Artificial Intelligence Review

, Volume 52, Issue 2, pp 1463–1493 | Cite as

Evaluating representational systems in artificial intelligence

  • John LicatoEmail author
  • Zhitian Zhang


All artificial reasoners work within representational systems. These systems, which may have varying levels of formality or detail, determine the space of possible representations over which the artificial reasoner can operate, by defining the syntactic and semantic properties of the symbols, structures, and inferences that they manipulate. But we are now seeing an increasing need for the ability to reason over representational systems, rather than just working within them. A prerequisite of performing such reasoning is the ability to evaluate and compare representational objects (and to know the difference between them). We survey the criteria that are used for such evaluations in AI, machine learning, and other AI-related fields. To aid our survey, we introduce a formalism of representations, representational systems, and representational spaces that lends itself nicely to an analysis of the criteria typically used for evaluating them.


Representational systems Representations Representational spaces Models Learning representations Reasoning 


  1. Abadi M, Agarwal A, Barham P, Brevdo E, Chen Z, Citro C, Corrado GS, Davis A, Dean J, Devin M, Ghemawat S, Goodfellow I, Harp A, Irving G, Isard M, Jia Y, Jozefowicz R, Kaiser L, Kudlur M, Levenberg J, Mané D, Monga R, Moore S, Murray D, Olah C, Schuster M, Shlens J, Steiner B, Sutskever I, Talwar K, Tucker P, Vanhoucke V, Vasudevan V, Viégas F, Vinyals O, Warden P, Wattenberg M, Wicke M, Yu Y, Zheng X (2015) TensorFlow: large-scale machine learning on heterogeneous systems. Software available from
  2. Anderson B (2011) The myth of computational level theory and the vacuity of rational analysis. Behav Brain Sci 34:189–190CrossRefGoogle Scholar
  3. Aouchiche M, Hansen P (2010) A survey of automated conjectures in spectral graph theory. Linear Algebra Appl. 432:2293MathSciNetzbMATHCrossRefGoogle Scholar
  4. Barker-Plummer D, Barwise J, Etchemendy J (2011) Language proof and logic, 2nd edn. Center for the Study of Language and Information, StanfordzbMATHGoogle Scholar
  5. Barwise J, Etchemendy J (1998) A computational architecture for heterogeneous reasoning.
  6. Bauer AJ, Just MA (2015) Monitoring the growth of the neural representations of new animal concepts. Hum Brain Mapp 36:3213CrossRefGoogle Scholar
  7. Bengio Y et al (2009) Learning deep architectures for AI. Found Trends Mach Learn 2(1):1–127zbMATHMathSciNetCrossRefGoogle Scholar
  8. Bengio Y, Courville A, Vincent P (2013) Representation learning: a review and new perspectives. IEEE Trans Pattern Anal Mach Intell 35(8):1798–1828CrossRefGoogle Scholar
  9. Besnard P, Garcia A, Hunter A, Modgil S, Prakken H, Simari G, Toni F (2014) Introduction to structured argumentation. Argum Comput 5(1):1–4CrossRefGoogle Scholar
  10. Borsboom D, Wagenmakers EJ, Romejin JW (2011) Mechanistic curiosity will not kill the Bayesian cat. Behav Brain Sci 34:192–194CrossRefGoogle Scholar
  11. Bowers JS, Davis CJ (2012a) Bayesian just-so stories in psychology and neuroscience. Psychol Bull 138(3):389–414CrossRefGoogle Scholar
  12. Bowers JS, Davis CJ (2012) Is that what Bayesians believe? Reply to Griffiths, Chater, Norris, and Pouget (2012). Psychol Bull 138(3):423–426CrossRefGoogle Scholar
  13. Bricker P (2016) Ontological commitment. In: Zalta EN (ed) The Stanford encyclopedia of philosophy, winter 2016 edn. Metaphysics Research Lab, Stanford University, StanfordGoogle Scholar
  14. Bringsjord S (1991) Is the connectionist–logicist clash one of AI’s wonderful red herrings? J Exp Theor AI 3(4):319–349CrossRefGoogle Scholar
  15. Bringsjord S, Ferrucci D (1998) Logic and artificial intelligence: divorced, separated, still married...? Mind Mach 8:273–308CrossRefGoogle Scholar
  16. Bringsjord S, Licato J, Bringsjord A (2016) The contemporary craft of creating characters meets today’s cognitive architectures: a case study in expressivity. In: Turner J, Nixon M, Bernardet U, DiPaola S (eds) Integrating cognitive architectures into virtual character design, Advances in computational intelligence and robotics (ACIR), Information science reference. IGI Global, HersheyGoogle Scholar
  17. Brooks RA (1990) Elephants don’t play chess. Robot Auton Syst 6:3–15CrossRefGoogle Scholar
  18. Brun G (2015) Explication as a method of conceptual re-engineering. Erkenntnis 1:1–31Google Scholar
  19. Bundy A, Ireland A, Hutter D, Basin D (2005) Rippling: meta-level guidance for mathematical reasoning, vol 56. Cambridge University Press, CambridgezbMATHCrossRefGoogle Scholar
  20. Carnap R (1950) Logical foundations of probability. University of Chicago Press, ChicagozbMATHGoogle Scholar
  21. Chater N, Goodman N, Griffiths TL, Kemp C, Oaksford M, Tenenbaum JB (2011) The imaginary fundamentalists: the unshocking truth about bayesian cognitive science. Behav Brain Sci 34:194–196CrossRefGoogle Scholar
  22. Cheng PCH (2002) Electrifying diagrams for learning: principles for complex representational systems. Cogn Sci 26:685–736CrossRefGoogle Scholar
  23. Cheng PCH (2016) What constitutes an effective representation? In: Jamnik M, Uesaka Y, Elzer Schwartz S (eds) Diagrammatic representation and inference: proceedings from the 9th international conference, Diagrams 2016, Lecture Notes in Computer Science vol 9781. SpringerGoogle Scholar
  24. Cunningham P (2009) A taxonomy of similarity mechanisms for case-based reasoning. IEEE Trans Knowl Data Eng 21(11):1532CrossRefGoogle Scholar
  25. Doumas LA, Hummel JE (2013) Comparison and mapping facilitate relation discovery and predication. PLoS ONE 8(6):e63889CrossRefGoogle Scholar
  26. Doumas LA, Hummel JE, Sandhofer C (2008) A theory of the discovery and predication of relational concepts. Psychol Rev 115(1):1–43CrossRefGoogle Scholar
  27. Eickenberg M, Gramfort A, Varoquaux G, Thirion B (2016) Seeing it all: convolutional network layers map the function of the human visual system. NeuroImage 152:184CrossRefGoogle Scholar
  28. Eliasmith C, Thagard P (2001) Integrating structure and meaning: a distributed model of analogical mapping. Cogn Sci 25(2):245–286CrossRefGoogle Scholar
  29. Emruli B, Sandin F (2013) Analogical mapping with sparse distributed memory: a simple model that learns to generalize from examples. Cogn Comput 6:74CrossRefGoogle Scholar
  30. Falkenhainer B, Forbus KD, Gentner D (1989) The structure-mapping engine: algorithm and examples. Artif Intell 41(1):1–63zbMATHCrossRefGoogle Scholar
  31. Fernbach PM, Sloman SA (2011) Don’t throw out the Bayes with the bathwater. Behav Brain Sci 34:198–199CrossRefGoogle Scholar
  32. Floridi L (2011a) A defence of constructionism: philosophy as conceptual engineering. Metaphilosophy 42(3):282–304CrossRefGoogle Scholar
  33. Floridi L (2011b) The philosophy of information. Oxford University Press, OxfordzbMATHCrossRefGoogle Scholar
  34. Fodor JA (1980) The language of thought, 2nd edn. Harvard University Press, CambridgeGoogle Scholar
  35. Fodor J (1998) Concepts: where cognitive science went wrong. Oxford University Press, New YorkCrossRefGoogle Scholar
  36. Fodor JA, Pylyshyn Z (1988) Connectionism and cogntive architecture: a critical analysis. Cognition 28(1–2):3–71CrossRefGoogle Scholar
  37. Forbus K, Mostek T, Ferguson R (2002) An analogy ontology for integrating analogical processing and first-principles reasoning. In: AAAI/IAAI, pp 878–885Google Scholar
  38. Forbus KD, Ferguson RW, Lovett A, Gentner D (2017) Extending SME to handle large-scale cognitive modeling. Cogn Sci 41:1152CrossRefGoogle Scholar
  39. Gauthier T, Kaliszyk C, Urban J, Vyskočil J (2016) Conjecturing over large corpora. In: Proceedings from the first conference on artificial intelligence and theorem proving (AITP 2016)Google Scholar
  40. Gentner D (1983) Structure-mapping: a theoretical framework for analogy. Cogn Sci 7(2):155–170CrossRefGoogle Scholar
  41. Gentner D, Forbus K (2011) Computational models of analogy. Wiley Interdiscip Rev Cogn Sci 2(3):266–276CrossRefGoogle Scholar
  42. Gerring J (1999) What makes a concept good? A criterial framework for understanding concept formation in the social sciences. Polity 31(3):357–393CrossRefGoogle Scholar
  43. Goodman N, Frank MC, Griffiths TL, Tenenbaum JB, Battaglia PW, Hamrick JB (2015) Relevant and robust: a response to Marcus and Davis (2013). Psychol Sci 26(4):539–541CrossRefGoogle Scholar
  44. Gopnik A (2011) Probabilistic models as theories of children’s minds. Behav Brain Sci 34:200–201CrossRefGoogle Scholar
  45. Griffiths TL, Chater N, Norris D, Pouget A (2012) How the Bayesians got their beliefs (and what those beliefs actually are): comment on Bowers and Davis (2012). Psychol Bull 138(3):415–422CrossRefGoogle Scholar
  46. Guo J, Wang C, Roman-Rangel E, Chao H, Rui Y (2016) Building hierarchical representations for oracle character and sketch recognition. IEEE Trans Image Process 25(1):104–118MathSciNetzbMATHCrossRefGoogle Scholar
  47. Gust H, Kühnberger Ku, Schmid U (2003) Anti-Unification of Axiomatic Systems. University of Osnabrück, Technical reportGoogle Scholar
  48. Gust H, Kühnberger Ku, Schmid U (2006) Metaphors and heuristic-driven theory projection (HDTP). Theor Comput Sci 354(1):98–117MathSciNetzbMATHCrossRefGoogle Scholar
  49. Han J, Zhang D, Wen S, Guo L, Liu T, Li X (2016) Two-stage learning to predict human eye fixations via SDAEs. IEEE Trans Cybern 46(2):487–498CrossRefGoogle Scholar
  50. Hansson SO (2000) Formalization in philosophy. Bull Symb Logic 6(2):162–175CrossRefGoogle Scholar
  51. Hinton GE, Zemel RS (1994) Autoencoders, minimum description length and Helmholtz free energy. In Advances in neural information processing systems, pp 3–10Google Scholar
  52. Hinton GE, McClelland J, Rumelhart DE (1986) Distributed representations. In: Rumelhart DE, McClelland J (eds) Parallel distributed processing: explorations in the microstructure of cognition, vol 1. MIT Press, CambridgeGoogle Scholar
  53. Hofstadter DR (2001) Epilogue: analogy as the core of cognition. In: Gentner D, Holyoak KJ, Kokinov BN (eds) The analogical mind: perspectives from cognitive science, chap 15. The MIT Press, CambridgeGoogle Scholar
  54. Hofstadter DR, Sander E (2013) Surfaces and essences: analogy as the fuel and fire of thinking. Basic Books, LondonGoogle Scholar
  55. Holyoak KJ, Hummel JE (2000) The proper treatment of symbols in a connectionist architecture. In: Deitrich E, Markman A (eds) Cognitive dynamics: conceptual change in humans and machines. MIT Press, CambridgeGoogle Scholar
  56. Hummel JE (2001) Complementary solutions to the binding problem in vision: implications for shape perception and object recognition. Vis Cogn 8(3):489–517CrossRefGoogle Scholar
  57. Hummel JE (2010) Symbolic versus associative learning. Cogn Sci 34:958–965CrossRefGoogle Scholar
  58. Hummel JE (2016) Putting distributed representations into context. Lang Cogn Neurosci 32:359CrossRefGoogle Scholar
  59. Hummel JE, Biederman I (1992) Dynamic binding in a neural network for shape recognition. Psychol Rev 99(3):480–517CrossRefGoogle Scholar
  60. Hummel JE, Holyoak KJ (1997) Distributed representations of structure: a theory of analogical access and mapping. Psychol Rev 104(3):427–466CrossRefGoogle Scholar
  61. Hummel JE, Holyoak KJ (2003) Relational reasoning in a neurally-plausible cognitive architecture: an overview of the LISA Project. Cogn Stud Bull Jpn Cogn Sci Soc 10:58–75Google Scholar
  62. Ireland A, Bundy A (1996) Productive use of failure in inductive proof. J Autom Reason 16(1–2):79–111MathSciNetzbMATHCrossRefGoogle Scholar
  63. Jones M, Love BC (2011) Bayesian fundamentalism or enlightenment? On the explanatory status and theoretical contributions of Bayesian models of cognition. Behav Brain Sci 34:169–231CrossRefGoogle Scholar
  64. Kahneman D (2011) Thinking, fast and slow. Farrar, Straus and Girous, New YorkGoogle Scholar
  65. Kotseruba I, Gonzalez OJA, Tsotsos JK (2016) A review of 40 years of cognitive architecture research: focus on perception, attention, learning and applications. arXiv:1610.08602v1
  66. Li Y, Yosinski J, Clune J, Lipson H, Hopcroft J (2016) Convergent learning: do different neural networks learn the same representations? In: Proceedings of international conference on learning representation (ICLR)Google Scholar
  67. Licato J (2015) Analogical constructivism: the emergence of reasoning through analogy and action schemas. PhD thesis, Rensselaer Polytechnic Institute, TroyGoogle Scholar
  68. Licato J (2017) Two paradoxes and their implications for AI-assisted analysis. In: Proceedings of the 2017 conference of the International Association for Computing and Philosophy (IACAP 2017)Google Scholar
  69. Licato J, Bringsjord S (2016) A physically realistic, general-purpose simulation environment for developmental AI systems. In: Proceedings of the ECAI 2016 workshop on evaluating general-purpose AI (EGPAI 2016)Google Scholar
  70. Licato J, Govindarajulu NS, Bringsjord S, Pomeranz M, Gittelson L (2013) Analogico-deductive generation of Gödel’s first incompleteness theorem from the liar paradox. In: Proceedings of the 23rd annual international joint conference on artificial intelligence (IJCAI-13)Google Scholar
  71. Licato J, Bringsjord S, Govindarajulu NS (2014a) How models of creativity and analogy need to answer the tailorability concern. In: Besold TR, Kühnberger KU, Schorlemmer M, Smaill A (eds) Computational creativity research: towards creative machines, chap 5. Atlantis Press, ParisGoogle Scholar
  72. Licato J, Sun R, Bringsjord S (2014b) Using a hybrid cognitive architecture to model children’s errors in an analogy task. In: Proceedings of CogSci 2014Google Scholar
  73. Licato J, Marton N, Dong B, Sun R, Bringsjord S (2015) Modeling the creation and development of cause-effect pairs for explanation generation in a cognitive architecture. In: Proceedings of the 2015 international workshop on artificial intelligence and cognition (AIC 2015)Google Scholar
  74. Macagno F, Walton D (2009) Argument from analogy in law, the classical tradition, and recent theories. Philos Rhetor 42(2):154CrossRefGoogle Scholar
  75. Maher P (2007) Explication defended. Stud Log 86(2):331–341MathSciNetzbMATHCrossRefGoogle Scholar
  76. Marcus G, Davis E (2012) How robust are probabilistic models of higher-level cognition? Psychol Sci 24(12):2351–2360CrossRefGoogle Scholar
  77. Marcus G, Davis E (2015) Still searching for principles: a response to Goodman et al (2015). Psychol Sci 26(4):542–544CrossRefGoogle Scholar
  78. Markman AB, Otto AR (2011) Cognitive systems optimize energy rather than information. Behav Brain Sci 34:207CrossRefGoogle Scholar
  79. Marr D (1982) Vision: a computational approach. Freeman and Co., New YorkGoogle Scholar
  80. McClamrock R (1991) Marr’s three levels: a re-evaluation. Mind Mach 1(2):185–196CrossRefGoogle Scholar
  81. McCulloch WS, Pitts W (1943) A logical calculus of the ideas immanent in nervous activity. Bull Math Biophys 5(4):115–133MathSciNetzbMATHCrossRefGoogle Scholar
  82. Mikolov T, Chen K, Corrado G, Dean J (2013a) Efficient estimation of word representations in vector space. arXiv preprint arXiv:1301.3781
  83. Mikolov T, Sutskever I, Chen K, Corrado GS, Dean J (2013b) Distributed representations of words and phrases and their compositionality. In: Advances in neural information processing systems, pp 3111–3119Google Scholar
  84. Newell A (1982) The knowledge level. Artif Intell 18(1):87–127MathSciNetCrossRefGoogle Scholar
  85. Novaes CD, Reck E (2017) Carnapian explication, formalisms as cognitive tools, and the paradox of adequate formalization. Synthese 194(1):195–215MathSciNetzbMATHCrossRefGoogle Scholar
  86. Pearl J (1996) The art and science of cause and effect. Lecture given as part of the UCLA Faculty Research Lectureship ProgramGoogle Scholar
  87. Peirce CS (1933) Existential graphs. In: Hartshorne C, Weiss P (eds) The simplest mathematics, The collected papers of Charles Sanders Peirce, vol 4. Harvard University Press, Cambridge, pp 347–584Google Scholar
  88. Podsakoff PM, McKenzie SB, Podsakoff NP (2016) Recommendations for creating better concept definitions in the organizational, behavioral, and social sciences. Organ Res Methods 19(2):159–203CrossRefGoogle Scholar
  89. Pylyshyn Z (1984) Computation and cognition. MIT Press, CambridgeGoogle Scholar
  90. Rachkovskij DA, Kussul EM, Baidyk TN (2013) Building a world model with structure-sensitive sparse binary distributed representations. Biologically inspired cognitive architectures 3:64–86CrossRefGoogle Scholar
  91. Reed C, Rowe G (2004) Araucaria: software for argument analysis, diagramming and representation. Int J AI Tools 14(3–4):961–980CrossRefGoogle Scholar
  92. Reed C, Budzynska K, Duthie R, Janier M, Konat B, Lawrence J, Pease A, Snaith M (2017) The argument web: an online ecosystem of tools, systems and services for argumentation. Philos Technol 30(2):137–160CrossRefGoogle Scholar
  93. Satel S, Lilenfeld SO (2013) Brainwashed: the seductive appeal of mindless neuroscience, kindle edition. Basic Books, LondonGoogle Scholar
  94. Schmidt M, Krumnack U, Gust H, Kühnberger KU (2014) Heuristic-driven theory projection: an overview. In: Computational approaches to analogical reasoning: current trends studies in computational intelligence, vol 548Google Scholar
  95. Schwering A, Krumnack U, Kühnberger Ku, Gust H (2009) Syntactic principles of heuristic-driven theory projection. Cogn Syst Res 10(3):251–269CrossRefGoogle Scholar
  96. Searle J (2004) Mind: a brief introduction. Oxford University Press, New YorkGoogle Scholar
  97. Smith P (2007) An introduction to Gödel’s theorems. Cambridge University Press, CambridgezbMATHCrossRefGoogle Scholar
  98. Stapleton G, Jamnik M, Shimojima A (2015) Effective representation of information: generalizing free rides. In: Proceedings of the 9th international conference on diagrammatic representation and inference, pp 296–299Google Scholar
  99. Stewart T, Eliasmith C (2012) Compositionality and biologically plausible models. In: Hinzen W, Werning M, Machery E (eds) Oxford handbook of compositionality. Oxford University Press, OxfordGoogle Scholar
  100. Sun R (1991) Connectionist models of rule-based reasoning. In: Proceedings of the 13th cognitive science society conference. Lawrence Erlbaum, pp 437–442Google Scholar
  101. Sun R (2001a) Computation, reduction and teleology of consciousness. J Cogn Syst Res 1(4):241–249CrossRefGoogle Scholar
  102. Sun R (2001b) From implicit skills to explicit knowledge: a bottom-up model of skill learning. Cogn Sci 25(2):203–244CrossRefGoogle Scholar
  103. Sun R (2002) Duality of the mind: a bottom up approach toward cognition. Lawrence Erlbaum, MahwahGoogle Scholar
  104. Sun R (2004) Desiderata for cognitive architectures. Philos Psychol 17(3):341–373Google Scholar
  105. Taddeo M, Floridi L (2007) A praxical solution of the symbol grounding problem. Mind Mach 17(4):369–389CrossRefGoogle Scholar
  106. Thibodeau PH, Sikos L, Durgin FH (2016) What do we learn from rating metaphors? In: Proceedings from the 2016 conference of the Cognitive Science Society (CogSci 2016)Google Scholar
  107. Turner R, Angius N (2017) The philosophy of computer science. In: Zalta EN (ed) The Stanford encyclopedia of philosophy, spring 2017 edn. Metaphysics Research Lab, Stanford University, StanfordGoogle Scholar
  108. Uesaka Y, Igarashi M, Suetsugu R (2016) Promoting multi-perspective integration as a 21st century skill: the effects of instructional methods encouraging students’ spontaneous use of tables for organizing information. In: Jamnik M, Uesaka Y, Elzer Schwartz S (eds) Diagrammatic representation and inference: proceedings from the 9th international conference, Diagrams 2016, Lecture Notes in Computer Science, vol 9781. SpringerGoogle Scholar
  109. Urbas M, Jamnik M (2014) A framework for heterogeneous reasoning in formal and informal domains. In: Proceedings of the third international conference on diagrammatic representation and inference, pp 277–292Google Scholar
  110. Vernon D, van Hofsten C, Fadiga L (2016) Desiderata for developmental cognitive architectures. Biol Inspir Cogn Archit 18:116–127Google Scholar
  111. Vincent P, Larochelle H, Lajoie I, Bengio Y, Manzagol PA (2010) Stacked denoising autoencoders: learning useful representations in a deep network with a local denoising criterion. J Mach Learn Res 11:3371–3408MathSciNetzbMATHGoogle Scholar
  112. Vorms M (2009) Formats of Representation in Scientific Theorising. In: Models and simulations 3: emergence, computation, and reality, Charlottesville, VA, USAGoogle Scholar
  113. Walton D (1985) Arguer’s position: a pragmatic study of ad hominem attack, criticism, refutation, and fallacy. Greenwood Press, WestportGoogle Scholar
  114. Walton D (1999) One-sided arguments: a dialectical analysis of bias. State University of New York Press, AlbanyGoogle Scholar
  115. Walton D, Reed C, Macagno F (2008) Argumentation schemes. Cambridge University Press, CambridgezbMATHCrossRefGoogle Scholar
  116. Willingham DB, Nissen MJ, Bullemer P (1989) On the development of procedural knowledge. J Exp Psychol Learn Mem Cogn 15:1047–1060CrossRefGoogle Scholar
  117. Winograd T (1975) Frame representations and the declarative-procedural controversy. In: Bobrow D, Collins A (eds) Representation and understanding: studies in cognitive science. Academic Press, New YorkGoogle Scholar
  118. Wyss M, Thieme A, Licato J (2017) Can AI reason over representational systems? In: Licato J, Hayes A (eds) Proceedings of the 28th modern artificial intelligence and cognitive science (MAICS) conferenceGoogle Scholar
  119. Xing C, Corter JE, Zahner D (2016) Diagrams affect choice of strategy in probability problem solving. In: Jamnik M, Uesaka Y, Elzer Schwartz S (eds) Diagrammatic representation and inference: proceedings from the 9th international conference, Diagrams 2016. Lecture Notes in Computer Science, vol 9781. SpringerGoogle Scholar
  120. Zoph B, Le QV (2017) Neural architecture search with reinforcement learning. CoRR arXiv:1611.01578

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Authors and Affiliations

  1. 1.University of South FloridaTampaUSA
  2. 2.Purdue University, Fort WayneFort WayneUSA

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