Licensed Unlicensed Requires Authentication Published online by De Gruyter Mouton December 27, 2021

Text as tautology: an exploration in inference, transitivity, and logical compression

Andrew Potter ORCID logo
From the journal Text & Talk
https://doi.org/10.1515/text-2020-0230

Abstract

Rhetorical structure theory (RST) and relational propositions have been shown useful in analyzing texts as expressions in propositional logic. Because these expressions are systematically derived, they may be expected to model discursive reasoning as articulated in the text. If this is the case, it would follow that logical operations performed on the expressions would be reflected in the texts. In this paper the logic of relational propositions is used to demonstrate the applicability of transitive inference to discourse. Starting with a selection of RST analyses from the research literature, analyses of the logic of relational propositions are performed to identify their corresponding logical expressions and within each expression to identify the inference path implicit within the text. By eliminating intermediary relational propositions, transitivity is then used to progressively compress the expression. The resulting compressions are applied to the corresponding texts and their compressed RST analyses. The application of transitive inference to logical expressions results in abridged texts that are intuitively coherent and logically compatible with their originals. This indicates an underlying isomorphism between the inferential structure of logical expressions and discursive coherence, and it confirms that these expressions function as logical models of the text. Potential areas for application include knowledge representation, logic and argumentation, and RST validation.

Keywords: coherence relations; discourse analysis; inference; propositional logic; relational propositions; rhetorical structure theory
Corresponding author: Andrew Potter, Department of Computer Science & Information Systems, University of North Alabama, 236 Keller Hall, 35632, Florence, AL, USA, E-mail:

  1. Research funding: Not applicable.

  2. Availability of data and material: Not applicable.

  3. Code availability: Not applicable.

  4. Competing interests: Not applicable.

Appendix: Source articles

References

Abelen, Eric, Gisela Redeker & Sandra Thompson. 1993. The rhetorical structure of US-American and Dutch fund-raising letters. Text 3. 323–350. https://doi.org/10.1515/text.1.1993.13.3.323.Search in Google Scholar

Asher, Nicholas & Alex Lascarides. 1994. Intentions and information in discourse. In Proceedings of the 32nd annual meeting on Association for Computational Linguistics, 34–41. Las Cruces, NM: Association for Computational Linguistics.10.3115/981732.981738Search in Google Scholar

Asher, Nicholas & Alex Lascarides. 2003. Logics of conversation. Cambridge: Cambridge University Press.Search in Google Scholar

Brandom, Robert B. 2000. Articulating reasons. Cambridge, MA: Harvard University Press.10.4159/9780674028739Search in Google Scholar

Copi, Irving M. 1967. Symbolic logic. New York: Macmillan.Search in Google Scholar

Copi, Iving M. 1972. Introduction to logic. New York: Macmilllan.Search in Google Scholar

Danlos, Laurence. 2008. Strong generative capacity of RST, SDRT and discourse dependency DAGSs. In Anton Benz & Peter Kühnlein (eds.), Constraints in discourse, 69–95. Amsterdam: Benjamins.10.1075/pbns.172.04danSearch in Google Scholar

Das, Debopam. 2019. Nuclearity in RST and signals of coherence relations. In Amir Zeldes, Debopam Das, Erick Maziero Galani, Juliano Desiderato Antonio & Mikel Iruskieta (eds.), Proceedings of the Workshop on Discourse Relation Parsing and Treebanking 2019, 30–37. Minneapolis, MN: Association for Computational Linguistics.Search in Google Scholar

Fuchs, Norbert E. 2018. Understanding texts in Attempto Controlled English. In Brian Davis, C. Maria Keet & Adam Wynder (eds.), Controlled natural language: Proceedings of the Sixth International Workshop, 75–84. Maynooth, Ireland: IOS Press.Search in Google Scholar

González, Montserrat & Montserrat Ribas. 2008. The construction of epistemic space via causal connectives. In Istvan Kecskes & Jacob Mey (eds.), Intention, common ground and the egocentric speaker-hearer, 127–149. Berlin: de Gruyter.Search in Google Scholar

Groenendijk, Jeroen. 2009. Inquisitive semantics: Two possibilities for disjunction. In Peter Bosch, David Gabelaia & Jérôme Lang (eds.), Logic, language, and computation, 80–94. Berlin, Heidelberg: Springer Berlin Heidelberg.10.1007/978-3-642-00665-4_8Search in Google Scholar

Hobbs, Jerry R. 1979. Coherence and coreference. Cognitive Science 3. 67–90. https://doi.org/10.1207/s15516709cog0301_4.Search in Google Scholar

Hobbs, Jerry R. 1985. On the coherence and structure of discourse. Stanford, CA: Center for the Study of Language and Information, Stanford University.Search in Google Scholar

Hou, Shengluan, Shuhan Zhang & Chaoqun Fei. 2020. Rhetorical structure theory: A comprehensive review of theory, parsing methods and applications. Expert Systems with Applications 157. 1–16. https://doi.org/10.1016/j.eswa.2020.113421.Search in Google Scholar

Hurley, Patrick J. 2012. A concise introduction to logic, 11th edn. Boston, MA: Wadsworth Publishing.Search in Google Scholar

Kamp, Hans & Uwe Reyle. 1993. From discourse to logic: Introduction to model-theoretic semantics of natural language, formal logic and discourse representation theory. Dordrecht: Kluwer.Search in Google Scholar

Kamp, Hans, Josef Van Genabith & Uwe Reyle. 2011. Discourse representation theory. In D. Gabbay & F. Guenthner (eds.), Handbook of philosophical logic, vol. 15, 125–294. Dordrecht: Springer.10.1007/978-94-007-0485-5_3Search in Google Scholar

Kowalski, Robert. 2020. Logical English. Paper presented at the Logic and Practice of Programming (LPOP) Workshop.Search in Google Scholar

Mann, William C. & Sandra A. Thompson. 1985. Assertions from discourse structure. Marina del Rey, CA: Information Sciences Institute.10.3115/1077146.1077177Search in Google Scholar

Mann, William C. & Sandra A. Thompson. 1986. Relational propositions in discourse. Discourse Processes 9(1). 57–90. https://doi.org/10.1080/01638538609544632.Search in Google Scholar

Mann, William C. & Sandra A. Thompson. 1987a. Rhetorical Structure Theory: A framework for the analysis of texts. IPRA Papers in Pragmatics 1. 1–21.10.1075/iprapip.1.1.03thoSearch in Google Scholar

Mann, William C. & Sandra A. Thompson. 1987b. Rhetorical structure theory: A theory of text organization. Marina del Rey, CA: University of Southern California, Information Sciences Institute (ISI).10.1515/text.1.1988.8.3.243Search in Google Scholar

Mann, William C. & Sandra A. Thompson. 1988. Rhetorical structure theory: Toward a functional theory of text organization. Text 8(3). 243–281. https://doi.org/10.1515/text.1.1988.8.3.243.Search in Google Scholar

Mann, William C. & Sandra A. Thompson. 1992. Rhetorical structure theory and text analysis. Discourse description: Diverse linguistic analyses of a fund-raising text, 39–78. Amsterdam: John Benjamins.10.1075/pbns.16.04manSearch in Google Scholar

Mann, William, C. & Sandra, A. Thompson. 2000. Two views of rhetorical structure theory. In Proceedings of the 10th Annual Meeting of the Society for Text and Discourse. Lyon, France: Society for Text and Discourse.Search in Google Scholar

Marcu, Daniel. 1996. Building up rhetorical structure trees. In Proceedings of the Thirteenth National Conference on Artificial Intelligence, 1069–1074. Portland, Oregon: American Association for Artificial Intelligence.Search in Google Scholar

Marcu, Daniel. 2000. The theory and practice of discourse parsing and summarization. Cambridge, MA: MIT Press.10.7551/mitpress/6754.001.0001Search in Google Scholar

Moore, Johanna Doris & Martha E. Pollack. 1992. A problem for RST: The need for multi-level discourse analysis. Computational Linguistics 18(4). 527–544.Search in Google Scholar

Peregrin, Jaroslav. 2014. Inferentialism: Why rules matter. New York: Palgrave Macmillan UK.10.1057/9781137452962Search in Google Scholar

Popoola, Olu. 2017. Using Rhetorical Structure Theory for detection of fake online reviews. In Proceedings of the 6th Workshop Recent Advances in RST and Related Formalisms, 58–63. Santiago de Compostela, Spain: Association for Computational Linguistics.10.18653/v1/W17-3608Search in Google Scholar

Potter, Andrew. 2007. A discourse approach to explanation aware knowledge representation. In Thomas Roth-Berghofer, Stefan Schulz, David B. Leake & Daniel Bahls (eds.), Explanation-aware computing: Papers from the 2007 AAAI Workshop 56–63. Menlo Park, CA: AAAI Press.Search in Google Scholar

Potter, Andrew. 2010. Rhetorical compositions for controlled natural languages. In Norbert E. Fuchs (ed.), Controlled Natural Language: Workshop on Controlled Natural Language, CNL 2009, Marettimo Island, Italy, June 8-10, 2009, Revised Papers, 21–35. Heidelberg: Springer.10.1007/978-3-642-14418-9_2Search in Google Scholar

Potter, Andrew. 2018. Reasoning between the lines: A logic of relational propositions. Dialogue and Discourse 9(2). 80–110.10.5087/dad.2018.203Search in Google Scholar

Potter, Andrew. 2020. The rhetorical structure of Modus Tollens: An exploration in logic-mining. In Allyson Ettinger, Ellie Pavlich & Brandon Prickett (eds.), Proceedings of the Society for Computation in Linguistics, 170–179. New Orleans, LA: SCiL.Search in Google Scholar

Potts, Christopher. 2005. The logic of conventional implicatures. Oxford, UK: Oxford University Press.10.1093/acprof:oso/9780199273829.001.0001Search in Google Scholar

Sanders, Ted J. M., W. P. M. Spooren & L. G. M. Noordman. 1992. Toward a taxonomy of coherence relations. Discourse Processes 15. 1–35. https://doi.org/10.1080/01638539209544800.Search in Google Scholar

Sanders, Ted J. M., Demberg Vera, Jet Hoek, Merel C. J. Scholman, Torabi Asr Fatemeh, Sandrine Zufferey & Jacqueline Evers-Vermeul. 2018. Unifying dimensions in coherence relations: How various annotation frameworks are related. Corpus Linguistics and Linguistic Theory 17. 1–71. https://doi.org/10.1515/cllt-2016-0078.Search in Google Scholar

Stede, Manfred. 2008. RST revisited: Disentangling nuclearity. In Cathrine Fabricius-Hansen & Wiebke Ramm (eds.), ‘Subordination’ versus ‘coordination’ in sentence and text – from a cross-linguistic perspective, 33–58. Amsterdam: Benjamins.10.1075/slcs.98.03steSearch in Google Scholar

Stede, Manfred, Maite Taboada & Debopam Das. 2017. Annotation guidelines for rhetorical structure. Potsdam & Burnaby: University of Potsdam & Simon Fraser University.Search in Google Scholar

Thompson, Sandra A. & William C. Mann. 1987. Antithesis: A study in clause combining and discourse structure. In Ross Steele & Threadgold Terry (eds.), Language topics: Essays in honour of Michael Halliday, vol. II, 359–381. Amsterdam: John Benjamins.10.1075/z.lt2.70thoSearch in Google Scholar

Toulmin, Stephen. 1958. The uses of argument. Cambridge, UK: Cambridge University Press.Search in Google Scholar

Wærn, Yvonne & Robert Ramberg. 2004. Distributed knowledge by explanation networks. In HICSS ’04: Proceedings of the Proceedings of the 37th Annual Hawaii International Conference on System Sciences (HICSS’04) - Track 5, 50132b. Washington, DC: IEEE Computer Society.10.1109/HICSS.2004.1265332Search in Google Scholar

Wong, Wing-Kwong C. 1986. A theory of argument coherence. Austin, TX: Artificial Intelligence Laboratory.Search in Google Scholar

Zeldes, Amir & Yang Liu. 2020. A neural approach to discourse relation signal detection. Dialogue and Discourse 11(2). 1–33. https://doi.org/10.5087/dad.2020.201.Search in Google Scholar
Received: 2020-12-29
Accepted: 2021-11-30
Published Online: 2021-12-27

© 2021 Walter de Gruyter GmbH, Berlin/Boston

From the journal
Text & Talk
Text & Talk

Journal