{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,17]],"date-time":"2026-02-17T11:15:02Z","timestamp":1771326902904,"version":"3.50.1"},"reference-count":40,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2012,12,20]],"date-time":"2012-12-20T00:00:00Z","timestamp":1355961600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>What is information? Although researchers have used the construct of information liberally to refer to pertinent forms of domain-specific knowledge, relatively few have attempted to generalize and standardize the construct. Shannon and Weaver (1949) offered the best known attempt at a quantitative generalization in terms of the number of discriminable symbols required to communicate the state of an uncertain event. This idea, although useful, does not capture the role that structural context and complexity play in the process of understanding an event as being informative. In what follows, we discuss the limitations and futility of any generalization (and particularly, Shannon\u2019s) that is not based on the way that agents extract patterns from their environment. More specifically, we shall argue that agent concept acquisition, and not the communication of states of uncertainty, lie at the heart of generalized information, and that the best way of characterizing information is via the relative gain or loss in concept complexity that is experienced when a set of known entities (regardless of their nature or domain of origin) changes. We show that Representational Information Theory perfectly captures this crucial aspect of information and conclude with the first generalization of RIT to continuous domains.<\/jats:p>","DOI":"10.3390\/info4010001","type":"journal-article","created":{"date-parts":[[2012,12,20]],"date-time":"2012-12-20T11:27:57Z","timestamp":1356002877000},"page":"1-30","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["Complexity over Uncertainty in Generalized Representational Information Theory (GRIT): A Structure-Sensitive General Theory of Information"],"prefix":"10.3390","volume":"4","author":[{"given":"Ronaldo","family":"Vigo","sequence":"first","affiliation":[{"name":"Center for the Advancement of Cognitive Science, Ohio University, 318 Porter Hall, Athens, OH 45701, USA"}]}],"member":"1968","published-online":{"date-parts":[[2012,12,20]]},"reference":[{"key":"ref_1","unstructured":"Devlin, K. (1991). Logic and Information, Cambridge University Press."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1037\/1089-2680.7.2.183","article-title":"Whatever happened to information theory in psychology?","volume":"7","author":"Luce","year":"2003","journal-title":"Rev. Gen. Psychol."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Floridi, L. (2011). The Philosophy of Information, Oxford University Press.","DOI":"10.1093\/acprof:oso\/9780199232383.001.0001"},{"key":"ref_4","first-page":"20","article-title":"Claude Shannon, 1916\u20132001","volume":"21","author":"Devlin","year":"2001","journal-title":"Focus News. Math. Assoc. Am."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1002\/j.1538-7305.1928.tb01236.x","article-title":"Transmission of information","volume":"7","author":"Hartley","year":"1928","journal-title":"Bell Syst. Tech. J."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_7","unstructured":"Shannon, C.E., and Weaver, W. (1949). The Mathematical Theory of Communication, University of Illinois Press."},{"key":"ref_8","unstructured":"Bishop, C.M. (2006). Pattern Recognition and Machine Learning, Springer."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"4847","DOI":"10.1016\/j.ins.2011.05.020","article-title":"Representational information: A new general notion and measure of information","volume":"181","author":"Vigo","year":"2011","journal-title":"Inf. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Klir, G.J. (2006). Uncertainty and Information: Foundations of Generalized Information Theory, John Wiley & Sons, Inc.","DOI":"10.1002\/0471755575"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1037\/h0043158","article-title":"The magical number seven, plus or minus two: Some limits on our capacity for processing information","volume":"63","author":"Miller","year":"1956","journal-title":"Psychol. Rev."},{"key":"ref_12","unstructured":"Laming, D.R.J. (1968). Information Theory of Choice-Reaction Times, Academic Press."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1088\/0954-898X_10_4_303","article-title":"How to measure the information gained from one symbol","volume":"10","author":"Deweese","year":"1999","journal-title":"Network"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1088\/0954-898X_14_2_301","article-title":"How much information is associated with a particular stimulus?","volume":"14","author":"Butts","year":"2003","journal-title":"Network"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Benferhat, S., and Besnard, P. (2001). Symbolic and Quantitative Approaches to Reasoning with Uncertainty, Springer-Verlag.","DOI":"10.1007\/3-540-44652-4"},{"key":"ref_16","unstructured":"Dretske, F. (1981). Knowledge and the Flow of Information, MIT Press."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/0010-0285(73)90033-9","article-title":"Availability: A heuristic for judging frequency and probability","volume":"5","author":"Tversky","year":"1973","journal-title":"Cogn. Psychol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1037\/0033-295X.90.4.293","article-title":"Extension versus intuitive reasoning: The conjunction fallacy in probability judgment","volume":"90","author":"Tversky","year":"1983","journal-title":"Psychol. Rev."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1017\/S1477175609990297","article-title":"A dialogue on concepts","volume":"9","author":"Vigo","year":"2010","journal-title":"Think"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/j.jmp.2009.04.009","article-title":"Categorical invariance and structural complexity in human concept learning","volume":"53","author":"Vigo","year":"2009","journal-title":"J. Math. Psychol."},{"key":"ref_21","unstructured":"Carlson, L., H\u00d6lscher, C., and Shipley, T. (2011, January 21). Towards a law of invariance in human conceptual behavior. Proceedings of the 33rd Annual Conference of the Cognitive Science Society, Austin, TX, USA."},{"key":"ref_22","unstructured":"Vigo, R. (2012). The gist of concepts. Cognition, Submitted for publication."},{"key":"ref_23","unstructured":"Feldman, D., and Crutchfield, J. (A survey of \u201cComplexity Measures\u201d, 1998). A survey of \u201cComplexity Measures\u201d."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1016\/j.jmp.2006.05.007","article-title":"A note on the complexity of Boolean concepts","volume":"50","author":"Vigo","year":"2006","journal-title":"J. Math. Psychol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1080\/09528130802113422","article-title":"Modal similarity","volume":"21","author":"Vigo","year":"2009","journal-title":"J. Exp. Artif. Intell."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Vigo, R., and Basawaraj, B. (2012). Will the most informative object stand? Determining the impact of structural context on informativeness judgments. J. Cogn. Psychol., in press.","DOI":"10.1080\/20445911.2012.755510"},{"key":"ref_27","unstructured":"Vigo, R., Zeigler, D., and Halsey, A. (2012). Gaze and information processing during category learning: Evidence for an inverse law. Vis. Cogn., Submitted for publication."},{"key":"ref_28","unstructured":"Bourne, L.E. (1966). Human Conceptual Behavior, Allyn and Bacon."},{"key":"ref_29","unstructured":"Estes, W.K. (1994). Classification and Cognition; Oxford Psychology Series 22, Oxford University Press."},{"key":"ref_30","unstructured":"Garner, W.R. (1974). The Processing of Information and Structure, Wiley."},{"key":"ref_31","unstructured":"Garner, W.R. (1962). Uncertainty and Structure as Psychological Concepts, Wiley."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1037\/0033-295X.99.1.22","article-title":"ALCOVE: An exemplar-based connectionist model of category learning","volume":"99","author":"Kruschke","year":"1992","journal-title":"Psychol. Rev."},{"key":"ref_33","unstructured":"Aiken, H.H. (1951). Synthesis of Electronic Computing and Control Circuits, Harvard University Press."},{"key":"ref_34","unstructured":"Higonnet, R.A., and Grea, R.A. (1958). Logical Design of Electrical Circuits, McGraw-Hill."},{"key":"ref_35","unstructured":"For the readers\u2019 convenience, the parameterized variants of Equations (10) and (11) (see main text) respectively as introduced by Vigo (2009, 2011) are as follows:  and . The parameter  in both expressions stands for a human observer\u2019s degree of sensitivity to (i.e., extent of detection of) the invariance pattern associated with the i-th dimension (this is usually a number in the closed real interval  such that ). k is a scaling parameter in the closed real interval  (D is the number of dimensions associated with the category) that indicates the overall ability of the subject to discriminate between dimensions (a larger number indicates higher discrimination) and c is a constant parameter in the closed interval which captures possible biases displayed by observers toward invariant information (c is added to the numerator and the denominator of the ratios that make up the logical or structural manifold of the well-defined category). Finally, s is a parameter that indicates the most appropriate measure of distance as defined by the generalized Euclidean metric (i.e., the Minkowski distance measure). In our investigation, the best predictions are achieved when s = 2 (i.e., when using the Euclidean metric). Optimal estimates of these free parameters on the aggregate data provide a baseline to assess any individual differences encountered in the pattern perception stage of the concept learning process and may provide a basis for more accurate measurements of subjective representational information"},{"key":"ref_36","unstructured":"We could simply define the representational information of a well-defined category as the derivative of its structural complexity. We do not because our characterization of the degree of invariance of a concept function is based on a discrete counterpart to the notion of a derivative in the first place."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1037\/0278-7393.10.1.104","article-title":"Choice, similarity, and the context theory of classification","volume":"10","author":"Nosofsky","year":"1984","journal-title":"J. Exp. Psychol. Learn. Mem. Cogn."},{"key":"ref_38","unstructured":"Shepard, R.N., and Romney, A.K. (1972). Multidimensional Scaling: Theory and Applications in the Behavioral Sciences, Seminar Press."},{"key":"ref_39","unstructured":"Kruskal, J.B., and Wish, M. (1978). Multidimensional Scaling; Sage University Paper series on Quantitative Application in the Social Sciences 07-011, Beverly Hills and London."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1317","DOI":"10.1126\/science.3629243","article-title":"Towards a universal law of generalization for psychological science","volume":"237","author":"Shepard","year":"1987","journal-title":"Science"}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/4\/1\/1\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:54:24Z","timestamp":1760219664000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/4\/1\/1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12,20]]},"references-count":40,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2013,3]]}},"alternative-id":["info4010001"],"URL":"https:\/\/doi.org\/10.3390\/info4010001","relation":{},"ISSN":["2078-2489"],"issn-type":[{"value":"2078-2489","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,12,20]]}}}