Autumn 2010

23 September: Room DZ 6

Vague Desire: the Sorites and Money Pump

David Etlin,
University of Leuven

14 October: Room DZ 10

The Barcan Formula and Completeness of First-Order Modal Logic

Eric Pacuit,
TiLPS

In this talk, we will survey some recent work on completeness of first-order
modal logics. In particular we will look at the role that the Barcan
formula(s) play in various completeness proofs. We will focus on non-normal
systems (cf. “First-Order Classical Modal Logic” by Horacio Arlo-Costa and
Eric Pacuit, Studia Logica 84(2), 2006) and general completeness theorems
(cf. “A General Semantics for Quantified Modal Logic” by Robert Goldblatt
and Edwin Mares, Advances in Modal Logic 6, 2006). Time permitting we will
also look at alternative semantics for the first-order modal language.

28 October: Room DZ 8

Agreeing to Disagree in Probabilistic Dynamic Epistemic Logic

Lorenz Demey,
University of Leuven, ILLC

In this talk I will discuss Aumann’s celebrated agreeing to disagree
theorem from the perspective of probabilistic dynamic epistemic logic.
I will first introduce Aumann’s own formal statement of the theorem, and
its intuitive motivation. Next I will introduce probabilistic Kripke
models and various ways of updating them. These tools are then used to
model several versions of the agreement theorem. I will also introduce
sound and complete agreement logics. On the basis of these technical
results I will make some philosophical/methodological points about the
agreement theorem, in particular about the role of common knowledge and
the underlying dynamics. If time permits, I will also compare my approach
with another way of modeling the agreement theorem in DEL, which has been
developed by Dégremont and Roy.

11 November: Room DZ 6

Adjectives, Scales and Zeros

Galit Weidman Sassoon,
ILLC

Degree questions such as “how tall is John?” and equatives such as “John is
as tall as Mary” do not imply that John is tall, while their negative
counterparts (“how short is John?” and “John is as short as Mary”) do imply
that John is short. Existing theories attempt to explain this by means of a
competition between unmarked (positive) and marked (negative) antonyms, and
by means of a null morpheme that introduces a standard-variable into the
derivation (in analogy with the standard analysis of the positive form “John
is tall/short”; cf. Rett 2007). This talk attempts to present data that
challenge these theories, as well as an alternative analysis for the facts
based on the existence of an absolute zero or its lack thereof, in the
interpretation of, e.g., ‘tall’ and ‘short’, respectively. Implications for
additional dominant linguistic analyses of scalar adjectives will be
discussed, pertaining to differences between absolute and relative
adjectives (cf. Winter and Rothstein 2005; Kennedy and McNally 2005; Kennedy
2007).

9 December: Room DZ 6

Sense and Circularity: Recursion in Higher Order Logic

Reinhard Muskens,
TiLPS

In this talk I will report on ongoing work with the goal of developing a
higher order logic that is not only truly intensional, in the sense that
necessarily coextensional objects need not have the same properties, but in
which it is also possible to model Fregean senses as algorithms
along the lines of Moschovakis [1]. In this influential paper Moschovakis
succeeds in combining an account of the procedural character of meaning with
an account of circular statements such as the Liar and
Truthteller—these circular statements are associated with looping
algorithms. Moschovakis [1] uses a first order logic, while higher order
logics are more suitable for natural language description. This is remedied
in Moschovakis [2] by adding recursors to the simply typed lambda calculus,
but while [2] succeeds admirably in modeling the procedural character of
language, the possibility of modeling circularity is lost, as an acyclicity
requirement is necessary. My aim here is to remedy this situation. I will
discuss the idea of taking the intensional logic of [5] (‘classical higher
order logic minus Extensionality’) and partializing it along the lines of
[3]. In partial logics some extra connectives become available, but terms in
the classical part of the language exhibit monotonicity behaviour with
respect to the definedness ordering. I will discuss the possibility of
defining a sublanguage which contains the classical fragment but
additionally has a simultaneous fixpoint operator similar to Moschovakis’
and using it to model procedurality and circularity in ordinary language.

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