Abstract
In this chapter, we introduce a new dialogical system for first order classical logic which is close to natural language argumentation, and we prove its completeness with respect to usual classical validity. We combine our dialogical system with the Grail syntactic and semantic parser developed by the second author in order to address automated textual entailment, that is, we use it for deciding whether or not a sentence is a consequence of a short text. This work—which connects natural language semantics and argumentation with dialogical logic—can be viewed as a step towards an inferentialist view of natural language semantics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
Our system is able to deal with metaphoric use, like the The cash machine ate my credit card. see e.g., [37].
- 2.
The patterns in the well-known corpus for testing Textual Entailment recognition called FraCaS [11] greatly vary in difficulty. We expect only some of them (monotonicity, syllogisms) to be handled easily, whereas we expect others (plurals, temporal inference for aspectual classes) to be much more difficult for systems based on automated theorem provers, or, indeed, for any automated system.
- 3.
The words “question” and “answer” are called “attack” and “defence” by Felscher in [16]; we deviate from this terminology because we will rather use the terms “attack” and “defence” exclusively for the moves in a game, avoiding possible confusion.
- 4.
We ignore the product connectives ‘\(\bullet \)’ here, since it has somewhat more complicated natural deduction rules and it is not used in the examples.
References
Abramsky, S., McCusker, G.: Game semantics. In: Berger, U., Schwichtenberg, H. (eds.) Computational Logic, pp. 1–55. Springer, Berlin (1999)
Amblard, M., Beysson, C., de Groote, P., Guillaume, B., Pogodalla, S.: A French version of the FraCaS test suite. In: LREC 2020 - Language Resources and Evaluation Conference (2020)
Asher, N., Lascarides, A.: Logics of Conversation. Cambridge University Press, Cambridge (2003)
Boritchev, M., Amblard, M.: Picturing questions and answers - a formal approach to slam. In: Amblard, M., Musiol, M., Rebuschi, M. (eds.) (In)coherence of discourse - Formal and Conceptual issues of Language, Language, Cognition and Mind. Springer, Berlin (2019). To appear
Brandom, R.: Articulating Reasons: An Introduction to Inferentialism. Harvard University Press, Harvard (2000)
Breitholtz, E.: Enthymemes in dialogue: a micro-rhetorical approach. Ph.D. thesis, Humanistiska fakulteten. Göteborgs universitet (2014)
Castelnérac, B., Marion, M.: Arguing for inconsistency: dialectical games in the academy. In: Primiero, G. (ed.) Acts of Knowledge: History, Philosophy and Logic. College Publications (2009)
Castelnérac, B., Marion, M.: Antilogic. Balt. Int. Yearb. Cogn., Log. Commun. 8(1) (2013). https://doi.org/10.4148/1944-3676.1079
Catta, D., Pellissier, L., Retoré, C.: Inferential semantics as argumentative dialogues. In: González, S., González-Briones, A., Gola, A., Katranas, G., Ricca, M., Loukanova, R., Prieto, J. (eds.) Distributed Computing and Artificial Intelligence, Special Sessions, 17th International Conference, Advances in Intelligent Systems and Computing, pp. 72–81 (2020). https://doi.org/10.1007/978-3-030-53829-3_7
Cooper, R.: Update conditions and intensionality in a type-theoretic approach to dialogue semantics. In: Fernández, R., Isard, A. (eds.) Proceedings of the 17th Workshop on the Semantics and Pragmatics of Dialogue (2013)
Cooper, R., Crouch, D., Eijck, J.V., Fox, C., Genabith, J.V., Jaspars, J., Kamp, H., Milward, D., Pinkal, M., Poesio, M., Pulman, S., Briscoe, T., Maier, H., Konrad, K.: Using the framework (1996). FraCaS deliverable D16
Cozzo, C.: Meaning and Argument: A Theory of Meaning Centred on Immediate Argumental Role. Stockholm Studies in Philosophy. Almqvist & Wiksell International (1994)
Dagan, I., Roth, D., Sammons, M., Zanzotto, F.M.: Recognizing textual entailment: models and applications. Synthesis Lectures on Human Language Technologies, vol. 6(4). Morgan & Claypool Publishers, San Rafael (2013). https://doi.org/10.2200/S00509ED1V01Y201305HLT023
Dummett, M.A.E.: What is a theory of meaning? In: Guttenplan, S. (ed.) Mind and Language. Oxford University Press, Oxford (1975)
Dummett, M.A.E.: The Logical Basis of Metaphysics. Harvard University Press, Harvard (1991)
Felscher, W.: Dialogues as a foundation for intuitionistic logic. In: Gabbay, D.M., Guenthner, F. (eds.) Handbook of Philosophical Logic, pp. 115–145. Springer Netherlands, Dordrecht (2002). http://dx.doi.org/10.1007/978-94-017-0458-8_2
Fouqueré, C., Quatrini, M.: Argumentation and inference a unified approach. In: The Baltic International Yearbook of Cognition, Logic and Communication Volume 8: Games, Game Theory and Game Semantics, pp. 1–41. New Paririe Press (2013)
Francez, N.: Proof Theoretical Semantics. Studies in Logic, vol. 57. College Publication (2015)
Frege, G.: The thought: a logical inquiry. Mind 65(259), 289–311 (1956). https://doi.org/10.1093/mind/65.1.289
Ginzburg, J.: The Interactive Stance. Oxford University Press, Oxford (2012)
Girard, J.Y.: Proof-Theory and Logical Complexity – vol. I. Studies in Proof Theory. Bibliopolis, Napoli (1987)
Girard, J.Y.: Locus solum. Math. Struct. Comput. Sci. 11(3), 301–506 (2001)
Herbelin, H.: Séquents qu’on calcule : de l’interprétation du calcul des séquents comme calcul de \(\lambda \)-termes et comme calcul de stratégies gagnantes. Thèse d’université, Université Paris 7 (1995)
Hunter, J., Asher, N., Lascarides, A.: A formal semantics for situated conversation. Semant. Pragmat. 11, 1–52 (2018). https://doi.org/10.3765/sp.11.10
Hyland, M.: Game semantics. In: Pitts, A., Dybjer, P. (eds.) Semantics and Logics of Computation, pp. 131–182. Cambridge University Press, Cambridge (1997)
Kamp, H., Reyle, U.: From Discourse to Logic. Kluwer Academic Publishers, Dordrecht (1993)
Lecomte, A.: Meaning, Logic and Ludics. Imperial College Press, London (2011)
Lorenzen, P., Lorenz, K.: Dialogische Logik. Wissenschaftliche Buchgesellschaft (1978). https://books.google.fr/books?id=pQ5sQgAACAAJ
Montague, R.: English as a formal language. In: Visentini, B. (ed.) Linguaggi nella Societa e nella Tecnica, pp. 189–224. Edizioni di Communità, Milan, Italy (1970). (Reprinted in R. Thomason (ed) The collected papers of Richard Montague. Yale University Press, 1974.)
Moot, R.: A type-logical treebank for French. J. Lang. Model. 3(1), 229–264 (2015). http://dx.doi.org/10.15398/jlm.v3i1.92
Moot, R.: The Grail theorem prover: type theory for syntax and semantics. In: Chatzikyriakidis, S., Luo, Z. (eds.) Modern Perspectives in Type Theoretical Semantics, pp. 247–277. Springer, Berlin (2017). https://doi.org/10.1007/978-3-319-50422-3_10
Moot, R.: The Grail family of theorem provers (syntactic and semantic parser) (2018). https://richardmoot.github.io
Moot, R., Retoré, C.: Natural language semantics and computability. J. Log., Lang. Inf. 28, 287–307 (2019). https://doi.org/10.1007/s10849-019-09290-7
Moss, L.: Natural logic. In: Lappin, S., Fox, C. (eds.) The Handbook of Contemporary Semantic Theory, 2 edn., pp. 559–592. Blackwell, Hoboken (2015)
Novaes, C.D.: Medieval “obligationes” as logical games of consistency maintenance. Synthese 145(3), 371–395 (2005). http://www.jstor.org/stable/20118602
Prawitz, D.: The epistemic significance of valid inference. Synthese 187(3), 887–898 (2012). https://doi.org/10.1007/s11229-011-9907-7
Retoré, C.: The montagovian generative lexicon \(\Lambda Ty_n\): a type theoretical framework for natural language semantics. In: Matthes, R., Schubert, A. (eds.) 19th International Conference on Types for Proofs and Programs (TYPES 2013), Leibniz International Proceedings in Informatics (LIPIcs), vol. 26, pp. 202–229. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany (2014). https://doi.org/10.4230/LIPIcs.TYPES.2013.202
Sabah, G., Prince, V., Vilnat, A., Ferret, O., Vosniadiou, S., Dimitracopoulou, A., Papademetriou, E., Tsivgouli, M.: What dialogue analysis can tell about teacher strategies related to representational changes. In: Kayser, D., Vosniadou, S. (eds.) Modelling Changes in Understanding: Case Studies in Physical Reasoning, Advances in Learning and Instruction, pp. 223–279. Pergamon Press, Oxford (2000)
Troelstra, A.S., Schwichtenberg, H.: Basic Proof Theory. Cambridge University Press, USA (1996)
Wittgenstein, L.: Philosophische Untersuchungen/Philosophical Investigations. Oxford University Press, Oxford (1953). Translated by G. E. M, Anscombe/Bilingual edition
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Catta, D., Moot, R., Retoré, C. (2021). Dialogical Argumentation and Textual Entailment. In: Loukanova, R. (eds) Natural Language Processing in Artificial Intelligence—NLPinAI 2020. Studies in Computational Intelligence, vol 939. Springer, Cham. https://doi.org/10.1007/978-3-030-63787-3_7
Download citation
DOI: https://doi.org/10.1007/978-3-030-63787-3_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-63786-6
Online ISBN: 978-3-030-63787-3
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)