# Meeting in honour of Dag Westerståhl on the occasion of his retirement

We have the great pleasure to celebrate Dag Westerståhl on the occasion of his retirement from the University of Gothenburg with a one day scientific meeting on the philosophy, logic and linguistics related to Westerståhl’s work.

The event took place on Friday 3rd May 2013 at the Department of Philosophy, Linguistics and Theory of Science at the University of Gothenburg.

### Speakers

Denis Bonnay (Université Paris Ouest)

Robin Cooper (University of Gothenburg)

Lauri Hella (University of Tampere)

Peter Pagin (Stockholm University)

Stanley Peters (Stanford University)

Jouko Väänänen (University of Helsinki and University of Amsterdam)

Everyone is welcome to attend the talks. The preliminary timetable is as follows:

9:15-10:30 Peter Pagin, Compositionality by currying

10:35-11:50 Stanley Peters, Descriptive Quantifiers

Lunch (Fond)

13:30-14:45 Lauri Hella, Generalized quantifiers and logics with built-in relations

14:50-16:05 Denis Bonnay, Dynamic vs Classical Consequence

Coffee

16:30-17:45 Robin Cooper, Quantifiers and the nature of intensionality

17:50-19:05 Jouko Väänänen, Foundational and model theoretic aspects of second order logic

19:30- Dinner (Familjen)

There is a Google map of the relevant locations at: http://goo.gl/maps/PoFDm.

Please don’t hesitate to email Fredrik Engström, with questions.

**Denis Bonnay** *Dynamic vs Classical Consequence*

I will present some recent joint work with Dag on logical consequence. As all of us know, logical consequence is about what follows from what. But this seemingly unambiguous, albeit vague, characterization does become ambiguous when one starts thinking in terms of information flow. One may ask what follows from the information possessed, or what follows from the information received. I will make these notions precise in a dynamic framework and discuss the relationships between them, in particular when the information is represented within Dynamic Epistemic Logic.

**Robin Cooper** *Quantifiers and the nature of intensionality*

I will discuss the intensional quantifiers and suggest that the kind of intensionality involved is not quite the same as that we need for attitude reports. I will suggest a way to approach this situation using a type theoretical analysis of generalized quantifiers.

**Lauri Hella** *Generalized quantifiers and logics with built-in relations*

Built-in relations have an important role in descriptive complexity theory: for example, the famous Immerman-Vardi characterization of PTIME by Least Fixed Point Logic is only valid in the presence of built-in linear order. Similarly, all the known logical characterizations of circuit complexity classes require the presence of built-in artithmetical relations. However, a general theory of abstract logics and generalized quantifiers with built-in relations has been lacking up to now. In this talk, I describe an approach towards developing such a theory. The talk is based on joint work with Juha Kontinen and Kerkko Luosto.

**Peter Pagin** *Compositionality by currying*

Suppose that we have a semantics μ that gives values for expressions of a language L at evaluation points. If L contains operators that shift evaluation points (an example is quantifiers in first-order logic with assignments as points), μ may not be compositional. But if μ is compositional for the shifting-operator-free fragment, then the curried semantics μ* will be compositional, where μ* gives values to expressions that are functions from evaluation points to the values of μ. I plan to take a first look at how this works for the semantics of second-order logic, and its relation to the semantics for games of imperfect information, as given by Hodges.

**Stanley Peters** *Descriptive Quantifiers*

Natural languages employ a number of type <1,1> quantifiers that are not invariant under isomorphism because the quantification they express is partly determined by a descriptive element. Examples include possessives such as Mary’s and exceptives like no __ except Sunnis. Like isomorphism invariant ones, these quantifiers can be rigorously analyzed logically, provided due attention is given to the role played by their descriptive elements. Joint work with Dag has shown that the analytic process often brings out linguistically significant features of descriptive quantifiers that were not previously recognized.

**Jouko Väänänen** *Foundational and model theoretic aspects of second order logic*

I formulate a “second order logic view”, an approach to foundations of mathematics giving second order logic a dominant role, and compare it with what I call “set theory view”. I give some model theoretic results about second order logic and discuss their implications to the “second order logic view”, and to the concept of second order logic in general.