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{{user draft|date=September 2014}}
'''Dynamic logic''' (DL) has been created by [[Leonid Perlovsky]] to overcome [[computational complexity]] encountered since the 1960s in artificial intelligence, modeling the mind, and in many areas of applied and engineering mathematics <ref>Perlovsky, L.I. 2001. Neural Networks and Intellect: using model based concepts. New York: Oxford University Press.</ref>,<ref>Perlovsky, L.I. (2006). Toward Physics of the Mind: Concepts, Emotions, Consciousness, and Symbols. Phys. Life Rev. 3(1), pp.22-55.</ref>. ▼
▲Dynamic logic (DL) has been created by [[Leonid Perlovsky]] to overcome [[computational complexity]] encountered since the 1960s in artificial intelligence, modeling the mind, and in many areas of applied and engineering mathematics <ref>Perlovsky, L.I. 2001. Neural Networks and Intellect: using model based concepts. New York: Oxford University Press.</ref>,<ref>Perlovsky, L.I. (2006). Toward Physics of the Mind: Concepts, Emotions, Consciousness, and Symbols. Phys. Life Rev. 3(1), pp.22-55.</ref>.
▲1. Combinatorial Complexity
The [[combinatorial complexity]] (CC) is often encountered due to a need to consider combinations of multiple elements. For example, in [[recognition]], [[detection]], or in modeling [[perception]] abilities of the mind, an object of interest should be found among many other objects. To find an object usually its observed [[pattern]] (on the screen or visual cortex) should be matched to a [[prototype]] or "mental [[representation]]" of this object. In this process a [[prototype]] or "mental [[representation]]" should be modified in many ways to match the observed pattern. This might require many computations. But even worse complexity is due to the fact that the process needs to identify pixels making up the object, and those belonging to other objects. In other words, surrounding objects have to be identified in parallel. Thus many [[prototypes]] (or [[representations]]) have to be matched to many patterns. This requires considering [[combinations]] of many patterns and [[prototypes]]. 100 objects in the field of view is not too many. But [[combinations] of 100 objects and prototypes is a very large number, 100100. This number is larger than all interactions of all [[elementary particles]] in the [[Universe]] in its entire lifetime. Thus this relatively simple problem seems unsolvable.
If [[Gödelian arguments]] leading to fundamental difficulties of [[logic]] ([[incompleteness]]) are applied to a finite system (a computer, or mind), the arguments do not lead to fundamental difficulty, but to CC <ref>Perlovsky, L.I. 2001. Neural Networks and Intellect: using model based concepts. New York: Oxford University Press.</ref>. Practically, from an algorithmic point of view CC is as bad as fundamental difficulty of logic. Or in other way, CC is as fundamental as [[Gödelian incompleteness]]. For this reason, any algorithm using [[classical logic]] (or simply [[logic]] for shortness) encounters CC. Moreover, algorithmic methods created specifically to overcome limitations of logic, such as [[neural networks]] or [[fuzzy systems]], still make logical steps, such as during [[training]], or during setting degree of [[fuzziness]], and thus encounter CC.
For the above reasons creating a mathematical technique capable of solving complex problems without using [[logic]] has been a fundamental problem. DL accomplishes this
by considering not logical states. Whereas [[classical logic]] operates with static logical states (e.g. "this is a chair"), DL operates with processes. DL processes proceed "from vague to crisp." From vague states ( or representations to crisp ones. Crisp, approximately logical states ([[prototypes]], [[representations]]") are achieved at the end of a DL process. Initial DL states are highly vague, so that any [[prototype]] matches all [[representation]] and there is no need to consider combinations of [[representations]]. In this way DL overcomes CC.
DL can be considered an extension of FL toward dynamic fuzziness.
DL algorithms solved many engineering problems unsolvable for decades, and problems from emerging areas, which could not have even be formulated mathematically. These include detection of objects below noise, tracking of objects below noise ("track before detect"), fusion of objects from diverse sources, swarm intelligence, learning situations, integration of language and cognition, emotionality of languages, hierarchical intelligence, cognitive models of conscious and unconscious, evolution of cultures, symbol processes, perceptual symbol system, grounding, binding, and others <ref> Perlovsky, L.I., Deming R.W., & Ilin, R. (2011). Emotional Cognitive Neural Algorithms with Engineering Applications. Dynamic Logic: from vague to crisp. Springer, Heidelberg, Germany </ref>.
DL has been experimentally demonstrated to be an adequate model of [[perception]] and [[cognition]] <ref> Bar, M.; Kassam, K.S.; Ghuman, A.S.; Boshyan, J.; Schmid, A.M.; Dale, A.M.; Hämäläinen, M.S.; Marinkovic, K.; Schacter, D.L.; Rosen, B.R.; et al. (2006). Top-down facilitation of visual recognition. Proc. Natl. Acad. Sci. USA, 103, 449–454</ref>; <ref> Perlovsky, L.I. (2009). ‘Vague-to-Crisp’ Neural Mechanism of Perception. IEEE Trans. Neural Networks, 20(8), 1363-1367</ref>.
DL is a mathematical foundation for cognitive models describing interaction between cognition and language <ref> Perlovsky, L.I. (2009). Language and Cognition. Neural Networks, 22(3), 247-257; doi:10.1016/j.neunet.2009.03.007</ref>; <ref> Perlovsky, L.I. & Ilin, R. (2010). Neurally and Mathematically Motivated Architecture for Language and Thought. Special Issue "Brain and Language Architectures: Where We are Now?" The Open Neuroimaging Journal, 4, 70-80; http://www.bentham.org/open/tonij/openaccess2.htm</ref>. These models made a number of unique observable predictions, some of them were confirmed, none were disconfirmed.
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This is a previously unsolved problem in cognition, psychology, and philosophy; in particular, musical emotions Aristotle considered an unsolved problem, and Darwin considered the greatest mystery <ref> Perlovsky, L.I. (2014a). Aesthetic emotions, what are their cognitive functions? Front. Psychol. 5:98; http://www.frontiersin.org/Journal/10.3389/fpsyg.2014.00098/full; doi:10.3389/fpsyg.2014.0009</ref>. DL predicts certain difficulties in measuring aesthetic emotions <ref> Perlovsky, L.I. (2014b). Mystery in experimental psychology, how to measure aesthetic emotions? http://journal.frontiersin.org/Journal/10.3389/fpsyg.2014.01006/impact#impact; doi: 10.3389/fpsyg.2014.01006 </ref>. These models have made a number of unique, experimentally verifiable predictions, in particular that emotions of the [[beautiful]] are related to the meaning of life (which is mostly unconscious), and [[musical emotions]] are related to overcoming [[cognitive dissonances]] and keeping in mind contradictory knowledge; the later one has been experimentally confirmed <ref> Masataka, N. & Perlovsky, L.I. (2012). The efficacy of [[musical emotions]] provoked by Mozart's music for the reconciliation of [[cognitive dissonance]]. Scientific Reports 2, Article number: 694 doi:10.1038/srep00694 http://www.nature.com/srep/2013/130619/srep02028/full/srep02028.html</ref>, <ref> Perlovsky, L.I., Cabanac, A., Bonniot-Cabanac, M-C., Cabanac, M. (2013). Mozart Effect, Cognitive Dissonance, and the Pleasure of Music. ArXiv 1209.4017; Behavioural Brain Research, 244, 9-14 </ref>.
[[Aristotle]] was specific in emphasizing that [[logic]] is not a fundamental mechanism of the [[mind]] and suggested a theory of the mind similar to DL: [[forms]] of the [[mind]] ([[representations]]) are initially not logical, they become logical after "the mind meets matter" (in interaction of [[top-down]] with [[bottom-up]] signals) <ref> Perlovsky, L.I. (2013d). Learning in brain and machine - complexity, Gödel, Aristotle. Frontiers in Neurorobotics; doi: 10.3389/fnbot.2013.00023;
http://www.frontiersin.org/Neurorobotics/10.3389/fnbot.2013.00023/full</ref>.
==References==
{{reflist}}
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