Skip to main content
SpringerLink
Log in

Equivalences Among Polarity Algorithms

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

The concept of polarity is pervasive in natural language. It relates syntax, semantics and pragmatics narrowly (Giannakidou, in: Maienborn, von Heusinger, Portner (eds.), Semantics: an international handbook of natural language meaning, De Gruyter Mouton, Berlin, 2011; Israel in The grammar of polarity: pragmatics, sensitivity, and the logic of scales, Cambridge studies in linguistics, Cambridge University Press, Cambridge, 2014), it refers to items of many syntactic categories such as nouns, verbs and adverbs. Neutral polarity items appear in affirmative and negative sentences, negative polarity items cannot appear in affirmative sentences, and positive polarity items cannot appear in negative sentences. A way of reasoning in Natural Language is through Natural Logic (van Benthem in Essays in logical semantics, vol. 29 of Studies in linguistics and philosophy, Reidel, Dordrecht, 1986; Language in action: categories, lambdas, and dynamic logic, vol. 130 of Studies in logic, Elsevier, Amsterdam, 1991). This logic is based on the concept of polarity in order to make the meaning of a sentence weaker o stronger without changing its truth value. There exist many proposals to compute polarity in the Natural Logic context, the most widely known are the ones by: van Benthem  (1986, 1991), Sánchez-Valencia (Studies on natural logic and categorial grammar, Ph.D. thesis, Universiteit van Amsterdam, 1991), Dowty (Proceedings of the 4th conference on semantics and theoretical linguistics, Cornel University, CLC Publications, Rochester, 1994), and van Eijck (in: ten Cate, Zeevat (eds.), 6th international Tbilisi symposium on logic, language, and computation, Batumi, Georgia, Springer, 2007). If Natural Logic is going to be used, as an inferential mechanism between text fragments, in Natural Language Processing applications such as text summarization, question answering, and information extraction, it is a priority to know what the existing relationship among the aforementioned algorithms is; for example, to implement the most general. We show in this paper the equivalence among the analyzed algorithms, filling a gap in Natural Logic research, particularly in computing polarity, and the soundness of their algorithms.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ajdukiewicz, K., Syntactic Connexion (1936), Springer, Dordrecht, 1978, pp. 118–139.

  2. Bach, E., Categorial Grammars as Theories of Language, Springer, Dordrecht, 1988, pp. 17–34.

  3. Dagan, I., O. Glickman, and B. Magnini, The Pascal recognising textual entailment challenge, in Proceedings of the First International Conference on Machine Learning Challenges: Evaluating Predictive Uncertainty Visual Object Classification, and Recognizing Textual Entailment, MLCW’05, Springer, Berlin, 2006, pp. 177–190.

  4. Dagan, I., R. Dan, M. Sammons, and F.M. Zanzotto, Recognizing Textual Entailment: Models and Applications, Synthesis Lectures on Human Language Technologies, Morgan & Claypool Publishers, San Rafael, 2013.

  5. Dowty, D., The role of negative polarity and concord marking in natural language reasoning, in Proceedings of the 4th Conference on Semantics and Theoretical Linguistics, Cornel University, CLC Publications, Rochester, 1994.

  6. Giannakidou, A., Positive polarity items and negative polarity items: variation, licensing, and compositionality, in C. Maienborn, K. von Heusinger, and P. Portner (eds.), Semantics: An International Handbook of Natural Language Meaning, De Gruyter Mouton, Berlin, 2011, pp. 1660–1712.

  7. Icard III, T.F., and L.S. Moss, Recent progress on monotonicity. Perspectives on semantic representations for textual inference, Linguistic Issues in Language Technology 9:167–194, 2014.

  8. Israel, M., The Grammar of Polarity: Pragmatics, Sensitivity, and the Logic of Scales, Cambridge Studies in Linguistics, Cambridge University Press, Cambridge, 2011.

    Book  Google Scholar 

  9. Karttunen, L., From natural logic to natural reasoning, in A. Gelbukh (ed.), Computational Linguistics and Intelligent Text Processing, vol. 9041 of Lecture Notes in Computer Science, Springer, Berlin, 2015, pp. 295–309.

  10. MacCartney, B., and C.D. Manning, Natural logic for textual inference, in Proceedings of the ACL-PASCAL Workshop on Textual Entailment and Paraphrasing, Association for Computational Linguistics, Prague, 2007, pp. 193–200.

  11. Moot, R., and C. Retoré, The Logic of Categorial Grammars, A Deductive Account of Natural Language Syntax and Semantics, Springer, Berlin, 2012.

    Book  Google Scholar 

  12. Moss, L.S., The soundness of internalized polarity marking, Studia Logica 100(4):683–704, 2012.

    Article  Google Scholar 

  13. Sánchez-Valencia, V., Studies on natural logic and categorial grammar, Ph.D. thesis, Universiteit van Amsterdam, 1991.

  14. van Benthem, J., Essays in Logical Semantics, vol. 29 of Studies in Linguistics and Philosophy, Reidel, Dordrecht, 1986.

  15. van Benthem, J., Language in Action: Categories, Lambdas, and Dynamic Logic, vol. 130 of Studies in Logic, Elsevier, Amsterdam, 1991.

  16. van Benthem, J., A brief history of natural logic, Tech. rep., 2007. Available at https://www.illc.uva.nl/Research/Publications/Reports/PP-2008-05.text.pdf.

  17. van Eijck, J., Natural logic for natural language, in B. ten Cate and H. Zeevat (eds.), 6th International Tbilisi Symposium on Logic, Language, and Computation, Batumi, Georgia, Springer, 2007, pp. 216–230.

Download references

Author information

Authors and Affiliations

  1. Coordinación de Ciencias Computacionales, Instituto Nacional de Astrofísica Óptica y Electrónica, Luis Enrique Erro # 1, Tonantzintla, Puebla, Mexico

    José-de-Jesús Lavalle-Martínez, Manuel Montes-y-Gómez & Luis Villaseñor-Pineda

  2. Facultad de Ciencias de la Computación, Benemérita Universidad Autónoma de Puebla, Avenida 14 Sur esquina Avenida, San Claudio, San Manuel, Puebla, Mexico

    José-de-Jesús Lavalle-Martínez

  3. División de Ciencias de la Comunicación y Diseño, Universidad Autónoma Metropolitana-Unidad Cuajimalpa, Torre III, 5to. piso. Avenida Vasco de Quiroga 4871, Colonia Santa Fé Cuajimalpa, Ciudad de México, Mexico

    Héctor Jiménez-Salazar

  4. CONACYT, Universidad Veracruzana, Av. Xalapa esq. Ávila Camacho s/n, Xalapa, Mexico

    Ismael-Everardo Bárcenas-Patiño

Authors
  1. José-de-Jesús Lavalle-Martínez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Manuel Montes-y-Gómez
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Luis Villaseñor-Pineda
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Héctor Jiménez-Salazar
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ismael-Everardo Bárcenas-Patiño
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to José-de-Jesús Lavalle-Martínez.

Additional information

Presented by Yde Venema

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lavalle-Martínez, JdJ., Montes-y-Gómez, M., Villaseñor-Pineda, L. et al. Equivalences Among Polarity Algorithms. Stud Logica 106, 371–395 (2018). https://doi.org/10.1007/s11225-017-9743-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11225-017-9743-y

Keywords

Search

Navigation