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Concept Combination in Weighted DL

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Logics in Artificial Intelligence (JELIA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14281))

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Abstract

Building on previous work on Weighted Description Logic (WDL), we present and assess an algorithm for concept combination grounded in the experimental research in cognitive psychology. Starting from two WDL formulas representing concepts in a way similar to Prototype Theory and a knowledge base (KB) modelling background knowledge, the algorithm outputs a new WDL formula which represent the combination of the input concepts. First, we study the logical properties of the operator defined by our algorithm. Second, we collect data on the prototypical representation of concepts and their combinations and learn WDL formulas from them. Third, we evaluate our algorithm and the role of the KB by comparing the algorithm’s outputs with the learned WDL formulas.

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Notes

  1. 1.

    This algorithm revises the original one [35].

  2. 2.

    Similar weighted accounts can be introduced in languages other than DL [29].

  3. 3.

    The algorithm can however accept more general inputs.

  4. 4.

    The algorithm guarantees that \({\mathbf {\bar{sft}}(\mathbb {K}{:}{\textsf{M}}{\circ }{\textsf{H}}) = \textbf{snc}(\mathbb {K}{:}{\textsf{M}}{\circ }{\textsf{H}})}\), see Phase 3.

  5. 5.

    We also dropped the feature Are of different sizes that applies to the whole concept and would have been tricky in the extensional evaluation of the weights, see below.

  6. 6.

    “The model first proposes that the intension of a conjunction is formed as the union of the constituent attribute sets” [20, p.56].

  7. 7.

    We add 1 to both counts to avoid potential infinities.

References

  1. Baader, F., Ecke, A.: Reasoning with prototypes in the description logic \({\cal{ALC}}\) using weighted tree automata. In: Dediu, A.-H., Janoušek, J., Martín-Vide, C., Truthe, B. (eds.) LATA 2016. LNCS, vol. 9618, pp. 63–75. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-30000-9_5

    Chapter  MATH  Google Scholar 

  2. Baader, F., Horrocks, I., Lutz, C., Sattler, U.: An Introduction to Description Logic. Cambridge University Press, Cambridge (2017). https://doi.org/10.1017/9781139025355

    Book  MATH  Google Scholar 

  3. Bishop, C.M., Nasrabadi, N.M.: Pattern Recognition and Machine Learning, vol. 4. Springer, New York (2006)

    Google Scholar 

  4. Bonatti, P.A., Sauro, L.: On the logical properties of the nonmonotonic description logic DLN. Artif. Intell. 248, 85–111 (2017)

    Article  MATH  Google Scholar 

  5. Britz, K., Heidema, J., Meyer, T.A.: Modelling object typicality in description logics. In: Description Logics. CEUR Workshop Proceedings, vol. 477. CEUR-WS.org (2009)

    Google Scholar 

  6. Britz, K., Heidema, J., Meyer, T.A.: Semantic preferential subsumption. In: Brewka, G., Lang, J. (eds.) Principles of Knowledge Representation and Reasoning: Proceedings of the Eleventh International Conference, KR 2008, Sydney, Australia, September 16–19, 2008, pp. 476–484. AAAI Press (2008), http://www.aaai.org/Library/KR/2008/kr08-046.php

  7. Casini, G., Straccia, U.: Rational closure for defeasible description logics. In: Janhunen, T., Niemelä, I. (eds.) JELIA 2010. LNCS (LNAI), vol. 6341, pp. 77–90. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15675-5_9

    Chapter  MATH  Google Scholar 

  8. Confalonieri, R., Galliani, P., Kutz, O., Porello, D., Righetti, G., Troquard, N.: Almost certain termination for \(\cal{ALC} \) weakening. In: Marreiros, G., Martins, B., Paiva, A., Ribeiro, B., Sardinha, A. (eds.) EPIA 2022. LNCS, vol. 13566, pp. 663–675. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-16474-3_54

    Chapter  Google Scholar 

  9. De Deyne, S., et al.: Exemplar by feature applicability matrices and other Dutch normative data for semantic concepts. Behav. Res. Methods 40(4), 1030–1048 (2008)

    Article  Google Scholar 

  10. Eppe, M., et al.: A computational framework for conceptual blending. Artif. Intell. 256, 105–129 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  11. Fauconnier, G., Turner, M.: The Way We Think: Conceptual Blending and the Mind’s Hidden Complexities. Basic Books, New York (2003)

    Google Scholar 

  12. Fodor, J., Lepore, E.: The red herring and the pet fish: why concepts still can’t be prototypes. Cognition 58(2), 253–270 (1996)

    Article  Google Scholar 

  13. Galliani, P., Kutz, O., Porello, D., Righetti, G., Troquard, N.: On knowledge dependence in weighted description logic. In: Calvanese, D., Iocchi, L. (eds.) GCAI 2019. Proceedings of the 5th Global Conference on Artificial Intelligence, Bozen/Bolzano, Italy, 17–19 September 2019. EPiC Series in Computing, vol. 65, pp. 68–80. EasyChair (2019). https://doi.org/10.29007/hjt1, https://doi.org/10.29007/hjt1

  14. Galliani, P., Kutz, O., Troquard, N.: Succinctness and complexity of \(\cal{ALC} \) with counting perceptrons. In: Principles of Knowledge Representation and Reasoning: Proceedings of the 20th International Conference (KR 2023). Rhodes, Greece, September 2–8, 2023 (2023)

    Google Scholar 

  15. Galliani, P., Righetti, G., Kutz, O., Porello, D., Troquard, N.: Perceptron connectives in knowledge representation. In: Keet, C.M., Dumontier, M. (eds.) EKAW 2020. LNCS (LNAI), vol. 12387, pp. 183–193. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-61244-3_13

    Chapter  Google Scholar 

  16. Gärdenfors, P.: Conceptual Spaces - The Geometry of Thought. MIT Press, Cambridge (2000)

    Book  Google Scholar 

  17. Giordano, L., Gliozzi, V., Olivetti, N., Pozzato, G.L.: Preferential description logics. In: Dershowitz, N., Voronkov, A. (eds.) LPAR 2007. LNCS (LNAI), vol. 4790, pp. 257–272. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-75560-9_20

    Chapter  Google Scholar 

  18. Giordano, L., Gliozzi, V., Olivetti, N., Pozzato, G.L.: A non-monotonic description logic for reasoning about typicality. Artif. Intell. 195, 165–202 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  19. Goguen, J.A., Harrell, D.F.: Style: a computational and conceptual blending-based approach. In: Argamon, S., Burns, K., Dubnov, S. (eds.) The structure of style, pp. 291–316. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-12337-5_12

    Chapter  Google Scholar 

  20. Hampton, J.A.: Inheritance of attributes in natural concept conjunctions. Memory Cogn. 15(1), 55–71 (1987)

    Article  Google Scholar 

  21. Hampton, J.A.: Overextension of conjunctive concepts: evidence for a unitary model of concept typicality and class inclusion. J. Exp. Psychol. Learn. Mem. Cogn. 14(1), 12–32 (1988)

    Article  Google Scholar 

  22. Hampton, J.A.: Testing the prototype theory of concepts. J. Mem. Lang. 34(5), 686–708 (1995)

    Article  Google Scholar 

  23. Hampton, J.A.: Compositionality and concepts. In: Hampton, J.A., Winter, Y. (eds.) Compositionality and Concepts in Linguistics and Psychology, pp. 95–121. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-45977-6

    Chapter  Google Scholar 

  24. Hedblom, M.M., Kutz, O., Neuhaus, F.: Image schemas in computational conceptual blending. Cogn. Syst. Res. 39, 42–57 (2016)

    Article  Google Scholar 

  25. Hedblom, M.M., Righetti, G., Kutz, O.: Deciphering the cookie monster: a case study in impossible combinations. In: ICCC, pp. 222–225 (2021)

    Google Scholar 

  26. Jackendoff, R.: English Noun-noun Compounds in Conceptual Semantics. The Semantics of Compounding, pp. 15–37 (2016)

    Google Scholar 

  27. Lewis, M., Lawry, J.: Hierarchical conceptual spaces for concept combination. Artif. Intell. 237, 204–227 (2016). https://doi.org/10.1016/j.artint.2016.04.008

    Article  MathSciNet  MATH  Google Scholar 

  28. Lieto, A., Pozzato, G.L.: A description logic framework for commonsense conceptual combination integrating typicality, probabilities and cognitive heuristics. J. Exp. Theor. Artif. Intell. 32(5), 769–804 (2020). https://doi.org/10.1080/0952813X.2019.1672799

    Article  Google Scholar 

  29. Masolo, C., Porello, D.: Representing concepts by weighted formulas. In: Formal Ontology in Information Systems - Proceedings of the 10th International Conference, FOIS 2018, Cape Town, South Africa, 19–21 September 2018, pp. 55–68 (2018)

    Google Scholar 

  30. Murphy, G.L.: Noun phrase interpretation and conceptual combination. J. Mem. Lang. 29(3), 259–288 (1990)

    Article  MathSciNet  Google Scholar 

  31. Murphy, G.L.: The Big Book of Concepts. MIT press, Cambridge (2002)

    Book  Google Scholar 

  32. Murphy, G.L., Medin, D.: The role of theories in conceptual coherence. Psychol. Rev. 92, 289–316 (1985)

    Article  Google Scholar 

  33. Osherson, D.N., Smith, E.E.: On the adequacy of prototype theory as a theory of concepts. Cognition 9(1), 35–58 (1981)

    Article  Google Scholar 

  34. Porello, D., Kutz, O., Righetti, G., Troquard, N., Galliani, P., Masolo, C.: A toothful of concepts: Towards a theory of weighted concept combination. In: Proceedings of DL Workshop, vol. 2373. CEUR-WS.org (2019)

    Google Scholar 

  35. Righetti, G., Masolo, C., Troquard, N., Kutz, O., Porello, D.: Concept combination in weighted description logics. In: JOWO 2021. Proceedings of the Joint Ontology Workshops, Bozen/Bolzano, Italy, 13–17 September 2021. CEUR Workshop Proceedings (2021)

    Google Scholar 

  36. Righetti, G., Porello, D., Confalonieri, R.: Evaluating the interpretability of threshold operators. In: Corcho, Ó., Hollink, L., Kutz, O., Troquard, N., Ekaputra, F.J. (eds.) EKAW 2022. LNCS, vol. 13514, pp. 136–151. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-17105-5_10

    Chapter  Google Scholar 

  37. Righetti, G., Porello, D., Kutz, O., Troquard, N., Masolo, C.: Pink panthers and toothless tigers: three problems in classification. In: Proceedings of the 7th International Workshop on Artificial Intelligence and Cognition (AIC 2019), pp. 39–53 (2019)

    Google Scholar 

  38. Righetti, G., Porello, D., Troquard, N., Kutz, O., Hedblom, M., Galliani, P.: Asymmetric hybrids: dialogues for computational concept combination. In: Formal Ontology in Information Systems: Proceedings of the 12th International Conference (FOIS 2021). IOS Press (2021)

    Google Scholar 

  39. Righetti, G., Porello, D., Troquard, N., Kutz, O., Hedblom, M.M., Galliani, P.: Asymmetric hybrids: dialogues for computational concept combination (extended abstract). In: Raedt, L.D. (ed.) Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence, IJCAI 2022, Vienna, Austria, 23–29 July 2022, pp. 5329–5333. ijcai.org (2022). https://doi.org/10.24963/ijcai.2022/745

  40. Rosch, E.: Cognitive representations of semantic categories. J. Exp. Psychol. Gen. 104, 192–233 (1975)

    Article  Google Scholar 

  41. Ross, S.M.: Introduction to Probability and Statistics for Engineers and Scientists. Academic press, Cambridge (2020)

    MATH  Google Scholar 

  42. Schorlemmer, M., Plaza, E.: A uniform model of computational conceptual blending. Cogn. Syst. Res. 65, 118–137 (2021)

    Article  Google Scholar 

  43. Smith, E.E., Medin, D.L.: Categories and concepts, vol. 9. Harvard University Press, Cambridge (1981)

    Book  Google Scholar 

  44. Varzinczak, I.: A note on a description logic of concept and role typicality for defeasible reasoning over ontologies. Log. Univers. 12, 297–325 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  45. Veale, T.: From conceptual mash-ups to badass blends: a robust computational model of conceptual blending. In: Veale, T., Cardoso, F. (eds.) Computational Creativity. CSCS, pp. 71–89. Springer, Cham (2019). https://doi.org/10.1007/978-3-319-43610-4_4

    Chapter  Google Scholar 

  46. Wisniewski, E.J.: When concepts combine. Psychon. Bull. Rev. 4(2), 167–183 (1997)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Free University of Bozen-Bolzano, Bolzano, Italy

    Guendalina Righetti

  2. Università degli studi dell’Insubria, Varese, Italy

    Pietro Galliani

  3. Laboratory for Applied Ontology, ISTC-CNR, Trento, Italy

    Claudio Masolo

Authors
  1. Guendalina Righetti
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  2. Pietro Galliani
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  3. Claudio Masolo
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Corresponding author

Correspondence to Pietro Galliani .

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Editors and Affiliations

  1. TU Dresden, Dresden, Germany

    Sarah Gaggl

  2. Artificial Intelligence Research Institute - IIIA CSIC, Barcelona, Spain

    Maria Vanina Martinez

  3. Umeå University, Umeå, Sweden

    Magdalena Ortiz

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Righetti, G., Galliani, P., Masolo, C. (2023). Concept Combination in Weighted DL. In: Gaggl, S., Martinez, M.V., Ortiz, M. (eds) Logics in Artificial Intelligence. JELIA 2023. Lecture Notes in Computer Science(), vol 14281. Springer, Cham. https://doi.org/10.1007/978-3-031-43619-2_27

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