Logic and Natural Language Semantics

at RSISE11, Canberra (Australia)

Raffaella Bernardi

DISI, University of Trento, Italy

Description | Prerequisites | Structure and Slides | References| Related Courses |


Gottlob Frege is considered to be the father of Philosophy of Language. Several of Frege's ideas are at the foundations of Formal Semantics of Natural Language promoted by those people who look at natural language with the logician's view. Formal semanticists have focused on Frege view of natural language signs as "references" and studied how to compose them and how to represent them with First Order Logic. Frege principle of compositionality has been seen has establishing a strong connection between syntax and semantics that has found elegant implementation in the research line based on the "parsing as deduction" slogan.

We will show that to parse natural language structure a Non-classical logic is needed. We will start from the minimum logic of residuation, non associative Lambek calculus, and extend its expressivity has required by the syntax-semantics interface of natural language structure and look at a symmetric version of it. Furthermore, by focusing on this application, we will introduce the lambda-calculus and its Curry-Howard Correspondence with the Lambek Calculi. The main goal of this first part will be to show how algebraic semantics can be used as a unifying framework for studying substructural logics, and how these logics can be applied to other fields, such as Linguistics.

We will then end the course by giving a look at applications of the logic view to natural language semantics within language technology systems. By looking at these applications, we will highlight some strengths and weakness of the logic view and introduce a complementary analysis of natural language semantics, called Distributional Semantics, showing how Logic and Distributional Models can be combined to better capture the analysis of natural language semantics. We will claim that DS and FS models are two faces of a same story as foreseen by Frege, namely the representation of "sense" and "reference" of linguistic sign, respectively.


The course is addressed to any student interested in logic, language and in their connections. Only basic background on propositional logic is required and no knowledge of Linguistics is needed. Students with knowledge of model and proof theory will obtain further profit.

Structure and Slides^

The course consists of two main parts: In Lectures 1-3, we will introduce the logic view to natural language syntax-semantic interface, with a focus on Substructural Logics. In Lectures 4 and 5: the discussion of the applications of the logic view on natural language semantics will help us highlighting some of its strength and weakness and prepare the floor for the introduction to distributional models, an alternative and complementary view to the problem. We will also show how Frege, Montague and Lambek's ideas on compositionality, function application and syntax-semantic interface traditionally employed by the logic view have been recently employed to enhance Distributional Models.

Main conferences and mailing lists:


Related Courses at RSISE '11^

The course is related in particular to two of the first week courses, namely Introduction to Modal and Temporal Logic (Kripke Models, Hilbert Calculi, Frame Correspondences). Non-Classical Logic

Raffaella Bernardi
Last modified: Sat July 2 14:16:23 CET 2011