# On the learning difficulty of visual and auditory modal concepts: Evidence for a single processing system

## Abstract

The logic operators (e.g., “and,” “or,” “if, then”) play a fundamental role in concept formation, syntactic construction, semantic expression, and deductive reasoning. In spite of this very general and basic role, there are relatively few studies in the literature that focus on their conceptual nature. In the current investigation, we examine, for the first time, the learning difficulty experienced by observers in classifying members belonging to these primitive “modal concepts” instantiated with sets of acoustic and visual stimuli. We report results from two categorization experiments that suggest the acquisition of acoustic and visual modal concepts is achieved by the same general cognitive mechanism. Additionally, we attempt to account for these results with two models of concept learning difficulty: the generalized invariance structure theory model (Vigo in Cognition 129(1):138–162, 2013, Mathematical principles of human conceptual behavior, Routledge, New York, 2014) and the generalized context model (Nosofsky in J Exp Psychol Learn Mem Cogn 10(1):104–114, 1984, J Exp Psychol 115(1):39–57, 1986).

## Keywords

Concept learning Auditory concepts Logic operators Categorization behavior## Supplementary material

## References

- Archer EJ (1962) Concept identification as a function of obviousness of relevant and irrelevant information. J Exp Psychol 63(6):616–620CrossRefPubMedGoogle Scholar
- Bourne LE (1970) Knowing and using concepts. Psychol Rev 77(6):546–556CrossRefGoogle Scholar
- Bourne LE, Guy DE (1968) Learning conceptual rules. II: the role of positive and negative instances. J Exp Psychol 77(3):488–494CrossRefPubMedGoogle Scholar
- Bourne LE, Ekstrand BR, Montogomery B (1969) Concept learning as a function of the conceptual rule and the availability of positive and negative instances. J Exp Psychol 82(3):538–544CrossRefGoogle Scholar
- Bruner JS, Goodnow JJ, Austin GA (1956) A study of thinking. Transaction Publishers, New YorkGoogle Scholar
- Bulgarella RG, Archer EJ (1962) Concept identification of auditory stimuli as a function of amount of relevant and irrelevant information. J Exp Psychol 63(3):254–257CrossRefPubMedGoogle Scholar
- Byrne RM, Johnson-Laird PN (2009) ‘If’ and the problems of conditional reasoning. Trends Cogn Sci 13(7):282–287CrossRefPubMedGoogle Scholar
- Conant MB, Trabasso T (1964) Conjunctive and disjunctive concept formation under equal-information conditions. J Exp Psychol 67(3):250–255CrossRefPubMedGoogle Scholar
- Dijkstra S, Dekker PH (1982) Inference processes in learning well-defined concepts. Acta Physiol (Oxf) 51:181–205Google Scholar
- Dobson DJG, Dobson KS (1981) Problem-solving strategies in depressed and nondepressed college students. Cognit Ther Res 5(3):237–249CrossRefGoogle Scholar
- Feldman J (2000) Minimization of Boolean complexity in human concept learning. Nature 407:630–633CrossRefPubMedGoogle Scholar
- Feldman J (2003) A catalog of Boolean concepts. J Math Psychol 47:75–89CrossRefGoogle Scholar
- Feldman J (2006) An algebra of human concept learning. J Math Psychol 50:339–368CrossRefGoogle Scholar
- Goode RL (2001) Auditory physiology of the external ear. In: Jahn AF, Santos-Sacchi J (eds) Physiology of the ear, 2nd edn. Singular, San Diego, pp 147–160Google Scholar
- Goodwin GP, Johnson-Laird PN (2011) Mental models of Boolean concepts. Cogn Psychol 63:34–59CrossRefPubMedGoogle Scholar
- Halberstadt J, Sherman SJ, Sherman JW (2011) Why Barack Obama is black: a cognitive account of hypodescent. Psychol Sci 22(1):29–33CrossRefPubMedGoogle Scholar
- Haygood DH (1965) Audio-visual concept formation. J Educ Psychol 56(3):126–132CrossRefPubMedGoogle Scholar
- Haygood RC, Bourne LE (1965) Attribute- and rule-learning aspects of conceptual behavior. Psychol Rev 72(3):175–195CrossRefPubMedGoogle Scholar
- Higonnet RA, Grea RA (1958) Logical design of electrical circuits. McGraw-Hill, New YorkGoogle Scholar
- Hull CL (1920) Quantitative aspects of the evolution of concepts. Psychol Monogr 28(1):1–86CrossRefGoogle Scholar
- Khemlani S, Orenes I, Johnson-Laird PN (2014) The negations of conjunctions, conditionals, and disjunctions. Acta Physiol (Oxf) 151:1–7Google Scholar
- Kruschke JK (1992) ALCOVE: an exemplar-based connectionist model of category learning. Psychol Rev 99(1):22–44CrossRefPubMedGoogle Scholar
- Kurtz KJ, Levering KR, Stanton RD, Romero J, Morris SN (2012) Human learning of elemental category structures: revising the classic result of Shepard, Hovland, and Jenkins (1961). J Exp Psychol Learn Mem Cogn 39(2):552–572CrossRefPubMedGoogle Scholar
- Lordahl DS (1961) Concept identification using simultaneous audio and visual signals. J Exp Psychol 62(3):283–290CrossRefPubMedGoogle Scholar
- Luce RD (1959) Individual choice behavior: a theoretical analysis. Wiley, New YorkGoogle Scholar
- Miskiewicz A, Rakowski A (2012) A psychophysical pitch function determined by absolute magnitude estimation and its relation to the musical pitch scale. J Acoust Soc Am 131:987–992CrossRefPubMedGoogle Scholar
- Murphy GL (2002) The big book of concepts. MIT Press, CambridgeGoogle Scholar
- Neisser U, Weene P (1962) Hierarchies in concept attainment. J Exp Psychol 64(6):640–645CrossRefPubMedGoogle Scholar
- Newstead SE, Griggs RA, Chrostowski JJ (1984) Reasoning with realistic disjunctives. Q J Exp Psychol 36A:611–627CrossRefGoogle Scholar
- Nosofsky RM (1984) Choice, similarity, and the context theory of classification. J Exp Psychol Learn Mem Cogn 10(1):104–114CrossRefPubMedGoogle Scholar
- Nosofsky RM (1986) Attention, similarity, and the identification-categorization relationship. J Exp Psychol 115(1):39–57CrossRefGoogle Scholar
- Nosofsky RM, Johansen MK (2000) Exemplar-based accounts of “multiple-system” phenomena in perceptual classification. Psychon Bull Rev 7(3):375–402PubMedGoogle Scholar
- Nosofsky RM, Palmeri TJ (1996) Learning to classify integral-dimension stimuli. Psychon Bull Rev 3(2):222–226CrossRefPubMedGoogle Scholar
- Nosofsky RM, Gluck MA, Palmeri TJ, McKinley SC, Glauthier P (1994) Comparing models of rule-based classification learning: a replication and extension of Shepard, Hovland, and Jenkins (1961). Mem Cogn 22(3):352–369CrossRefGoogle Scholar
- Paivio A (1971) Imagery and verbal processes. Holt, Rinehart, and Winston, New YorkGoogle Scholar
- Paivio A (1986) Mental representations: a dual-coding approach. Oxford University Press, OxfordGoogle Scholar
- Pishkin V, Shurley JT (1965) Auditory dimensions and irrelevant information in concept identification of males and females. Percept Mot Skills 20:673–683CrossRefPubMedGoogle Scholar
- Rehder B, Hoffman AB (2005) Eyetracking and selective attention in category learning. Cogn Psychol 51:1–41CrossRefPubMedGoogle Scholar
- Reznick JS, Ketchum RD, Bourne LE (1978) Rule-specific dimensional interaction effects in concept learning. Bull Psychon Soc 12(4):314–316CrossRefGoogle Scholar
- Shepard RN (1987) Towards a universal law of generalization for psychological science. Science 237:1317–1323CrossRefPubMedGoogle Scholar
- Shepard RN, Hovland CI, Jenkins HM (1961) Learning and memorization of classifications. Psychol Monogr General Appl 75(13):1–42CrossRefGoogle Scholar
- Smith ER, Zarate MA (1992) Exemplar-based model of social judgment. Psychol Rev 99(1):3–21CrossRefGoogle Scholar
- JASP Team (2016) JASP (Version 0.8.0.0) [Computer software]Google Scholar
- Vigo R (2006) A note on the complexity of Boolean concepts. J Math Psychol 50:501–510CrossRefGoogle Scholar
- Vigo R (2009) Modal similarity. J Exp Theor Artif Intell 21:181–196CrossRefGoogle Scholar
- Vigo R (2013) The GIST of concepts. Cognition 129(1):138–162CrossRefPubMedGoogle Scholar
- Vigo R (2014) Mathematical principles of human conceptual behavior. Routledge, New YorkGoogle Scholar
- Vigo R, Allen C (2009) How to reason without words: inference as categorization. Cogn Process 10:77–88CrossRefPubMedGoogle Scholar
- Vigo R, Basawaraj B (2013) Will the most informative object stand? Determining the impact of structural context on informativeness judgments. J Cogn Psychol 25(3):248–266CrossRefGoogle Scholar
- Vigo R, Barcus M, Zhang Y, Doan C (2012) On the learnability of auditory concepts. Paper presented at the 146th meeting of the Acoustical Society of America, Kansas City, MOGoogle Scholar
- Walls RT, Rude SH, Gulkus SP (1975) Model and observer learning of low, medium, and high level concepts. Psychol Rep 37:671–675CrossRefGoogle Scholar