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Predicate Approaches to Modality (September 12, 2014)

Idea and Motivation

Predicate Approaches to modality are a viable alternative to the now standard operator approaches to modality. They allow for a uniform treatment of truth and the modal notions, are expressively rich and they fit in nicely with the relational analysis of propositional attitudes. The workshop is intended to further and foster research on predicate approaches to modality in philosophical and mathematical logic.

Topics and questions may include the following:

  • How should an adequate modal theory look like?
  • Axiomatic modal theories
  • Semantic modal theories.
  • How should or can we consistently combine modal theories to obtain multimodal theories?
  • Does the interaction of modal predicates create new phenomena such as paradoxes of interaction or greater expressive strength?
  • De re modality and predicate approaches to modality.
  • Can the expressive strength of the predicate approach be recovered within the operator approach?


We invite submissions of abstracts (500-1000 words).

To submit please send a pdf-file to one of the organizers, Johannes Stern ( or Martin Fischer (

We anticipate that there will be space for about two contributed talks.

Dates and Deadlines

  • Deadline for submission: June 22, 2014
  • Notification of acceptance: June 30, 2014
  • Conference: September 12, 2014

Keynote Speakers


10:00 - 11:15 Philip Welch: On some theories of truth and of set theory
11:15 - 12:30 Karl-Georg Niebergall: Remarks on intensionality and on the combination of first-order theories
12:30 - 14:15 Lunch
14:15 - 15:30 Volker Halbach: de re modality and modal predicates
15:30 - 16:15 Kyle Banick: Epistemic Analogues of the Halbach-Welch Fixed-Point Construction
16:15 - 16:45 Coffee
16:45 - 17:30 Catrin Campbell-Moore: Revision Semantics for Probabilities
17:30 - 18:45 Leon Horsten: Revision theories for untyped probability predicates
19:30 Dinner


Kyle Banick: Epistemic Analogues of the Halbach-Welch Fixed-Point Construction

I have tried to discern whether Halbach and Welch's strategy can be generalized from the intensional predicate of necessity to that of knowledge. In the talk I will present my results on this project. I first use extant literature in epistemic logic and epistemology to develop a formal framework for modeling epistemic theories with possible worlds structures. I then explain how I integrate these epistemic models with the Halbach-Welch construction. Finally, I present the basic problem that has blocked proof of the generalization in several interesting cases.

Catrin Campbell-Moore: Revision Semantics for Probabilities

I will consider a language with a type-free probability predicate and develop a revision semantics for this based on the ideas of relative frequency and near stability. This construction relates to the one given recently by Leitgeb.

Due to certain disadvantages of basing a construction on relative frequencies I shall also propose an alternative construction which differs in spirit from Leitgeb's construction and instead provides a semantics based on possible world structures in a style similar to Halbach, Leitgeb and Welch.

Volker Halbach: de re modality and modal predicates

If modalities are expressed as predicates, there are various options to treat de re modalities. I look at some of them and their pros and cons. Finally, I explore whether any conclusions can be drawn for modal

Leon Horsten: Revision theories for untyped probability predicates

Leitgeb has proposed a model for untyped probability. He has generated models using a revision sequence of models of length omega. At stage omega, a Banach-limit is taken.

In my presentation, I will explore an alternative revision theory for untyped probability. Using a revision procedure based on taking ultrapower models, this alternative approach generates revision procedures of transfinite length.

Karl-Georg Niebergall: Remarks on intensionality and on the combination of first-order theories


Philip Welch: On some theories of truth and of set theory

Semantic theories of truth involve some mathematical construction over a first order model. Typically such a model is taken as the standard model of the natural numbers to exemplify a paradigm case. The construction may be more, or less, involved, but for the more complicated ones set theoretical features begin to loom large. We review Kripke's theory of minimal fixed points using supervaluations, and Herzberger's Revision Theory. We consider possibilities of axiomatizing various levels of the truth sets the Herzberger sequence throws up. This brings out relationships between Cantini's VF (which was suggested by features of the supervaluation fixed point theory) and strong admissibility theory.


  • Seminarraum 021, Ludwigstr. 31

Contact and Attendance

Everybody is welcome to attend the conference free of charge. However, we ask to confirm your presence by sending an e-mail to one of the organizers: Martin Fischer ( or Johannes Stern (