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Gamma-Star Canonical Forms in the Type-Theory of Acyclic Algorithms

  • Roussanka LoukanovaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11352)

Abstract

This work elaborates on the theoretical results of the gamma-star reduction calculus and its potentials for applications in AI and other intelligent technologies. We strengthen the computational properties of the extended gamma-star calculus, by employing a stricter gamma-star rule and adding a formal, recursive definition of the gamma-star canonical forms. A term in a gamma-star normal form provides the algorithm for computing its denotation, without unnecessary calculations that can be required by the initial terms. The extended gamma-star reduction calculus redices every term to its gamma-star normal form.

Keywords

Recursion Types Semantics Algorithmic semantics Denotation Canonical computations 

References

  1. 1.
    Hamm, F., van Lambalgen, M.: Moschovakis’ notion of meaning as applied to linguistics. In: Logic Colloqium, vol. 1 (2004)Google Scholar
  2. 2.
    Hurkens, A.J.C., McArthur, M., Moschovakis, Y.N., Moss, L.S., Whitney, G.T.: The logic of recursive equations. J. Symbol. Log. 63(2), 451–478 (1998). http://projecteuclid.org/euclid.jsl/1183745513MathSciNetCrossRefGoogle Scholar
  3. 3.
    Loukanova, R.: Constraint based syntax of modifiers. In: 2011 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology, vol. 3, pp. 167–170 (2011). http://doi.ieeecomputersociety.org/10.1109/WI-IAT.2011.229
  4. 4.
    Loukanova, R.: From Montague’s rules of quantification to minimal recursion semantics and the language of acyclic recursion. In: Bel-Enguix, G., Dahl, V., Jiménez-López, M.D. (eds.) Biology, Computation and Linguistics – New Interdisciplinary Paradigms. Frontiers in Artificial Intelligence and Applications, vol. 228, pp. 200–214. IOS Press, Amsterdam (2011). http://ebooks.iospress.nl/volumearticle/6486
  5. 5.
    Loukanova, R.: Minimal recursion semantics and the language of acyclic recursion. In: Bel-Enguix, G., Dahl, V., Puente, A.O.D.L. (eds.) AI Methods for Interdisciplinary Research in Language and Biology, pp. 88–97. SciTePress – Science and Technology Publications, Rome, January 2011.  https://doi.org/10.5220/0003309800880097
  6. 6.
    Loukanova, R.: Modeling context information for computational semantics with the language of acyclic recursion. In: Pérez, J.B., et al. (eds.) Highlights in Practical Applications of Agents and Multiagent Systems. AISC, vol. 89, pp. 265–274. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-19917-2_32CrossRefGoogle Scholar
  7. 7.
    Loukanova, R.: Reference, co-reference and antecedent-anaphora in the type theory of acyclic recursion. In: Bel-Enguix, G., Jiménez-López, M.D. (eds.) Bio-Inspired Models for Natural and Formal Languages, pp. 81–102. Cambridge Scholars Publishing, Cambridge (2011). http://www.cambridgescholars.com/bio-inspired-models-for-natural-and-formal-languages-16
  8. 8.
    Loukanova, R.: Semantics with the language of acyclic recursion in constraint-based grammar. In: Bel-Enguix, G., Jiménez-López, M.D. (eds.) Bio-inspired Models for Natural and Formal Languages, pp. 103–134. Cambridge Scholars Publishing, Cambridge (2011). http://www.cambridgescholars.com/bio-inspired-models-for-natural-and-formal-languages-16
  9. 9.
    Loukanova, R.: Syntax-semantics interface for lexical inflection with the language of acyclic recursion. In: Bel-Enguix, G., Dahl, V., Jiménez-López, M.D. (eds.) Biology, Computation and Linguistics – New Interdisciplinary Paradigms, Frontiers in Artificial Intelligence and Applications, vol. 228, pp. 215–236. IOS Press, Amsterdam (2011). http://ebooks.iospress.nl/volumearticle/6487
  10. 10.
    Loukanova, R.: Algorithmic semantics of ambiguous modifiers by the type theory of acyclic recursion. In: IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology, vol. 3, pp. 117–121 (2012).  https://doi.org/10.1109/WI-IAT.2012.246
  11. 11.
    Loukanova, R.: Semantic information with type theory of acyclic recursion. In: Huang, R., Ghorbani, A.A., Pasi, G., Yamaguchi, T., Yen, N.Y., Jin, B. (eds.) AMT 2012. LNCS, vol. 7669, pp. 387–398. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-35236-2_39CrossRefGoogle Scholar
  12. 12.
    Loukanova, R.: Algorithmic granularity with constraints. In: Imamura, K., Usui, S., Shirao, T., Kasamatsu, T., Schwabe, L., Zhong, N. (eds.) BHI 2013. LNCS (LNAI), vol. 8211, pp. 399–408. Springer, Cham (2013).  https://doi.org/10.1007/978-3-319-02753-1_40CrossRefGoogle Scholar
  13. 13.
    Loukanova, R.: Algorithmic semantics for processing pronominal verbal phrases. In: Larsen, H.L., Martin-Bautista, M.J., Vila, M.A., Andreasen, T., Christiansen, H. (eds.) FQAS 2013. LNCS (LNAI), vol. 8132, pp. 164–175. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-40769-7_15CrossRefGoogle Scholar
  14. 14.
    Loukanova, R.: A predicative operator and underspecification by the type theory of acyclic recursion. In: Duchier, D., Parmentier, Y. (eds.) CSLP 2012. LNCS, vol. 8114, pp. 108–132. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-41578-4_7CrossRefGoogle Scholar
  15. 15.
    Loukanova, R.: Situation theory, situated information, and situated agents. In: Nguyen, N.T., Kowalczyk, R., Fred, A., Joaquim, F. (eds.) Transactions on Computational Collective Intelligence XVII. LNCS, vol. 8790, pp. 145–170. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-662-44994-3_8CrossRefGoogle Scholar
  16. 16.
    Loukanova, R.: Representing parametric concepts with situation theory. In: Ganzha, M., Maciaszek, L., Paprzycki, M. (ed.) Proceedings of the 2015 Federated Conference on Computer Science and Information Systems, vol. 5, pp. 89–100. IEEE (2015). (Ann. Comput. Sci. Inf. Syst.).  https://doi.org/10.15439/2015F409
  17. 17.
    Loukanova, R.: Underspecified relations with a formal language of situation theory. In: Loiseau, S., Filipe, J., Duval, B., van den Herik, J. (eds.) Proceedings of the 7th International Conference on Agents and Artificial Intelligence, vol. 1, pp. 298–309. SCITEPRESS – Science and Technology Publications, Lda. (2015).  https://doi.org/10.5220/0005353402980309
  18. 18.
    Loukanova, R.: Acyclic recursion with polymorphic types and underspecification. In: van den Herik, J., Filipe, J. (eds.) Proceedings of the 8th International Conference on Agents and Artificial Intelligence, vol. 2, pp. 392–399. SCITEPRESS – Science and Technology Publications, Lda. (2016).  https://doi.org/10.5220/0005749003920399
  19. 19.
    Loukanova, R.: Relationships between specified and underspecified quantification by the theory of acyclic recursion. ADCAIJ: Adv. Distrib. Comput. Artif. Intell. J. 5(4), 19–42 (2016). http://campus.usal.es/~revistas_trabajo/index.php/2255-2863/article/view/ADCAIJ2016541942CrossRefGoogle Scholar
  20. 20.
    Loukanova, R.: Specification of underspecified quantifiers via question-answering by the theory of acyclic recursion. In: Andreasen, T., et al. (eds.) Flexible Query Answering Systems 2015. AISC, vol. 400, pp. 57–69. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-26154-6_5CrossRefGoogle Scholar
  21. 21.
    Loukanova, R.: Binding operators in type-theory of algorithms for algorithmic binding of functional neuro-receptors. In: 2017 Federated Conference on Computer Science and Information Systems (FedCSIS), vol. 11, pp. 57–66. IEEE (2017).  https://doi.org/10.15439/2017F465
  22. 22.
    Loukanova, R.: Typed theory of situated information and its application to syntax-semantics of human language. In: Christiansen, H., Jiménez-López, M.D., Loukanova, R., Moss, L.S. (eds.) Partiality and Underspecification in Information, Languages, and Knowledge, pp. 151–188. Cambridge Scholars Publishing,Cambridge (2017). http://www.cambridgescholars.com/partiality-and-underspecification-in-information-languages-and-knowledge
  23. 23.
    Loukanova, R.: Gamma-star reduction in the type-theory of acyclic algorithms. In: Rocha, A.P., van den Herik, J. (eds.) Proceedings of the 10th International Conference on Agents and Artificial Intelligence (ICAART 2018), vol. 2, pp. 231–242. INSTICC, SciTePress – Science and Technology Publications, Lda. (2018). https://dx.doi.org/10.5220/0006662802310242
  24. 24.
    Loukanova, R., Jiménez-López, M.D.: On the syntax-semantics interface of argument marking prepositional phrases. In: Pérez, J.B., et al. (eds.) Highlights on Practical Applications of Agents and Multi-Agent Systems. Advances in Intelligent and Soft Computing, vol. 156, pp. 53–60. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-28762-6_7CrossRefGoogle Scholar
  25. 25.
    Moschovakis, Y.N.: The formal language of recursion. J. Symbol. Log. 54(04), 1216–1252 (1989)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Moschovakis, Y.N.: Sense and denotation as algorithm and value. In: Oikkonen, J., Vaananen, J. (eds.) Logic Colloquium’90. LNL, vol. 2, pp. 210–249. Springer, Heidelberg (1994)Google Scholar
  27. 27.
    Moschovakis, Y.N.: The logic of functional recursion. In: Dalla Chiara, M.L., Doets, K., Mundici, D., van Benthem, J. (eds.) Logic and Scientific Methods, vol. 259, pp. 179–207. Springer, Dordrecht (1997).  https://doi.org/10.1007/978-94-017-0487-8_10CrossRefzbMATHGoogle Scholar
  28. 28.
    Moschovakis, Y.N.: A logical calculus of meaning and synonymy. Linguist. Philos. 29(1), 27–89 (2006).  https://doi.org/10.1007/s10988-005-6920-7CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Stockholm UniversityStockholmSweden

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