Abstract
In this paper, we propose a cognitive semantic approach to represent part–whole relations. We base our proposal on the theory of conceptual spaces, focusing on prototypical structures in part–whole relations. Prototypical structures are not accounted for in traditional mereological formalisms. In our account, parts and wholes are represented in distinct conceptual spaces; parts are joined to form wholes in a structure space. The structure space allows systematic similarity judgments between wholes, taking into consideration shared parts and their configurations. A point in the structure space denotes a particular part structure; regions in the space represent different general types of part structures. We argue that the structural space can represent prototype effects: structural types are formed around typical arrangements of parts. We also show how structure space captures the variations in part structure of a given concept across different domains. In addition, we discuss how some taxonomies of part–whole relations can be understood within our framework.
This is a preview of subscription content, log in via an institution to check access.
Notes
The real meaning of the word “distinct” here depends on the actual way chosen to implement the conceptual spaces. Some representations tend to aggregate all possible concepts in a unique, comprehensive conceptual space including all domains. Others may represent the concepts in really distinct conceptual spaces, formed by the combination of the relevant quality domains.
An object-centered coordinate system seems to be preferable. Nonetheless, one can think of structural information based on an egocentric coordinate space, or even a retinal coordinate space (Newell et al. 2005).
More about the conceptual spaces and spatial relations can be found in Ligozat and Condotta (2005).
A main reason is that there is no general way of measuring the similarity between three graphs. There are some attempts to do so by converting tree graphs into graph spectra (e.g., Shokoufandeh et al. 2005), but the lack of isomorphism between the two kinds of representation prevents the use of graph spectra as a framework for implementing structure similarity.
Just as the botanist and the customer put different weights on different apple properties (Fig. 4), a filter can be seen as an attentional mechanism that picks out the aspects of the structural complex that are of interest to the user in a particular context.
References
Adams B, Raubal M (2009) Conceptual space markup language (CSML): towards the cognitive semantic web. In: IEEE international conference on semantic computing, 2009. ICSC’09. IEEE, pp 253–260
Aisbett J, Gibbon G (2001) A general formulation of conceptual spaces as a meso level representation. Artif Intell 133:189–232. doi:10.1016/S0004-3702(01)00144-8
Alexander RG, Zelinsky GJ (2012) Effects of part-based similarity on visual search: the Frankenbear experiment. Vis Res 54:20–30. doi:10.1016/j.visres.2011.12.004
Alvarez GA (2011) Representing multiple objects as an ensemble enhances visual cognition. Trends Cogn Sci 15:122–131. doi:10.1016/j.tics.2011.01.003
Augustine E, Smith LB, Jones SS (2011) Parts and relations in young children’s shape-based object recognition. J Cogn Dev 12:556–572. doi:10.1080/15248372.2011.560586
Behrmann M, Peterson MA, Moscovitch M, Suzuki S (2006) Independent representation of parts and the relations between them: evidence from integrative agnosia. J Exp Psychol Hum Percept Perform 32:1169–1184. doi:10.1037/0096-1523.32.5.1169
Biederman I (1987) Recognition-by-components: a theory of human image understanding. Psychol Rev 94:115–117. doi:10.1037/0033-295X.94.2.115
Chaffin R, Herrmann DJ, Winston M (1988) An empirical taxonomy of part-whole relations: effects of part-whole relation type on relation identification. Lang Cogn Process 3:17–48. doi:10.1080/01690968808402080
Chella A, Frixione M, Gaglio S (2001) Conceptual spaces for computer vision representations. Artif Intell Rev 16:137–152. doi:10.1023/A:1011658027344
Doumas LAA, Hummel JE (2010) A computational account of the development of the generalization of shape information. Cogn Sci 34:698–712. doi:10.1111/j.1551-6709.2010.01103.x
Edelman S (1998) Representation is representation of similarities. Behav Brain Sci 21:449–467
Farah MJ (1992) Is an object an object an object? Cognitive and neuropsychological investigations of domain specificity in visual object recognition. Curr Dir Psychol Sci 1:164–169
Fiorini SR, Abel M, Scherer CMS (2013) An approach for grounding ontologies in raw data using foundational ontology. Inf Syst 38:784–799. doi:10.1016/j.is.2012.11.013
Förster J (2009) Relations between perceptual and conceptual scope: how global versus local processing fits a focus on similarity versus dissimilarity. J Exp Psychol Gen 138:88–111. doi:10.1037/a0014484
Foster DH, Gilson SJ (2002) Recognizing novel three-dimensional objects by summing signals from parts and views. Proc R Soc Lond Ser B Biol Sci 269:1939–1947. doi:10.1098/rspb.2002.2119
Gärdenfors P (1997) Symbolic, conceptual and subconceptual representations. In: Cantoni V, Gesù VD, Setti A, Tegolo D (eds) Human and machine perception. Springer, Berlin, pp 255–270
Gärdenfors P (2000) Conceptual spaces: the geometry of thought. The MIT Press, Cambridge
Gärdenfors P (2004) How to make the semantic web more semantic. Formal ontology in information systems. In: Proceedings of the third international conference FOIS-2004. IOS Press, pp 17–34
Gärdenfors P, Zenker F (2011) Using conceptual spaces to model the dynamics of empirical theories. In: Olsson EJ, Enqvist S (eds) Belief revision meets philosophy of science. Springer, Berlin, pp 137–153
Garner WR (1974) The processing of information and structure. Lawrence Erlbaum, Oxford
Gerstl P, Pribbenow S (1995) Midwinters, end games, and body parts: a classification of part-whole relations. Int J Hum Comput Stud 43:865–889. doi:10.1006/ijhc.1995.1079
Goldstone RL (1994) The role of similarity in categorization: providing a groundwork. Cognition 52:125–157
Graf M (2006) Coordinate transformations in object recognition. Psychol Bull 132:920–945. doi:10.1037/0033-2909.132.6.920
Guarino N (1998) Formal ontology and information systems. Formal ontology in information systems. IOS press, Amsterdam, pp 3–15
Guarino N, Pribbenow S, Vieu L (1996) Modeling parts and wholes. Data Knowl Eng 20:257–258. doi:10.1016/S0169-023X(96)00009-2
Guizzardi G (2005) Ontological foundations for structural conceptual models. CTIT, The Netherlands
Hoffman DD, Singh M (1997) Salience of visual parts. Cognition 63:29–78. doi:10.1016/S0010-0277(96)00791-3
Hummel JE, Biederman I (1992) Dynamic binding in a neural network for shape recognition. Psychol Rev 99:480–517. doi:10.1037/0033-295X.99.3.480
Jäger G (2008) The evolution of convex categories. Linguist Philos 30:551–564. doi:10.1007/s10988-008-9024-3
Johansson I (2006) Formal mereology and ordinary language - Reply to Varzi. Appl Ontol 1:157–161
Johansson I (2012) Natural science and mereology. In: Hans B, Johanna S, Guido I (eds) Handbook of Mereology. Philosophia Verlag, München, Germany
Ligozat G, Condotta J-F (2005) On the relevance of conceptual spaces for spatial and temporal reasoning. Spat Cogn Comput 5:1–27. doi:10.1207/s15427633scc0501_1
Love BC, Rouder JN, Wisniewski EJ (1999) A structural account of global and local processing. Cogn Psychol 38:291–316. doi:10.1006/cogp.1998.0697
Maddox WT (1992) Perceptual and decisional separability. Multidimensional models of perception and cognition. Lawrence Erlbaum Associates Inc., Hillsdale, pp 147–180
Marr D (1982) Vision: a computational investigation into the human representation and processing of visual information. W. H. Freeman, San Francisco
Marr D, Nishihara HK (1978) Representation and recognition of the spatial organization of three-dimensional shapes. Proc R Soc Lon Ser B Biol Sci 200:269–294. doi:10.1098/rspb.1978.0020
Mash C (2006) Multidimensional shape similarity in the development of visual object classification. J Exp Child Psychol 95:128–152. doi:10.1016/j.jecp.2006.04.002
Melara RD (1992) The concept of perceptual similarity: from psychophysics to cognitive psychology. Psychophysical approaches to cognition. North-Holland, pp 303–388
Moltmann F (1996) A new notion of part structure for natural language. Data Knowl Eng 20:323–345. doi:10.1016/S0169-023X(96)00011-0
Newell FN, Sheppard DM, Edelman S, Shapiro KL (2005) The interaction of shape- and location-based priming in object categorisation: evidence for a hybrid “what + where” representation stage. Vis Res 45:2065–2080. doi:10.1016/j.visres.2005.02.021
Peissig JJ, Tarr MJ (2007) Visual object recognition: do we know more now than we did 20 years ago? Annu Rev Psychol 58:75–96. doi:10.1146/annurev.psych.58.102904.190114
Pentland AP (1986) Perceptual organization and the representation of natural form. Artif Intell 28:293–331. doi:10.1016/0004-3702(86)90052-4
Rector A, Welty C, Noy N, Wallace E (2005) Simple part-whole relations in OWL ontologies. http://www.w3.org/2001/sw/BestPractices/OEP/SimplePartWhole/index.html. Accessed 3 Feb 2012
Rosch E (1978) Principles of categorization. In: Margolis E, Laurence S (eds) Concepts: core readings. The MIT Press, Cambridge, pp 189–206
Rosch E, Mervis CB (1975) Family resemblances: studies in the internal structure of categories. Cogn Psychol 7:573–605. doi:10.1016/0010-0285(75)90024-9
Shepard RN (1987) Toward a universal law of generalization for psychological science. Science 237:1317–1323. doi:10.1126/science.3629243
Shokoufandeh A, Macrini D, Dickinson S et al (2005) Indexing hierarchical structures using graph spectra. IEEE Trans Patt Anal Mach Intell 27:1125–1140. doi:10.1109/TPAMI.2005.142
Simons P (2003) Parts: a study in ontology, [Repr.]. Clarendon Press, Oxford
Simons P (2006) Real wholes, real parts: mereology without algebra. J Philos 103:597–613
Smith LB (2009) From fragments to geometric shape: changes in visual object recognition between 18 and 24 months. Curr Dir Psychol Sci 18:290–294. doi:10.1111/j.1467-8721.2009.01654.x
Son JY, Smith LB, Goldstone RL (2008) Simplicity and generalization: short-cutting abstraction in children’s object categorizations. Cognition 108:626–638. doi:10.1016/j.cognition.2008.05.002
Tomlinson M, Love BC (2006) Learning abstract relations through analogy to concrete exemplars. In: Proceedings of the cognitive science society. Lawrence Erlbaum Associates, Mahwah, pp 2269–2274
Tversky A (1977) Features of similarity. Psychol Rev 84:327–352. doi:10.1037/0033-295X.84.4.327
Tversky B (1989) Parts, partonomies, and taxonomies. Dev Psychol 25:983–995
Tversky B, Hemenway K (1984) Objects, parts, and categories. J Exp Psychol Gen 113:169–193. doi:10.1037/0096-3445.113.2.169
Ullman S (2000) High-level vision: object recognition and visual cognition. MIT Press, Cambridge
Varzi AC (2006) A note on the transitivity of parthood. Appl Ontol 1:141–146
Varzi A (2011) Mereology. In: Edward NZ (ed) The Stanford Encyclopedia of Philosophy (Spring 2011 Edition). http://plato.stanford.edu/archives/spr2011/entries/mereology/
Winston ME, Chaffin R, Herrmann D (1987) A taxonomy of part-whole relations. Cogn Sci 11:417–444. doi:10.1016/S0364-0213(87)80015-0
Wu R, Mareschal D, Rakison DH (2010) Attention to multiple cues during spontaneous object labeling. Infancy 16:545–556. doi:10.1111/j.1532-7078.2010.00061.x
Zhu SC, Yuille AL (1996) FORMS: a flexible object recognition and modelling system. Int J Comput Vis. doi:10.1007/BF00208719
Acknowledgments
Sandro Fiorini is grateful for the support from CAPES Foundation, process number 1444-11-5, and ANP-Petrobras PRH-217. Mara Abel acknowledges the Brazilian Research Council (CNPq) support. Peter Gärdenfors gratefully acknowledges support from the Swedish Research Council for the Linnaeus environment Thinking in Time: Cognition, Communication and Learning. Also, we would like to thank Joel Carbonera, Ingvar Johansson, Joel Parthemore, Luan Fonseca Garcia, and anonymous reviewers for their comments.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rama Fiorini, S., Gärdenfors, P. & Abel, M. Representing part–whole relations in conceptual spaces. Cogn Process 15, 127–142 (2014). https://doi.org/10.1007/s10339-013-0585-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10339-013-0585-x