Logic and Natural Language Semantics
at RSISE11, Canberra (Australia)
DISI, University of Trento, Italy
Structure and Slides |
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.
- Lecture 1: December 12th, Tuesday
Topic: Formal Semantics
Description: Students will be introduced to Formal Semantics
focusing on the relation perspective first, and then on the
corresponding functional perspective by looking at Lambda Calculus.
References: Formal Semantics ref below
- Lecture 2: December 13th, Monday
Topic: Non-Classical Logic for Natural Language Syntax
Description: First of all, we introduce the concept of Formal
Grammar for Natural Languages by presenting some linguistic background
and the challenges such a grammar should face. Furthermore, we
motivate the use of a Logical Grammar to address such challanges and
the motivations for using non-classical logic. Finally, we move to
introduce non-classical logics by underlining the differences with
respect to classical logics and focus on the sub-family of
Substructural Logics known as Lambek Calculi or Logics of
References: Lambek Calculi ref below. In particular, R. Bernardi and
R. Goré'04 (Chapter
1) Goré '98, Restall '00, Restall '01, Lambek
'58, Moortgat '11
- Lecture 3: December 14th, Wednesday
Topic: Lambek Calculus and Natural Language
Description In this lecture, we move to consider the
application of the Lambek Calculi and the Lambda calculus to natural
langauge analysis. In particular, it will be shown how the Lambek
Calculi account for the composition of linguistic resources while
simultaneously allowing parsing, proving and the construction of
References: See Lambek Calculi ref
below. In particular Bernardi, Goré '04 (Chapter 4), Moortgat '10
Slides: [PDF],[Exercises]done on Thursday.
- Lecture 4: December 15th, Thursday
Topic: Natural Language Entailment Systems (NOT DONE)
Description: Application of Entailment in Natural Language
Systems: In this lecture, we will overview the Text Entailment
Recognition Task popular within the NLP community and zoom into those
systems exploiting Formal Semantics Representaiton and logic
entailment. By looking at these applications, we will highlight
strength and weakness of the formal semantics approach.
References:Textual Entailment and Controlled
Natural Language ref below.
Slides: [PDF] (NOT DONE)
- Lecture 5:December 16th, Friday
Topic: Distributional Semantics.
Description: In this lecture, we will present the
distributional view on lexical meaning proposed within the Corpus
Linguistics community and discuss how the logic and the distributional
views on natural language have been recently combined. Finally, we
will look back at the natural language systems of lecture 4 and show
how the revised view on natural language meaning could be exploited by
References: See Distributional Semantics ref below.
Main conferences and mailing lists:
- R. Bernardi and R. Goré Display
Logic meets Categorial Type Logic, ESSLLI'04, Nancy [PDF]
- R. Bernardi and M. Moortgat ESSLLI'07
Course on Symmetric Categorial Grammar
- R. Bernardi and M. MoortgatContinuation
Semantics for the Lambek-Grishin Calculus. Information and
Computation 208 (2010) pp. 397–416. On this topic see Moortgat's
slides for an update [ PDF]
- About Continuation Semantics see also the work by Chris Barker and
- N. Kurtonina, Frames and Labels. A Modal Analysis of Categorial Inference [Zip]
- J. Lambek
The mathematics of sentence structure. American Mathematical Monthly, 65:154--169, 1958. [HTML]
- M. Moortgat (2011), "Categorial type logics". Chapter 2 in
J. van Benthem en A. ter Meulen (eds.) Handbook of Logic and
Language. Elsevier/MIT Press. 2nd Edition. DOI:
- M. Moortgat (2010),
Typelogical Grammar. In Stanford Encyclopedia of Philosophy.
- R. Moot (2000), Proof nets for linguisitic analysis
J. van Benthem and A. ter Meulen (eds.) Handbook of Logic, Language and Information
- Logic for Natural
Language Processing Portal part of CoLogNET portal.
Formal Semantics ^
- A. Burchardt, A. Koller and S. Walter On-line
Course on Computational Semantics, ESSLLI '04,
- J. Bos and P. Blackburn, Representation and Inference for Natural Language
- H. de Swart Introduction to Natural Language Semantics, CSLI Publication, 1998.
- L.T.F. Gamut, Logic, language, and meaning
- B. Partee, A. ter Meulen and R. E. Wall, Mathematical methods in linguistics, 1990.
Textual Entailment and Controlled Natural
- I. Dagan, B. Dolan, B. Magnini and D. Roth Recognizing textual
entailment: Rational, evaluation and approaches.
Controlled Natural Language
Distributional Semantics ^
- Peter D. Turney and Patrick Pantel From Frequency to Meaning: Vector Space Models of Semantics.
- Jeff Mitchell and Mirella
Lapata. Composition in Distributional Models of
- For literature on Distributional Semantics
in Trento, visit
Substructural Logics ^
- G. Restall, An Introduction to Substructural Logics. Routledge,
- T.Brauener Introduction to Linear
Logic BRICS LS-96-6. [PDF ]
Logic", Theoretical Computer Science, London Mathematical
50:1, pp. 1-102, 1987. Restored by Pierre Boudes.
- R. Goré, Substructural Logics on
Display. Logic Journal of the
Interest Group in Pure and Applied Logics. 6(3):451-504, 1998. [Zip]
- R. K. Meyer and R. Routley "Algebraic Analysis of Entailment" In Loqique et Analyse, n.s, 15, 407-428.
- R. K. Meyer and R. Routley "Classical Relevant Logics (I)" In Studia Logica, 32, 51-66.
- G. Restall Relevant and Substructural Logics, ESSLLI '01, Helsinki [PDF]
- P. Schroeder-Heister and K. Dosen Substructural Logics (eds). Studies in Logic and Computation, Oxford Science Publications, 1993.
- Sørensen, Morten Heine B. and Pawel Urzyczyn, Lectures on the Curry-Howard Isomorphism. ESSLLI '99, Utrecht.
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
Last modified: Sat July 2 14:16:23 CET 2011