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# Gothenburg-Stockholm Workshop on Proof Theory, Model Theory, and Probability in Natural Language

The Gothenburg-Stockholm Workshop on Proof Theory, Model Theory, and Probability in Natural Language is organized by CLASP, FLoV, University of Gothenburg. It will take place at Room L100, Lennart Torstenssonsgatan 6 on February 7, 2018. The workshop program is as follows:

(important note: due to unforeseen circumstances, Per Martin-Löf will not be able to give his talk. The program will start a bit later as shown below)

10:00-11:00: Peter Pagin, University of Stockholm

Compositionality, Computability, and Complexity

The standard argument for the claim that natural languages have a

compositional semantics proceed from the need of hearers to compute the meaning of novel complex expressions. But

computability does not entail compositionality. Is there a reason for believing that natural languages have a semantics that is both computable and compositional? Yes, for it turns out that keeping the complexity of semantic interpretation low requires a compositional semantics. We shall look at the notionof a recursive semantic function, and provide a framework for estimating the time complexity of semantics by means of term rewriting systems.

11:00-11:30: Fika

11:30-12:30: Dag Westerståhl, University of Stockholm

Making Exceptions (joint work with Stanley Peters)

We present a novel account of the semantics of “except", in phrases of the form "Det N except NP". The account is based on careful analysis of the notions of generalization and exceptions to generalizations. It improves on earlier analyses, in particular von Fintel (1993), Moltmann (1995), and Peters and Westerståhl (2006), as regards both simplicity and empirical correctness. And it covers universal as well as non-universal generalizations with exceptions; the ubiquity of the latter was first observed by García-Álvarez (2003).

12:30-13:30: lunch (light sandwich lunch on site)

13:30-14:10: Thierry Coquand, Chalmers University of Technology

Sheaf Models of Type Theory

Sheaf/Beth models have been essential for the meta-theory of higher order logic (Church’s simple theory of types). In this talk, we explore a formulation of this notion of models for dependent type theory. We explain the main difficulty, which is how to model the notion of universes, and why the situation is there more complex than for presheaf/Kripke models. We then mention three potential applications: consistency with Brouwer’s fan theorem, extension of type theory with a type of indiscernable atoms, and finally an extension of type theory with probabilistic proofs/programs.

14:10-14:50: Aarne Ranta University of Gothenburg

Concept Alignment for Compositional Translation

Translation between natural languages is not compositional in a naive word-to-word sense. But many problems can be solved by using higher-level concepts, implementable as abstract syntax constructors in type theory together together with compositional linearization functions in Grammatical Framework (GF). The question then arises: what are these constructors for a given set of languages? A whole spectrum of possibilities suggests itself: word senses (as in WordNet), multiword phrases (as in statistical machine translation), predication frames (as in FrameNet), syntactic deep structures (as in GF Resource Grammar Library), and lexico-syntactic constructions (as in Construction Grammar). The talk will study the problem in the light of experiences for building a cross-lingual lexicon of concepts in the General Data Protection Regulation (GDPR) in five languages. We have identified over 3000 concepts of varying complexity. A lot of manual work has been needed in the process, but some ideas have emerged toward a computational approach that can suggest concept alignments by automated analysis.

14:50-15:10: fika

15:10-15:50: Staffan Larsson, Robin Cooper, Simon Dobnik, and Shalom Lappin, University of Gothenburg,

Bayesian Classification and Learning in ProbTTR

We presented a probabilistic type theory in Cooper et. al. (2014 and 2015), which extends Cooper's Type Theory with Records (Cooper 2012). This theory, Probabilistic Type Theory with Records (ProbTTR), assigns probability values, rather than Boolean truth-values, to type judgements. In this paper we suggest a way of incorporating a Bayesian inference, classification and learning theory into ProbTTR.

15:50-16:30: Jean Phililppe Bernardy, University of Gothenburg

A fuzzy type-theory and elementary remarks about probabilistic logics

In this talk I will present a simple extension to type theory which makes it suitable for fuzzy reasoning. The idea is to associate weights with propositions and propagate them suitably in the typing rules. This weight-propagation has been proposed earlier to accommodate linear-style variants of type theory (McBride 2016). The variant presented here is essentially a relaxation. If time allows I will also make some remarks about probabilistic logics, outlining certain constraints that they should obey. The hop is to highlight certain difficulties that one might face when devising a probabilistic logic.

16:30-17:00: fika

17:00-18:30: Discussion of Workshop topics

19:00: Dinner for Workshop participants