Mathematical Model of Embodied Symbols: Cognition and Perceptual Symbol System

Leonid Perlovsky, Roman Ilin

Air Force Research Laboratory, Wright-Patterson Air Force Base, Greene & Montgomery, Ohio, USA.
Harvard University, Cambridge, USA.

DOI: 10.4236/jbbs.2012.22024                

Abstract

A mathematical model of perceptual symbol system is developed. This development requires new mathematical methods of dynamic logic (DL), which have overcome limitations of classical artificial intelligence and connectionist approaches. The paper discusses these past limitations, relates them to combinatorial complexity (exponential explosion) of algorithms in the past, and relates it further to the static nature of classical logic. DL is a process-logic; its salient property is evolution of vague representations into crisp. We first consider one aspect of PSS: situation learning from object perceptions. Next DL is related to PSS mechanisms of concepts, simulators, grounding, embodiment, productiveity, binding, recursion, and to the mechanisms relating embodied-grounded and amodal symbols. We discuss DL capability for modeling cognition on multiple levels of abstraction. PSS is extended toward interaction between cognition and language. Experimental predictions of the theory are discussed. They might influence experimental psychology and impact future theoretical developments in cognitive science, including knowledge representation, and mechanisms of interaction between perception, cognition, and language. All mathematical equations are also discussed conceptually, so mathematical understanding is not required. Experimental evidence for DL and PSS in brain imaging is discussed as well as future research directions.

Keywords

Perceptual Symbol System; Embodied Cognition; Perception; Knowledge Representation; Grounded Symbols; Dynamic Logic

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	L. W. Barsalou, “Perceptual Symbol Systems,” Behavioral and Brain Sciences, Vol. 22, No. 4, 1999, pp. 577-660.
[2]	S. M. Kosslyn, “Image and Mind,” Harvard University Press, Cambridge, 1980.
[3]	S. M. Kosslyn, “Image and Brain,” MIT Press, Cambridge, 1994.
[4]	L. W. Barsalou, “Abstraction as Dynamic Interpretation in Perceptual Symbol Systems,” In: L Gershkoff-Stowe, D. Rakison, Eds., Building Object Categories, Carnegie Symposia Series, Erlbaum, Mahwah, 2005, pp. 389-431.
[5]	L. W. Barsalou, “Grounding Symbolic Operations in the Brain’s Modal Systems,” In: G. R. Semin and E. R. Smith, Eds., Embodied Grounding: Social, Cognitive, Affective, and Neuroscientific Approaches, Cambridge University Press, New York, 2007.
[6]	L. W. Barsalou and C. R. Hale, “Components of Conceptual Representation: From Feature Lists to Recursive Frames,” In: I. Van Mechelen, J. Hampton, R. Michalski and P. Theuns, Eds., Categories and Concepts: Theoretical Views and Inductive Data Analysis, Academic Press, New York, 1993.
[7]	A. Cangelosi, A. Greco and S. Harnad, “From Robotic Toil to Symbolic Theft: Grounding Transfer from Entry-Level to Higher-Level Categories,” Connection Science, Vol. 12, No. 2, 2000, pp. 143-162. doi:10.1080/09540090050129763
[8]	A. Cangelosi and T. Riga, “An Embodied Model for Sensorimotor Grounding and Grounding Transfer: Experiments with Epigenetic Robots,” Cognitive Sciences, Vol. 30, No. 4, 2006, pp. 673-689. doi:10.1207/s15516709cog0000_72
[9]	W. K. Simmons and L. W. Barsalou, “The Similarity-in-Topography Principle: Reconciling Theories of Conceptual Deficits,” Cognitive Neuropsychology, Vol. 20, 2003, pp. 451-486. doi:10.1080/02643290342000032
[10]	L. I. Perlovsky, “Computational Concepts in Classification: Neural Networks, Statistical Pattern Recognition, and Model Based Vision,” Journal of Mathematical Imaging and Vision, Vol. 4, No. 1, 1994, pp. 81-110. doi:10.1007/BF01250006
[11]	L. I. Perlovsky, “Physical Concepts of Intellect,” Proceedings of Russian Academy of Sciences, Vol. 354, No. 3, 1997, pp. 320-323.
[12]	L. I. Perlovsky, “Neural Networks and Intellect: Using Model-Based Concepts,” 3rd Edition, Oxford University Press, New York, 2001.
[13]	L. I. Perlovsky, “Physical Theory of Information Processing in the Mind: Concepts and Emotions,” SEED on Line Journal, Vol. 2, No. 2, 2002, pp. 36-54.
[14]	L. I. Perlovsky, “Statistical Limitations on Molecular Evolution,” Journal of Biomolecular Structure and Dynamics, Vol. 19, No. 6, 2002, pp. 1031-1043.
[15]	L. I. Perlovsky, “Toward Physics of the Mind: Concepts, Emotions, Consciousness, and Symbols,” Physical Life Review, Vol. 3, No. 1, 2006, pp. 22-55. doi:10.1016/j.plrev.2005.11.003
[16]	L. I. Perlovsky, “Fuzzy Dynamic Logic,” New Mathematics and Natural Computation, Vol. 2, No. 1, 2006, pp. 43-55. doi:10.1142/S1793005706000300
[17]	L. I. Perlovsky, “Cognitive High Level Information Fusion,” Information Sciences, Vol. 177, 2007, pp. 2099-2118. doi:10.1016/j.ins.2006.12.026
[18]	S. Grossberg, “Neural Networks and Natural Intelligence,” MIT Press, Cambridge, 1988.
[19]	M. Bar, K. S. Kassam, A. S. Ghuman, J. Boshyan, A. M. Schmid, et al., “Top-Down Facilitation of Visual Recognition,” Proceedings of the National Academy of Sciences, Vol. 103, No. 2, 2006, pp. 449-454. doi:10.1073/pnas.0507062103
[20]	D. L. Schacter and D. R. Addis, “The Ghosts of Past and Future,” Nature, Vol. 445, No. 7123, 2007, p. 27. doi:10.1038/445027a
[21]	L. I. Perlovsky, “Conundrum of Combinatorial Complexity,” IEEE Transactions on PAMI, Vol. 20, No. 6, 1998, pp. 666-670. doi:10.1109/34.683784
[22]	R. E. Bellman, “Adaptive Control Processes,” Princeton University Press, Princeton, 1961.
[23]	M. L. Minsky, “A Framework for Representing Knowledge,” In: P. H. Whinston, Ed., The Psychology of Computer Vision, McGraw-Hill Book, New York, 1975.
[24]	P. H. Winston, “Artificial Intelligence,” Addison-Wesley. Reading, 1984.
[25]	N. Chomsky, “Language and Mind. Harcourt Brace Javanovich,” Harcourt Brace Jovanovich, Inc., New York, 1972.
[26]	R. Nevatia and T. O. Binford, “Description and Recognition of Curved Objects,” Artificial Intelligence, Vol. 8, No. 1, 1977, pp. 77-98. doi:10.1016/0004-3702(77)90006-6
[27]	P. P. Bonnisone, M. Henrion, L. N. Kanal and J. F. Lemmer, “Uncertainty in Artificial Intelligence 6,” North Holland, Amsterdam, 1991.
[28]	L. I. Perlovsky, “Multiple Sensor Fusion and Neural Networks,” DARPA Neural Network Study, 1987.
[29]	L. I. Perlovsky, “Cramer-Rao Bounds for the Estimation of Means in a Clustering Problem,” Pattern Recognition Letters, Vol. 8, No. 1, 1988, pp. 1-3. doi:10.1016/0167-8655(88)90015-3
[30]	L. I. Perlovsky, “Cramer-Rao Bounds for the Estimation of Normal Mixtures,” Pattern Recognition Letters, Vol. 10, No. 3, 1989, pp. 141-148. doi:10.1016/0167-8655(89)90079-2
[31]	L. I. Perlovsky, “A Model Based Neural Network for Transient Signal Processing,” Neural Networks, Vol. 7, No. 3, 1994, pp. 565-572. doi:10.1016/0893-6080(94)90113-9
[32]	L. I. Perlovsky, “Cramer-Rao Bound for Tracking in Clutter and Tracking Multiple Objects,” Pattern Recognition Letters, Vol. 18, No. 3, 1997, pp. 283-288. doi:10.1016/S0167-8655(97)00009-3
[33]	N. Chomsky, “Principles and Parameters in Syntactic Theory,” In: N. Hornstein and D. Lightfoot, Eds., Explanation in Linguistics. The Logical Problem of Language Acquisition, Longman, London, 1981.
[34]	R. A. Singer, R. G. Sea and R. B. Housewright, “Derivation and Evaluation of Improved Tracking Filters for Use in Dense Multitarget Environments,” IEEE Transactions on Information Theory, IT-20, 1974, pp. 423-432. doi:10.1109/TIT.1974.1055256
[35]	L. I. Perlovsky and M. M. McManus, “Maximum Likelihood Neural Networks for Sensor Fusion and Adaptive Classification,” Neural Networks, Vol. 4, No. 1, 1991, pp. 89-102. doi:10.1016/0893-6080(91)90035-4
[36]	L. I. Perlovsky, “Beauty and Mathematical Intellect,” Zvezda, Vol. 9, 2000, pp. 190-201.
[37]	L. I. Perlovsky, “Integrating Language and Cognition,” IEEE Connections, Feature Article, Vol. 2, No. 2, 2004, pp. 8-12.
[38]	L. I. Perlovsky, “The Mind vs Logic: Aristotle and Zadeh,” Society for Mathematics of Uncertainty, Critical Review, Vol. 1, No. 1, 2007, pp. 30-33.
[39]	L. I. Perlovsky, “‘Vague-to-Crisp’ Neural Mechanism of Perception,” IEEE Transactions on Neural Networks, Vol. 20, No. 8, 2009, pp. 1363-1367. doi:10.1109/TNN.2009.2025501
[40]	L. I. Perlovsky, “Intersections of Mathematical, Cognitive, and Aesthetic Theories of Mind,” Psychology of Aesthetics, Creativity, and the Arts, Vol. 4, No. 1, 2010, pp. 11-17. doi:10.1037/a0018147
[41]	L. I. Perlovsky, “Neural Mechanisms of the Mind, Aristotle, Zadeh, and fMRI,” IEEE Transactions on Neural Networks, Vol. 21, No. 5, 2010, pp. 718-733. doi:10.1109/TNN.2010.2041250
[42]	L. I. Perlovsky, “Evolution of Languages, Consciousness, and Cultures,” IEEE Computational Intelligence Magazine, Vol. 2, No. 3, 2007, pp. 25-39. doi:10.1109/MCI.2007.385364
[43]	L. I. Perlovsky, “Symbols: Integrated Cognition and Language,” In: R. Gudwin and J. Queiroz, Eds., Semiotics and Intelligent Systems Development, Idea Group, Hershey, 2007, pp. 121-151.
[44]	Aristotle, “The Complete Works,” J. Barnes, Ed., Princeton University Press, Princeton, 1995.
[45]	M. Davis, “The Universal Computer: The Road from Leibniz to Turing,” W. W. Norton and Company, New York, 2000.
[46]	D. Hilbert, “The Foundations of Mathematics,” In: J. van Heijenoort, Ed., From Frege to G?del, Harvard University Press, Cambridge, 1928/1967, p. 475.
[47]	K. G?del, “Collected Works, Vol. I, 1929-1936,” S. Feferman, J. W. Dawson, Jr. and S. C. Kleene, Eds., Oxford University Press, New York, 1994.
[48]	L. I. Perlovsky, “G?del Theorem and Semiotics. Proceedings of the Conference on Intelligent Systems and Semiotics’96,” Vol. 2, Gaithersburg, 1996, pp. 14-18.
[49]	L. I. Perlovsky, “Logic versus Mind,” Logica Universalis, 2012, in press.
[50]	E. E. Vityaev, L. I. Perlovsky, B. Y. Kovalerchuk and S. O. Speransky, “Probabilistic Dynamic Logic of the Mind and Cognition,” 2012, in press.
[51]	L. A. Zadeh, “Fuzzy Sets,” Information and Control, Vol. 8, No. 3, 1965, pp. 338-352. doi:10.1016/S0019-9958(65)90241-X
[52]	V. Kecman, “Learning and Soft Computing: Support Vector Machines, Neural Networks, and Fuzzy Logic Models (Complex Adaptive Systems),” The MIT Press, Cambridge, 2001.
[53]	R. Penrose, “Shadows of the Mind,” Oxford University Press, Oxford, 1994.
[54]	L. I. Perlovsky, “Music—The First Priciple,” Musical Theatre, 2006. http://www.ceo.spb.ru/libretto/kon_lan/ogl.shtml
[55]	L. I. Perlovsky, “Neural Networks, Fuzzy Models and Dynamic Logic,” In: R. K?hler and A. Mehler, Eds., Aspects of Automatic Text Analysis (Festschrift in Honor of Burghard Rieger), Springer, Heidelberg, 2007, pp. 363-386.
[56]	L. I. Perlovsky, “Neural Dynamic Logic of Consciousness: The Knowledge Instinct,” In: L. I. Perlovsky and R. Kozma, Eds., Neurodynamics of Higher-Level Cognition and Consciousness, Springer Verlag, Heidelberg, 2007. doi:10.1007/978-3-540-73267-9_5
[57]	L. I. Perlovsky, “Dynamic Logic,” 2010. http://www.scitopics.com/Dynamic_logic.html.
[58]	L. I. Perlovsky, “Dynamic Logic, Computational Complexity, Engineering and Mathematical Breakthroughs,” 2010. http://www.scitopics.com/Dynamic_logic_computational_complexity_engineering_and_mathematical_breakthroughs.ht ml
[59]	L. I. Perlovsky, “Dynamic Logic,” Cognitive Breakthroughs, 2010. http://www.scitopics.com/Dynamic_Logic_Cognitive_Breakthroughs.html
[60]	L. I. Perlovsky, “Mind Mechanisms: Concepts, Emotions, Instincts, Imagination, Intuition, Beautiful, Spiritually Sublime,” 2010. http://www.scitopics.com/Mind_mechanisms_concepts_emotions_instincts_imagination_intuition_beautiful_spiri tually_sublime.html
[61]	L. I. Perlovsky and R. Mayorga, “Preface,” In: R. Mayorga and L. I. Perlovsky, Eds., Sapient Systems, Springer, London, 2008.
[62]	L. I. Perlovsky and R. Kozma, “Editorial-Neurodynamics of Cognition and Consciousness,” In: L. Perlovsky and R. Kozma, Eds., Neurodynamics of Cognition and Consciousness, Springer Verlag, Heidelberg, 2007. doi:10.1007/978-3-540-73267-9_1
[63]	H. Harlow, “Mice, Monkeys, Men, and Motives,” Psychological Review, Vol. 60, No. 1, 1953, pp. 23-32. doi:10.1037/h0056040
[64]	L. Festinger, “A Theory of Cognitive Dissonance,” Row, Peterson, Evanston, 1957.
[65]	S. Grossberg and D. S. Levine, “Neural Dynamics of Attentionally Modulated Pavlovian Conditioning: Blocking, Inter-Stimulus Interval, and Secondary Reinforcement,” Psychobiology, Vol. 15, No. 3, 1987, pp. 195-240.
[66]	L. I. Perlovsky, “Aesthetics and Mathematical Theories of Intellect,” Iskusstvoznanie, Vol. 2, No. 2, 2002, pp. 558-594.
[67]	L. I. Perlovsky, “Sapience, Consciousness, and the Knowledge Instinct (Prolegomena to a Physical Theory),” In: R. Mayorga and L. I. Perlovsky, Eds., Sapient Systems, Springer, London, 2008.
[68]	R. W. Deming and L. I. Perlovsky, “Concurrent Multi-Target Localization, Data Association, and Navigation for a Swarm of Flying Sensors,” Information Fusion, Vol. 8, No. 3, 2007, pp. 316-330. doi:10.1016/j.inffus.2005.11.001
[69]	L. I. Perlovsky and R. W. Deming, “Neural Networks for Improved Tracking,” IEEE Transactions on Neural Networks, Vol. 18, No. 6, 2007, pp. 1854-1857. doi:10.1109/TNN.2007.903143
[70]	R. W. Deming, J. Schindler and L. I. Perlovsky, “Multitarget/Multisensor Tracking Using Only Range and Doppler Measurements,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 45, No. 2, 2009, pp. 593-611. doi:10.1109/TAES.2009.5089543
[71]	R. Mayorga and L. I. Perlovsky, Eds., “Sapient Systems,” Springer, London, 2008.
[72]	L. I. Perlovsky, R. P. Coons, R. L. Streit, T. E, Luginbuhl and S. Greineder, “Application of MLANS to Signal Classification,” Journal of Underwater Acoustics, Vol. 44, No. 2, 1994, pp. 783-809.
[73]	L. I. Perlovsky, and J. V. Jaskolski “Maximum Likelihood Adaptive Neural Controller,” Neural Networks, Vol. 7, No. 4, 1994, pp. 671-680. doi:10.1016/0893-6080(94)90044-2
[74]	L. I. Perlovsky, J. A. Chernick and W. H. Schoendorf, “Multi-Sensor ATR and Identification Friend or Foe Using MLANS,” Neural Networks, Vol. 8, No. 7-8, 1995, pp. 1185-1200. doi:10.1016/0893-6080(95)00078-X
[75]	L. I. Perlovsky, W. H. Schoendorf, D. M. Tye and W. Chang, “Concurrent Classification and Tracking Using Maximum Likelihood Adaptive Neural System,” Journal of Underwater Acoustics, Vol. 45, No. 2, 1995, pp. 399-414.
[76]	L. I. Perlovsky, C. P. Plum, P. R. Franchi, E. J. Tichovolsky, D. S. Choi and B. Weijers, “Einsteinian Neural Network for Spectrum Estimation,” Neural Networks, Vol. 10, No. 9, 1997, pp. 1541-1546. doi:10.1016/S0893-6080(97)00081-6
[77]	L. I. Perlovsky, W. H. Schoendorf, L. Garvin and C. Chang, “Development of Concurrent Classification and Tracking for Active Sonar,” Journal of Underwater Acoustics, Vol. 47, No. 2, 1997, pp. 375-388.
[78]	L. I. Perlovsky, W. H. Schoendorf, B. J. Burdick and D. M. Tye, “Model-Based Neural Network for Target Detection in SAR Images,” IEEE Transations on Image Processing, Vol. 6, No. 1, 1997, pp. 203-216. doi:10.1109/83.552107
[79]	L. I. Perlovsky, V. H. Webb, S. R. Bradley and C. A. Hansen, “Improved ROTHR Detection and Tracking Using MLANS,” AGU Radio Science, Vol. 33, No. 4, 1998, pp. 1034-1044.
[80]	R. Kozma, M. Puljic and L. I. Perlovsky, “Modeling Goal-Oriented Decision Making through Cognitive Phase Transitions,” New Mathematics and Natural Computation, Vol. 5, No. 1, 2009, pp. 143-157. doi:10.1142/S1793005709001246
[81]	B. Kovalerchuk, L. I. Perlovsky and G. Wheeler, “Modeling of Phenomena and Dynamic Logic of Phenomena,” Journal of Applied Non-Classical Logics, Vol. 22, No. 1, 2012, in press.
[82]	H. Yardley, L. I. Perlovsky and M. Bar, “Predictions and Incongruency in Object Recognition: A Cognitive Neuroscience Perspective,” In: Detection and Identification of Rare Audiovisual Cues. Studies in Computational Intelligence Series, Springer Publishing, 2012, in press. doi:10.1007/978-3-642-24034-8_12
[83]	L. I. Perlovsky and R. Kozma, Eds., “Neurodynamics of Higher-Level Cognition and Consciousness,” Springer-Verlag, Heidelberg, 2007.
[84]	L. I. Perlovsky, “Modeling Field Theory of Higher Cognitive Functions,” In: A. Loula, R. Gudwin and J. Queiroz, Eds., Artificial Cognition Systems, Idea Group, Hershey, 2007, pp. 64-105.
[85]	R. Ilin and L. I. Perlovsky, “Cognitively Inspired Neural Network for Recognition of Situations,” International Journal of Natural Computing Research, Vol. 1, No. 1, 2009, in print.
[86]	R. Ilin and L. I. Perlovsky, “Cognitively Inspired Neural Network for Recognition of Situations,” International Journal of Natural Computing Research, Vol. 1, No. 1, 2010, pp. 36-55. doi:10.4018/jncr.2010010102
[87]	S. Pinker, “The Language Instinct: How the Mind Creates Language,” William Morrow, New York, 1994.
[88]	S. Pinker, “The Stuff of Thought: Language as a Window into Human Nature,” Penguin, New York, 2008.
[89]	L. I. Perlovsky, “Language and Emotions: Emotional Sapir-Whorf Hypothesis,” Neural Networks, Vol. 22, No. 5-6, 2009, pp. 518-526. doi:10.1016/j.neunet.2009.06.034
[90]	L. I. Perlovsky, “Music and Emotions. Functions, Origins, Evolution,” 2010. http://www.scitopics.com/Music_and_Emotions_Functions_Origins_Evolution.html
[91]	L. I. Perlovsky, “‘High’ Cognitive Emotions in Language Prosody,” Physics of Life Reviews, Vol. 8, No. 4, 2011, pp. 408-409. doi:10.1016/j.plrev.2011.10.007
[92]	S. Petrov, F. Fontanari and L. I. Perlovsky, “Categories of Emotion Names in Web Retrieved Texts,” Emotions, 2012, in press.
[93]	L. I. Perlovsky, “Computational Intelligence Applications for Defense,” IEEE Computational Intelligence Magazine, Vol. 6, No. 1, 2011, pp. 20-28. doi:10.1109/MCI.2010.939581
[94]	L. I. Perlovsky, “Language and Cognition,” Neural Networks, Vol. 22, No. 3, 2009, pp. 247-257. doi:10.1016/j.neunet.2009.03.007
[95]	L. I. Perlovsky, “Language and Cognition Interaction Mechanisms,” 2010. http://www.scitopics.com/Language_and_Cognition_Interaction_Mechanisms.html
[96]	L. I. Perlovsky, “Beauty and art. Cognitive function and Evolution,” 2010. http://www.scitopics.com/Beauty_and_art_Cognitive_function_and_evolution.html
[97]	L. I. Perlovsky, “Science and Religion: New Cognitive Findings Bridge the Fundamental Gap,” 2010. http://www.scitopics.com/Science_and_Religion_New_cognitive_findings_bridge_the_fundamental_gap.html
[98]	L. I. Perlovsky, “Abstract Concepts in Language and Cognition,” Physics of Life Reviews, Vol. 8, No. 4, 2011, pp. 375-376. doi:10.1016/j.plrev.2011.10.006
[99]	L. I. Perlovsky, “Emotions of ‘Higher’ Cognition,” Brain and Behavior Sciences, 2012, in press.
[100]	L. I. Perlovsky, “Nonlinear Dynamics and Higher Cognitive Mental Functions,” Physics of Life Reviews, Vol. 9, No. 1, 2012, pp. 74-75. doi:10.1016/j.plrev.2011.12.004
[101]	L. I. Perlovsky and R. Ilin, “Neurally and Mathematically Motivated Architecture for Language and Thought, Special Issue ‘Brain and Language Architectures: Where We Are Now?’” The Open Neuroimaging Journal, Vol. 4, 2010, pp. 70-80. http://www.bentham.org/open/tonij/openaccess2.htm doi:10.2174/1874440001004020070
[102]	L. I. Perlovsky and R. Ilin, “CWW, Language, and Thinking, New Mathematics and Natural Computations,” 2012, in press.
[103]	E. Spelke, “Principles of Object Perception,” Cognitive Science, Vol. 14, No. 1, 1990, pp. 29-56. doi:10.1207/s15516709cog1401_3
[104]	M. D. Hauser, N. Chomsky and W. T. Fitch, “The Faculty of Language: What Is It, Who Has It, and How Did It Evolve?” Science, Vol. 298, No. 5988, 2002, pp. 1569-1579. doi:10.1126/science.298.5598.1569
[105]	L. W. Barsalou, “Abstraction in Perceptual Symbol Systems,” Philosophical Transactions of the Royal Society of London: Biological Sciences, Vol. 358, No. 1435, 2003, pp. 1177-1187. doi:10.1098/rstb.2003.1319
[106]	L. W. Barsalou, “Grounded Cognition,” Annual Review Psychology, Vol. 59, No. 1, 2008, pp. 617-645. doi:10.1146/annurev.psych.59.103006.093639
[107]	W. Yeh and L. W. Barsalou, “The Situated Nature of Concepts,” American Journal of Psychology, Vol. 119, No. 3, 2006, pp. 349-384. doi:10.2307/20445349
[108]	L. I. Perlovsky, “Joint Acquisition of Language and Cognition,” Webmed Central Brain, Vol. 1, No. 10, 2010, Article ID WMC00994. http://www.webmedcentral.com/article_view/994
[109]	L. I. Perlovsky, “Language, Emotions, and Cultures: Emotional Sapir-Whorf Hypothesis,” Webmed Central Psychology, Vol. 2, No. 2, 2011, Article ID WMC001580.
[110]	L. I. Perlovsky, “Language and Cognition Interaction Neural Mechanisms,” Computational Intelligence and Neuroscience, 2011, Article ID 454587. http://www.hindawi.com/journals/cin/contents/
[111]	L. I. Perlovsky, “Brain: Conscious and Unconscious Mechanisms of Cognition, Emotions, and Language,” Brain Sciences, Special Issue, 2012, in press.
[112]	L. I. Perlovsky, “The Cognitive Function of Emotions of Spiritually Sublime,” Review of Psychology Frontier, 2012, in press.
[113]	L. I. Perlovsky, “Emotionality of Languages Affects Evolution of Cultures,” Review of Psychology Frontier, 2012, in press.
[114]	L. I. Perlovsky, “Languages and Cultures: Emotional Sapir-Whorf Hypothesis (ESWH),” 2010. http://www.scitopics.com/Languages_and_Cultures_Emotional_Sapir_Whorf_Hypothesis_ESWH.html
[115]	J. F. Fontanari and L. I. Perlovsky, “Evolving Compositionality in Evolutionary Language Games,” IEEE Transactions on Evolutionary Computations, Vol. 11, No. 6, 2007, pp. 758-769.
[116]	L. I. Perlovsky, “Mirror Neurons, Language, and Embodied Cognition,” Neural networks, 2012, in press.
[117]	J. F. Fontanari and L. I. Perlovsky, “How Language Can Help Discrimination in the Neural Modeling Fields Frame-work,” Neural Networks, Vol. 21, No. 2-3, 2008, pp. 250-256. doi:10.1016/j.neunet.2007.12.007
[118]	J. F. Fontanari and L. I. Perlovsky, “A Game Theoretical Approach to the Evolution of Structured Communication Codes,” Theory in Biosciences, Vol. 127, No. 3, 2008, pp. 205-214. doi:10.1007/s12064-008-0024-1
[119]	J. F. Fontanari, V. Tikhanoff, A. Cangelosi, R. Ilin and L. I. Perlovsky, “Cross-Situational Learning of Object-Word mapping Using Neural Modeling Fields,” Neural Networks, Vol. 22, No. 5-6, 2009, pp. 579-585. doi:10.1016/j.neunet.2009.06.010
[120]	L. I. Perlovsky, “Jihadism and Grammars. Comment to “Lost in Translation,” Wall Street Journal, 2010. http://online.wsj.com/community/leonidperlovsky/activity
[121]	L. Boroditsky and M. Ramscar, “The Roles of Body and Mind in Abstract Thought,” Psychological Science, Vol. 13, No. 2, 2002, pp. 185-188. doi:10.1111/1467-9280.00434
[122]	V. Tikhanoff, J. F. Fontanari, A. Cangelosi and L. I. Perlovsky, “Language and Cognition Integration through Modeling Field Theory: Category Formation for Symbol Grounding,” Book Series in Computer Science, Vol. 4131, Springer, Heidelberg, 2006.
[123]	T. W. Deacon, “The Symbolic Species: The Co-Evolution of Language and the Brain,” Norton, New York, 1998.
[124]	F. De. Saussure, “Course in General Linguistics,” McGraw-Hill, New York, 1916/1965, p. 98.
[125]	C. S. Peirce, “Logic as Semiotic: The Theory of Signs,” 1897, 1903. In: Buchler, Ed., The Philosophical Writing of Peirce, Dover, In: Hartshorne and Weiss, Eds., Collected Papers V. II, Elements of Logic, Belknap, Cambridge, 1955.
[126]	C. G. Jung, “Psychological Types,” In: Collected Works, v.6, Bollingen Series XX, 1971, Princeton University Press, Princeton, 1921.
[127]	B. Russell, “Introduction to Mathematical Philosophy,” George Allen and Unwin, London, 1919, p. 175.
[128]	R. Carnap, “The Logical Syntax of Language,” Littlefield, Adams and Co, Totowa, 1959.
[129]	D. S. Levine and L. I. Perlovsky, “Neuroscientific Insights on Biblical Myths: Simplifying Heuristics versus Careful Thinking: Scientific Analysis of Millennial Spiritual Issues,” Zygon, Journal of Science and Religion, Vol. 43, No. 4, 2008, pp. 797-821.
[130]	L. I. Perlovsky, “Musical Emotions: Functions, Origin, Evolution,” Physics of Life Reviews, Vol. 7, No. 1, 2010, pp. 2-27. doi:10.1016/j.plrev.2009.11.001
[131]	L. I. Perlovsky, “The Mind Is Not a Kludge,” Skeptic, Vol. 15, No. 3, 2010, pp. 51-55.
[132]	L. I. Perlovsky, “Science and Religion: Scientific Understanding of Emotions of Religiously Sublime,” 2010, arXive.
[133]	L. I. Perlovsky, “Music. Cognitive Function, Origin, and Evolution of Musical Emotions,” Webmed Central PSYCHOLOGY, Vol. 2, No. 2, 2011, Article ID WMC001494.
[134]	L. I. Perlovsky, “Consciousness and Free Will, a Scientific Possibility Due to Advances in Cognitive Science,” Webmed Central Psychology, Vol. 2, No. 2, 2011, Article ID WMC001539
[135]	L. I. Perlovsky, “Free Will and Advances in Cognitive Science,” Open Journal of Philosophy, Vol. 2, No. 1, 2012, pp. 32-37. doi:10.4236/ojpp.2012.21005
[136]	L. I. Perlovsky, “Cognitive Function, Origin, and Evolution of Musical Emotions,” Musicae Scientiae, 2012, in press.
[137]	L. I. Perlovsky, “Cognitive Function of Music,” Interdisciplinary Science Reviews, 2012, in press.
[138]	L. I. Perlovsky, “Cognitive Function of Musical Emotions,” Psychomusicology, 2012, in press.
[139]	N. Masataka and L. I. Perlovsky, “Music Can Reduce Cognitive Dissonance,” 2012, in press.
[140]	L. I. Perlovsky, M.-C. Bonniot-Cabanac and M. Cabanac, “Curiosity and Pleasure,” 2010, arXive 1010.3009.
[141]	M. Bar, “The Proactive Brain: Using Analogies and Associations to Generate Predictions,” Trends in Cognitive Sciences, Vol. 11, No. 7, 2007, pp. 281-289. doi:10.1016/j.tics.2007.05.005
[142]	M. Bar, “Predictions: A Universal Principle in the Operation of the Human Brain (Introduction),” Philosophical Transactions of the Royal Society B, Vol. 364, No. 1521, 2009, pp. 1181-1182. doi:10.1098/rstb.2008.0321
[143]	L. Wu and L. W. Barsalou, “Perceptual Simulation in Conceptual Combination: Evidence from Property Generation,” Acta Psychologica, Vol. 132, No. 2, 2009, pp. 173-189. doi:10.1016/j.actpsy.2009.02.002
[144]	S. Van Danzig, D. Pecher, R. Zeelenberg and L. W. Barsalou, “Perceptual Processing Affects Conceptual Processing,” Cognitive Science, Vol. 32, 2008, pp. 579-590. doi:10.1080/03640210802035365
[145]	H. Brighton, K. Smith and S. Kirby, “Language as an Evolutionary System,” Physics of Life Reviews, Vol. 2, No. 3, 2005, pp. 177-226. doi:10.1016/j.plrev.2005.06.001
[146]	L. I. Perlovsky, “Evolving Agents: Communication and Cognition,” In: V. Gorodetsky, J. Liu and V. A. Skormin, Eds., Autonomous Intelligent Systems: Agents and Data Mining, Springer-Verlag GmbH, 2005, pp. 37-49. doi:10.1007/11492870_4
[147]	L. I. Perlovsky, “Jihad and Arabic Language. How Cognitive Science Can Help Us Understand the War on Terror,” 2010. http://www.scitopics.com/Jihad_and_Arabic_Language_How_Cognitive_Science_Can_Help_Us_Understand_the _War_on_Terror.html
[148]	L. I. Perlovsky, “New ‘Arrow of Time’: Evolution Increases Knowledge,” 2010. http://www.scitopics.com/New_Arrow_of_Time_Evolution_increases_knowledge.html
[149]	L. I. Perlovsky and A. Goldwag, “The Grammatical Roots of Jihadism: How Cognitive Science Can Help Us Understand the War on Terror,” Webmed Central Psychology, Vol. 2, No. 2, 2011, Article ID WMC001581.
[150]	L. F. Barrett and M. Bar, “See It with Feeling: Affective Predictions in the Human Brain,” Royal Society Philosophical B, Vol. 364, No. 1513, 2009, pp. 1325-1334.
[151]	L. I. Perlovsky, “Music and Consciousness,” Journal of Arts, Sciences and Technology, Vol. 41, No. 4, 2008, pp. 420-421.
[152]	J. F. Fontanari, M.-C. Bonniot-Cabanac, M. Cabanac and L. I. Perlovsky, “A Structural Model of Emotions of Cognitive Dissonances,” Neural Networks, 2012, in press. doi:10.1016/j.neunet.2012.04.007