Natural Language Syntax and Statistical Semantics with Modal Lambek Calculus
ESSLLI 2023, Week 1
14:00 - 15:30 daily
Instructors: Mehrnoosh Sadrzadeh and Gijs Wijnholds
Course Description
The Lambek Calculus models natural language grammar as a logic, rejecting the rules of commutativity, associativity, contraction and weakening. Controlled versions of these rules can be added via modalities and the resulting logic is known as Modal Lambek Calculus. Modal Lambek Calculus has a compositional interface to natural language semantics: to possible worlds via ternary frames, and to vector representations via algebraic constructions over syntax.
This course has two parts. The first part covers the core methodology behind the modelling with Lambek Calculus and its modal extensions; we derive examples of syntactic constructions and analyse their semantics. After that, we focus on the vector semantics and show how they are learnt via statistical machine learning, applying the results to semantic similarity and disambiguation tasks. Along the way, we offer the possibility to work with user-friendly tools that produce syntactic derivations and compute statistical representations, and datasets for empirical validations/applications.
Suggested Background Material
Suggested Readings:
Richard Moot & Christian Retoré, 2012. The Logic of Categorial Grammars: A deductive account of natural language syntax and semantics. Available online
Course Schedule
Day 1
Syntax and Semantics of Lambek Calculus
In a modular incremental and easy step-by-step manner, we introduce the syntax of Lambek Calculus and go through its linguistic examples.
Day 2
Adding Modalities
Modalities are added to the Lambek Calculus base.
Their applications to linguistic phenomena is argued and exemplified.
A natrual deduction proof system is introduced for Modal Lambek Calculus.
Day 3
Semantics
The Kripke semantics of Modal LC is introduced.
The principle of compositional interpretation is introduced.
Distributional semantics and its compositional interpretation are introduced.
The distributional compositional interpretation of modal Lambek Calculus in vector spaces is introduced and exemplified.
Day 4
Machine Learning the Semantics and Applications
Techniques for (compositional) representation learning using neural network algorithms are discussed.
Applications of the above to tasks such as textual similarity are explained and exemplified.
Day 5
Beyond Sentence Challenges and Open Problems
Further applications of modalities, e.g. in discourse analysis are discussed by Lachlan McPheat.
Connections to quantum circuits and string diagrams are explained by Ian Lo Kin.
An open problem about the vector space semantics of LC and Modal LC is shared.
Other applications of Lambek Calculus, e.g. for developing data to probe LLM's is discussed.