firmly on arithmetic, while nonclassical theories of truth often leave arithmetic to one side.

The main goal of the paper from which this talk is drawn is to work against this stumbling block. In particular, we seek to develop a noncontractive theory of transparent *and compositional* truth, one that can express and prove generalizations like "for all x and y, if x and y are sentences then the conjunction of x and y is true iff x is true and y is true". Such generalizations require a theory of syntax in the object language itself; we intend to develop this theory, as is usual, via arithmetic.

This talk will not get all the way to the full theory. (We don't yet have the system all wired up.) Instead, it will focus on developing arithmetic in a substructural setting, identifying some very minimal features of a logic that suffice for proving some familiar results about arithmetic. In particular, the talk will show that a wide variety of substructural logics have the resources to "weakly represent" all recursive functions.

16:20~17:20 Tomasz Kowalski

Title: Admissible rules in BCK and BCI (joint work in progress with Lloyd Humberstone)

Abstract: Using a simple proof-theretical technique we demonstrate that
certain families of inference rules are admissible but not derivable in
BCK and BCI.

17:30~18:30 Short drink (University house)

19:00~           Dinner (Gurkha's)