From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
From philosophy to computer science   How to formalise the cognitive linguistics results?   Adpositional grammars   Conclu...
Upcoming SlideShare
Loading in …5
×

A Constructive Mathematics approach for NL formal grammars

615 views

Published on

0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
615
On SlideShare
0
From Embeds
0
Number of Embeds
23
Actions
Shares
0
Downloads
14
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

A Constructive Mathematics approach for NL formal grammars

  1. 1. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions A Constructive Mathematics approach for Natural Language formal grammars An Introduction to Adpositional Grammars (AdGrams) Federico Gobbo and Marco Benini {federico.gobbo,marco.benini}@uninsubria.it University of Insubria, Varese, Italy CC Some rights reserved. ECAP09, UAB, Barcelona, July 2009 1/19
  2. 2. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Philosophers and natural language formalization How to clean natural languages (NLs) from ambiguity? 2/19
  3. 3. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Philosophers and natural language formalization How to clean natural languages (NLs) from ambiguity? Leibniz: characteristica universalis to catch the laws of human thought and lingua generalis as a quasi-natural Latin to be used as a written medium for scholars. Frege: Begriffsschrift and the definition of unsaturated expressions. Husserl: the meaning categories as the formal constituents of a logical grammar. 2/19
  4. 4. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Computer science and logic-based approaches to NL Goal: formalize NL grammars through mathematical formulae proved through computation. Some formalisms in use today (the list is not complete!): Based on Chomsky’s constituency and transformation notions: Minimalism, Tree-Adjoining Grammar (TAG), Head-Driven Phrase Structure Grammar (HPSG). 3/19
  5. 5. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Computer science and logic-based approaches to NL Goal: formalize NL grammars through mathematical formulae proved through computation. Some formalisms in use today (the list is not complete!): Based on Chomsky’s constituency and transformation notions: Minimalism, Tree-Adjoining Grammar (TAG), Head-Driven Phrase Structure Grammar (HPSG). Based on categorial calculus: Type-Logical Grammar (TLG), Thinking Through Grammar (TTG), Combinatory Categorial Grammar (CCG), Pre-group. 3/19
  6. 6. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Computer science and logic-based approaches to NL Goal: formalize NL grammars through mathematical formulae proved through computation. Some formalisms in use today (the list is not complete!): Based on Chomsky’s constituency and transformation notions: Minimalism, Tree-Adjoining Grammar (TAG), Head-Driven Phrase Structure Grammar (HPSG). Based on categorial calculus: Type-Logical Grammar (TLG), Thinking Through Grammar (TTG), Combinatory Categorial Grammar (CCG), Pre-group. Based on Tesni`re Dependency and Valency: Extensible e Dependency Grammar (XDG), Algebraic Syntax, Functional Generative Description (FGD), Mel‘cuk’s Dependency Syntax. 3/19
  7. 7. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Computer science and logic-based approaches to NL Goal: formalize NL grammars through mathematical formulae proved through computation. Some formalisms in use today (the list is not complete!): Based on Chomsky’s constituency and transformation notions: Minimalism, Tree-Adjoining Grammar (TAG), Head-Driven Phrase Structure Grammar (HPSG). Based on categorial calculus: Type-Logical Grammar (TLG), Thinking Through Grammar (TTG), Combinatory Categorial Grammar (CCG), Pre-group. Based on Tesni`re Dependency and Valency: Extensible e Dependency Grammar (XDG), Algebraic Syntax, Functional Generative Description (FGD), Mel‘cuk’s Dependency Syntax. How to choose the best one, i.e., the most expressive, in linguistic terms? 3/19
  8. 8. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Psychological interpretation of NL formalisms In recent years scholars got interested in strong psychological interpretations of their formalisms: “if I succeed to give a clear account of more psychological phenomena thanks to my formalism, this means that my formalism is better.” 4/19
  9. 9. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Psychological interpretation of NL formalisms In recent years scholars got interested in strong psychological interpretations of their formalisms: “if I succeed to give a clear account of more psychological phenomena thanks to my formalism, this means that my formalism is better.” Surprisingly, formal grammarians didn’t read the 20-year long results of cognitive linguistics, where linguistic phenomena are explained in psychological and cognitive terms. 4/19
  10. 10. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Cognitive linguistics and formalisation Cognitive linguistics (e.g., Taylor, Cruse) are not interested in formalisation, as their primary interest is in metaphor interpretation: concepts are not formalised per se. 5/19
  11. 11. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Cognitive linguistics and formalisation Cognitive linguistics (e.g., Taylor, Cruse) are not interested in formalisation, as their primary interest is in metaphor interpretation: concepts are not formalised per se. Nonetheless, Langacker borrowed the dichotomy trajector/landmark from the German school of Gestalt (e.g., Kurt Koffka and Max Wertheimer) into syntax. 5/19
  12. 12. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Cognitive linguistics and formalisation Cognitive linguistics (e.g., Taylor, Cruse) are not interested in formalisation, as their primary interest is in metaphor interpretation: concepts are not formalised per se. Nonetheless, Langacker borrowed the dichotomy trajector/landmark from the German school of Gestalt (e.g., Kurt Koffka and Max Wertheimer) into syntax. In other words, a cognitive account is inside the analytical framework, instead of being a serendipity. 5/19
  13. 13. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Trajector vs. landmark and the Tesnerian dependency a trajector is the most salient participant put in the focused position; the landmark is the reference point of observation performed by the trajector. 6/19
  14. 14. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Trajector vs. landmark and the Tesnerian dependency a trajector is the most salient participant put in the focused position; the landmark is the reference point of observation performed by the trajector. Our hypothesis is that the trajector/landmark relation is conveyed in NLs either by prepositions (most Hindo-European languages, like English or Catalan) or by postpositions (e.g., Turkish, Japanese) – i.e., adpositions, and from this term adpositional grammar. 6/19
  15. 15. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Trajectors, landmarks and the Tesnerian dependency Adpositional grammars (AdGrams) retain the concept of valency from Tesni`re, but it reconfigures the concept of dependency e thanks to the dichotomy trajector/landmark. 7/19
  16. 16. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Trajectors, landmarks and the Tesnerian dependency Adpositional grammars (AdGrams) retain the concept of valency from Tesni`re, but it reconfigures the concept of dependency e thanks to the dichotomy trajector/landmark. The structure of NLs (morphology + syntax) can be expressed with the following triple: 7/19
  17. 17. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Trajectors, landmarks and the Tesnerian dependency Adpositional grammars (AdGrams) retain the concept of valency from Tesni`re, but it reconfigures the concept of dependency e thanks to the dichotomy trajector/landmark. The structure of NLs (morphology + syntax) can be expressed with the following triple: there is a Governor (G), 7/19
  18. 18. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Trajectors, landmarks and the Tesnerian dependency Adpositional grammars (AdGrams) retain the concept of valency from Tesni`re, but it reconfigures the concept of dependency e thanks to the dichotomy trajector/landmark. The structure of NLs (morphology + syntax) can be expressed with the following triple: there is a Governor (G), there is a Dependent (D), 7/19
  19. 19. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Trajectors, landmarks and the Tesnerian dependency Adpositional grammars (AdGrams) retain the concept of valency from Tesni`re, but it reconfigures the concept of dependency e thanks to the dichotomy trajector/landmark. The structure of NLs (morphology + syntax) can be expressed with the following triple: there is a Governor (G), there is a Dependent (D), D and G have their Relation (R). 7/19
  20. 20. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Trajectors, landmarks and the Tesnerian dependency Adpositional grammars (AdGrams) retain the concept of valency from Tesni`re, but it reconfigures the concept of dependency e thanks to the dichotomy trajector/landmark. The structure of NLs (morphology + syntax) can be expressed with the following triple: there is a Governor (G), there is a Dependent (D), D and G have their Relation (R). Remark: R is often a phrasal or sentence adposition. 7/19
  21. 21. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Standing on the shoulder of which giants? AdGrams distinguish two directions of dependency: 8/19
  22. 22. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Standing on the shoulder of which giants? AdGrams distinguish two directions of dependency: Dependency, when D is the trajector, and G is the landmark; 8/19
  23. 23. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Standing on the shoulder of which giants? AdGrams distinguish two directions of dependency: Dependency, when D is the trajector, and G is the landmark; Government, when the trajector is G, and consequentially the landmark is D. 8/19
  24. 24. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Standing on the shoulder of which giants? AdGrams distinguish two directions of dependency: Dependency, when D is the trajector, and G is the landmark; Government, when the trajector is G, and consequentially the landmark is D. The advantage is that no assumption on semantics is made, i.e., we follow a strict world-model agnosticism: e.g., in some possibly SF world the hotel killed the rabbit is true. 8/19
  25. 25. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions This is the prototypical Dependency-based tree... q ¡e ¡→e ¡ R e ¡ e ¡ e D G Notation: D is always on the left branch, while G is always on the right. 9/19
  26. 26. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions ...while this one is the prototypical Government-based tree. q ¡e ¡←e ¡ R e ¡ e ¡ e D G Let’s see a couple of examples. 10/19
  27. 27. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions A Dependency-based phrase... q ¡e ¡→e ¡ e ¡ e ¡ e ∆ ∆ The torpedo sank... Figure: Adtree of The torpedo sank the ship. The trajector is the torpedo, while the landmark is sank the ship. Notation: delta (∆) means that some information is hidden. 11/19
  28. 28. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions ...and a Government-based phrase q ¡e ¡←e ¡ e ¡ e ¡ e ∆ ∆ The ship sank Figure: Adtree of The ship sank. The landmark is the ship, while the trajector is the act of sinking (in fact, the Agent and the Instrument are unexpressed here.) 12/19
  29. 29. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions A Dependency-based sentence... q ¡e ¡→e ¡ so e ¡ e ¡ e ∆ ∆ she can... A. is... Figure: Adtree for Alice is rich so she can pay The most salient information (trajector) is the fact that Alice can pay. Here, the adposition is so, which gives the Dependency structure. 13/19
  30. 30. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions ...and a Government-based sentence q ¡e ¡←e because ¡ e ¡ e ¡ e ∆ ∆ she is... A. can... Figure: Adtree for Alice can pay because she is rich Again, the most salient information is the fact that Alice can pay: in this case the trajector is the Governor. 14/19
  31. 31. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Why constructive mathematics for formalisation Unlike most other Dependency formal grammar frameworks, AdGrams use techniques of constructive mathematics, since constructive logics are the natural framework to model computation, as argumented by Troelstra and Barendregt. Surprisingly, mostly if not all formal NL grammars based on combinatorial calculus take Chomsky’s constituency for grant, using calculus “only” to build non-transformational grammars. 15/19
  32. 32. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions The novelties of adpositional grammars Our approach is different: constructivism permit to hide information in a very natural and precise way, and it defines the grammar as a specification in the language of logic, while the semantics of logic act as a computational engine, so that we can parse, generate and manipulate sentences essentially for free. Furthermore, we use a formal method for a non-constituency based grammar, ant this is the first attempt ever, at least as far as the authors know. 16/19
  33. 33. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Provisional results We have written an instance of AdGrams in the appropriate logical formalism, based on intuitionistic logic, together with specialized semantics. This first test is fit for the quasi-natural language Esperanto and it proved to cover approxiamtely 95% of the available corpora of language-in-use, except of the well-known open issues of quoting and name-entity recognition. 17/19
  34. 34. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Further directions We are currently work on a more general model – i.e., an instance of adpositional grammars which is cross-linguistically valid since the beginning – where the engine captures the structure of every NL. The intricacies are put in the lexicon – the part of semantics which is rightly computable in terms of meaning components and pragmatic participants. 18/19
  35. 35. From philosophy to computer science How to formalise the cognitive linguistics results? Adpositional grammars Conclusions Thanks. Any questions? Download these slides here: http://www.slideshare.net/goberiko/ C CC BY: $ Federico Gobbo 2009. Pubblicato in Italia. Attribuzione – Non commerciale – Condividi allo stesso modo 2.5 19/19

×