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Computational creativity (also known as artificial creativity, mechanical creativity or creative computation) is a multidisciplinary endeavour that is located at the intersection of the fields of artificial intelligence, cognitive psychology, philosophy, and the arts.
The goal of computational creativity is to model, simulate or replicate creativity using a computer, to achieve one of several ends:
- to construct a program or computer capable of human-level creativity
- to better understand human creativity and to formulate an algorithmic perspective on creative behavior in humans
- to design programs that can enhance human creativity without necessarily being creative themselves
The field of computational creativity concerns itself with theoretical and practical issues in the study of creativity. Theoretical work on the nature and proper definition of creativity is performed in parallel with practical work on the implementation of systems that exhibit creativity, with one strand of work informing the other.
As measured by the amount of activity in the field (e.g., publications, conferences and workshops), computational creativity is a growing area of research. But the field is still hampered by a number of fundamental problems:
- Creativity is very difficult, perhaps even impossible, to define in objective terms.
- Creativity takes many forms in human activity, some eminent (meaning "recognized" or "ingenious", e.g., Einstein's creativity; sometimes referred to as "Creativity" with a capital C) and some mundane.
- Creativity can mean different things in different contexts: Is it a state of mind, a talent or ability, or a process? Does it describe a person, an activity or an end-product? Can collaborative work in which exceptional products emerge from simple interactions be considered creative?
These are problems that complicate the study of creativity in general, but certain problems attach themselves specifically to computational creativity:
- Can creativity be hard-wired? In existing systems to which creativity is attributed, is the creativity that of the system or that of the system's programmer or designer?
- How do we evaluate computational creativity? What counts as creativity in a computational system? Are natural language generation systems creative? Are machine translation systems creative? What distinguishes research in computational creativity from research in artificial intelligence generally?
- If eminent creativity is about rule-breaking or the disavowal of convention, how is it possible for an algorithmic system to be creative? In essence, this is a variant of the Ada Lovelace objection to machine intelligence, as recapitulated by modern theorists such as Teresa Amabile: If a machine can do only what it was programmed to do, how can its behavior ever be called creative?
Defining creativity in computational terms
Since no single perspective or definition seems to offer a complete picture of creativity, the AI researchers Newell, Shaw and Simon developed the combination of novelty and usefulness into the corner-stone of a multi-pronged view of creativity, one that uses the following four criteria to categorize a given answer or solution as creative:
- The answer is novel and useful (either for the individual or for society)
- The answer demands that we reject ideas we had previously accepted
- The answer results from intense motivation and persistence
- The answer comes from clarifying a problem that was originally vague
Notice how these criteria touch on many of the stereotypical themes that are typically associated with creativity: newness and value (1), transformation and revolution (2), passion and drive (3), vision and insight (4). These four criteria also combine elements of the producer-perspective and the product-perspective described earlier: criterion (1) characterizes the two most important qualities of a creative product, while criteria (2) – (4) characterize the attitude and actions of the producer of such a product. A given product may satisfy all or none of these criteria, but we should expect products that exhibit all four to be widely perceived as creative, while products that exhibit just some of these criteria will be judged with greater subjectivity and variation. Though no criterion is likely to be either necessary or sufficient, criterion (1) is perhaps the most common hallmark of creativity and thus serves to anchor the others. From a computational perspective, then, one can consider (1) to be a must-have feature, and (2) – (4) as desirable extras.
Newell and Simon are best known for their contribution to the search-in-a-state-space paradigm of AI, sometimes caricatured as Good Old Fashioned AI (GOFAI), and it is interesting to consider how the GOFAI paradigm can incorporate these criteria. From a search perspective, criterion (1) characterizes the goal or end-state of a computational search, criterion (4) characterizes the starting state from which the search is launched, criterion (3) characterizes the scale of the search, suggesting that many dead-ends are likely to be encountered, while criterion (2) suggests that well-worn pathways through the search space are best avoided if a creative end-state is to be reached.
Some high-level and philosophical themes recur throughout the field of computational creativity.Template:Clarify me
P-creativity and H-creativity
Margaret Boden refers to creativity that is novel merely to the agent that produces it as "P-creativity" (or "psychological creativity"), and refers to creativity that is recognized as novel by society at large as "H-creativity" (or "historical creativity").
Exploratory and transformational creativity
Boden also distinguishes between the creativity that arises from an exploration within an established conceptual space, and the creativity that arises from a deliberate transformation or transcendence of this space. She labels the former as "exploratory creativity" and the latter as "transformational creativity", seeing the latter as a form of creativity far more radical, challenging, and rarer than the former. Following Newell and Simon’s criteria, we can see that both forms of creativity should produce results that are appreciably novel and useful (criterion 1), but exploratory creativity is more likely to arise from a thorough and persistent search of a well-understood space (criterion 3) while transformational creativity should involve the rejection of some of the constraints that define this space (criterion 2) or some of the assumptions that define the problem itself (criterion 4).
Boden’s insights have guided work in computational creativity at a very general level, providing more an inspirational touchstone for development work than a technical framework of algorithmic substance. However, Boden’s insights are the subject of formalization, most notably in the work by Geraint Wiggins.
Generation and evaluation
The criterion that creative products should be novel and useful means that creative computational systems are typically structured into two phases, generation and evaluation. In the first phase, novel (to the system itself, thus P-Creative) constructs are generated; unoriginal constructs that are already known to the system are filtered at this stage. This body of potentially creative constructs are then evaluated, to determine which are meaningful and useful and which are not. This two-phase structure conforms to the Geneplore model of Finke, Ward and Smith, which is a psychological model of creative generation based on empirical observation of human creativity.
A great deal, perhaps all, of human creativity can be understood as a novel combination of pre-existing ideas or objects. Common strategies for combinatorial creativity include:
- placing a familiar object in an unfamiliar setting (e.g., Marcel Duchamp's Fountain) or an unfamiliar object in a familiar setting (e.g., a fish-out-of-water story such as The Beverly Hillbillies)
- Blending two superficially different objects or genres (e.g., a sci-fi story set in the Wild West, with robot cowboys, as in Westworld; Jewish haiku poems, etc.)
- Comparing a familiar object to a superficially unrelated and semantically distant concept (e.g., "Makeup is the Western burka"; "A zoo is a gallery with living exhibits")
- Adding a new and unexpected feature to an existing concept (e.g., adding a scalpel to a Swiss Army knife; adding a camera to a mobile phone)
- Compressing two incongruous scenarios into the same narrative to get a joke (e.g., the Emo Philips joke “Women are always using me to advance their careers. Damned anthropologists!”)
- Using an iconic image from one domain in a domain for an unrelated or incongruous idea or product (e.g., using the Marlboro Man image to sell cars, or to advertise the dangers of smoking-related impotence).
The combinatorial perspective allows us to model creativity as a search process through the space of possible combinations. The combinations can arise from composition or concatenation of different representations, or through a rule-based or stochastic transformation of initial and intermediate representations. Genetic algorithms and neural networks can be used to generate blended or crossover representations that capture a combination of different inputs.
Arthur Koestler proposes a very general model of creative combination in his 1964 book The Act of Creation, claiming that scientific discovery, art and humour are all linked by a common mechanism called "bisociation". Koestler lacked a formal, computational vocabulary for describing bisociation, which he defined as a reconciliation of two orthogonal matrices of thought (conceptual structures, mental spaces).
Mark Turner and Gilles Fauconnier  propose a model called Conceptual Integration Networks that elaborates upon the ideas of Koestler by synthesizing ideas from Cognitive Linguistic research into mental spaces and conceptual metaphors. Their basic model defines an integration network as four connected spaces:
- A first input space (contains one conceptual structure or mental space)
- A second input space (to be blended with the first input)
- A generic space of stock conventions and image-schemas that allow the input spaces to be understood from an integrated perspective
- A blend space in which a selected projection of elements from both input spaces are combined; inferences arising from this combination also reside here, sometimes leading to emergent structures that conflict with the inputs.
Fauconnier and Turner describe a collection of optimality principles that are claimed to guide the construction of a well-formed integration network. In essence, they see blending as a compression mechanism in which two or more input structures are compressed into a single blend structure. This compression operates on the level of conceptual relations. For example, a series of similarity relations between the input spaces can be compressed into a single identity relationship in the blend.
Blending theory is an elaborate framework that provides a rich terminology for describing the products of creative thinking, from metaphors to jokes to neologisms to adverts. It is most typically applied retrospectively, to describe how a blended conceptual structure could have arisen from a particular pair of input structures. These conceptual structures are often good examples of human creativity, but blending theory is not a theory of creativity, nor – despite its authors’ claims – does it describe a mechanism for creativity. The theory lacks an explanation for how a creative individual chooses the input spaces that should be blended to generate a desired result.
Nonetheless, some computational success has been achieved with the blending model by extending pre-existing computational models of analogical mapping that are compatible by virtue of their emphasis on connected semantic structures. More recently, Francisco Câmara Pereira presented an implementation of blending theory that employs ideas both from GOFAI and from genetic algorithms to realize some aspects of blending theory in a practical form; his example domains range from the linguistic to the visual, and the latter most notably includes the creation of mythical monsters by combining 3-D graphical models.
Language provides continuous opportunity for creativity, evident in the generation of novel sentences, phrasings, puns, neologisms, rhymes, allusions, sarcasm, irony, similes, metaphors, analogies, witticisms, and jokes. Native speakers of morphologically rich languages (including all Slavic languages) frequently create new word-forms that are easily understood, although they will never find their way to the dictionary. The area of natural language generation has been well studied, but these creative aspects of everyday language have yet to be incorporated with any robustness or scale.
Substantial work has been conducted in this area of linguistic creation since the 1970s, with the development of James Meehan's TALE-SPIN  system. TALE-SPIN viewed stories as narrative descriptions of a problem-solving effort, and created stories by first establishing a goal for the story’s characters so that their search for a solution could be tracked and recorded. The MINSTREL system represents a complex elaboration of this basis approach, distinguishing a range of character-level goals in the story from a range of author-level goals for the story. Systems like Bringsjord's BRUTUS elaborate these ideas further to create stories with complex inter-personal themes like betrayal. Nonetheless, MINSTREL explicitly models the creative process with a set of Transform Recall Adapt Methods (TRAMs) to create novel scenes from old. The MEXICA model of Rafael Pérez y Pérez and Mike Sharples is more explicitly interested in the creative process of storytelling, and implements a version of the engagement-reflection cognitive model of creative writing.
Metaphor and simile
Example of a metaphor: "She was an ape."
Example of a simile: "Felt like a tiger-fur blanket." The computational study of these phenomena has mainly focused on interpretation as a knowledge-based process. Computationalists such as Yorick Wilks, James Martin, Dan Fass, John Barnden, and Mark Lee have developed knowledge-based approaches to the processing of metaphors, either at a linguistic level or a logical level. Tony Veale and Yanfen Hao have developed a system, called Sardonicus, that acquires a comprehensive database of explicit similes from the web; these similes are then tagged as bona-fide (e.g., "as hard as steel") or ironic (e.g., "as hairy as a bowling ball", "as pleasant as a root canal"); similes of either type can be retrieved on demand for any given adjective. They use these similes as the basis of an on-line metaphor generation system called Aristotle that can suggest lexical metaphors for a given descriptive goal (e.g., to describe a supermodel as skinny, the source terms “pencil”, “whip”, “whippet”, “rope”, “stick-insect” and “snake” are suggested).
The process of analogical reasoning has been studied from both a mapping and a retrieval perspective, the latter being key to the generation of novel analogies. The dominant school of research, as advanced by Dedre Gentner. views analogy as a structure-preserving process; this view has been implemented in the structure mapping engine or SME, the MAC/FAC retrieval engine (Many Are Called, Few Are Chosen), ACME (Analogical Constraint Mapping Engine) and ARCS (Analogical Retrieval Constraint System). Other mapping-based approaches include Sapper, which situates the mapping process in a semantic-network model of memory. Analogy is a very active sub-area of creative computation and creative cognition; active figures in this sub-area include Douglas Hofstadter, Paul Thagard, and Keith Holyoak. Also worthy of note here is Peter Turney and Michael Littman's machine learning approach to the solving of SAT-style analogy problems; their approach achieves a score that compares well with average scores achieved by humans on these tests.
Humour is an especially knowledge-hungry process, and the most successful joke-generation systems to date have focussed on pun-generation, as exemplified by the work of Kim Binsted and Graeme Ritchie. This work includes the JAPE system, which can generate a wide range of puns that are consistently evaluated as novel and humorous by young children. An improved version of JAPE has been developed in the guise of the STANDUP system, which has been experimentally deployed as a means of enhancing linguistic interaction with children with communication disabilities. Some limited progress has been made in generating humour that involves other aspects of natural language, such as the deliberate misunderstanding of pronominal reference (in the work of Hans Wim Tinholt and Anton Nijholt), as well as in the generation of humorous acronyms in the HAHAcronym system of Oliviero Stock and Carlo Strapparava.
The blending of multiple word forms is a dominant force for new word creation in language; these new words are commonly called "blends" or "portmanteau words" (after Lewis Carroll). Tony Veale has developed a system called ZeitGeist that harvests neological headwords from Wikipedia and interprets them relative to their local context in Wikipedia and relative to specific word senses in WordNet. ZeitGeist has been extended to generate neologisms of its own; the approach combines elements from an inventory of word parts that are harvested from WordNet, and simultaneously determines likely glosses for these new words (e.g., "food traveller" for "gastronaut" and "time traveller" for "chrononaut"). It then uses Web search to determine which glosses are meaningful and which neologisms have not been used before; this search identifies the subset of generated words that are both novel ("H-creative") and useful. Neurolinguistic inspirations have been used to analyze the process of novel word creation in the brain, understand neurocognitive processes responsible for intuition, insight, imagination and creativity and to create a server that invents novel names for products, based on their description.
Like jokes, poems involve a complex interaction of different constraints, and no general-purpose poem generator adequately combines the meaning, phrasing, structure and rhyme aspects of poetry. Nonetheless, Pablo Gervás has developed a noteworthy system called ASPERA that employs a case-based reasoning (CBR) approach to generating poetic formulations of a given input text via a composition of poetic fragments that are retrieved from a case-base of existing poems. Each poem fragment in the ASPERA case-base is annotated with a prose string that expresses the meaning of the fragment, and this prose string is used as the retrieval key for each fragment. Metrical rules are then used to combine these fragments into a well-formed poetic structure. Example software projects include:
And poetry collections include:
Computational creativity in the music domain has focussed both on the generation of musical scores for use by human musicians, and on the generation of music for performance by computers. The domain of generation has included classical music (with software that generates music in the style of Mozart and Bach) and jazz. Most notably, David Cope has written a software system called "Experiments in Musical Intelligence" (or "EMI") that is capable of analyzing and generalizing from existing music by a human composer to generate novel musical compositions in the same style. EMI's output is convincing enough to persuade human listeners that its music is human-generated to a high level of competence[How to reference and link to summary or text].
Creativity research in jazz has focussed on the process of improvisation and the cognitive demands that this places on a musical agent: reasoning about time, remembering and conceptualizing what has already been played, and planning ahead for what might be played next.[citations needed]
The robot Shimon, developed by Gil Weinberg of Georgia Tech, has demonstrated jazz improvisation.
Visual and artistic creativity
Computational creativity in the generation of visual art has had some notable successes in the creation of both abstract art and representational art. The most famous program in this domain is Harold Cohen's AARON, which has been continuously developed and augmented since 1973. Though formulaic, Aaron exhibits a range of outputs, generating black-and-white drawings or colour paintings that incorporate human figures (such as dancers), potted plants, rocks, and other elements of background imagery. These images are of a sufficiently high quality to be displayed in reputable galleries.
Other software artists of note include the NEvAr system (for "Neuro-Evolutionary Art") of Penousal Machado. NEvAr uses a genetic algorithm to derive a mathematical function that is then used to generate a coloured three-dimensional surface. A human user is allowed to select the best pictures after each phase of the genetic algorithm, and these preferences are used to guide successive phases, thereby pushing NEvAr’s search into pockets of the search space that are considered most appealing to the user.
The Painting Fool is an ambitious system developed by Simon Colton that originated as a system for overpainting digital images of a given scene in a choice of different painting styles, colour palettes and brush types. Given its dependence on an input source image to work with, the earliest iterations of the Painting Fool raised as questions about the extent of, or lack of, creativity in a computational art system. Nonetheless, in more recent work, The Painting Fool has been extended to create novel images, much as AARON does, from its own limited imagination. Images in this vein include cityscapes and forests, which are generated by a process of constraint satisfaction from some basic scenarios provided by the user (e.g., these scenarios allow the system to infer that objects closer to the viewing plane should be larger and more color-saturated, while those further away should be less saturated and appear smaller). Artistically, the images now created by the Painting Fool appear on a par with those created by Aaron, though the extensible mechanisms employed by the former (constraint satisfaction, etc.) may well allow it to develop into a more elaborate and sophisticated painter.
The community of computational creativity has held a dedicated workshop, the International Joint Workshop on Computational Creativity, every year since 1999. Usually held as part of a larger conference event, this workshop series is now autonomous; the most recent stand-alone event was held in September 2008 at the Facultad de Informática, Universidad Complutense de Madrid, Spain. Previous events in this series include:
- IJWCC 2003, Acapulco, Mexico, as part of IJCAI'2003
- IJWCC 2004, Madrid, Spain, as part of ECCBR'2004
- IJWCC 2005, Edinburgh, UK, as part of IJCAI'2005
- IJWCC 2006, Riva del Garda, Italy, as part of ECAI'2006
- IJWCC 2007, London, UK, a stand-alone event
The steering committee for these events comprises the following researchers:
- Amilcar Cardoso (University of Coimbra, Portugal)
- Simon Colton (Imperial College London, UK)
- Pablo Gervás (Universidad Complutense de Madrid, Spain)
- Francisco C Pereira (University of Coimbra, Portugal)
- Tony Veale (University College Dublin, Ireland)
- Geraint A. Wiggins (Goldsmiths, University of London, UK)
In addition to the proceedings of these workshops, the computational creativity community has thus far produced two special journal issues dedicated to the topic:
- Journal of Knowledge-Based Systems, volume 9, issue 7, November 2006
- New Generation Computing, volume 24, issue 3, 2006
- ↑ Amabile, Teresa (1983), The social psychology of creativity, New York, NY: Springer-Verlag
- ↑ Newell, Allen, Shaw, J. G., and Simon, Herbert A. (1963), The process of creative thinking, H. E. Gruber, G. Terrell and M. Wertheimer (Eds.), Contemporary Approaches to Creative Thinking, pp 63 – 119. New York: Atherton
- ↑ Newell, Allen, Simon, Herbert A. (1972), Human Problem Solving, Englewood Cliffs, NJ: Prentice Hall.
- ↑ Newell, Allen, Simon, Herbert A. (1963), GPS, A Program that Simulates Human Though, E. A. Feigenbaum and J. Feldman (eds.), R. Oldenbourg KG
- ↑ Boden, Margaret (1990), The Creative Mind: Myths and Mechanisms, London: Weidenfeld and Nicholson
- ↑ Boden, Margaret (1999), Computational models of creativity., Handbook of Creativity, pp 351–373
- ↑ Wiggins, Geraint (2006), A Preliminary Framework for Description, Analysis and Comparison of Creative Systems, Journal of Knowledge Based Systems 19(7), pp. 449-458
- ↑ Finke, R., Ward, T., and Smith, S. (1992), Creative cognition: Theory, research and applications, Cambridge: MIT press.
- ↑ Koestler, Arthur (1964), The Act of Creation, Macmillan
- ↑ Fauconnier, Gilles, Turner, Mark (2007), The Way We Think, Basic Books
- ↑ Fauconnier, Gilles, Turner, Mark (2007), Conceptual Integration Networks, Cognitive Science, 22(2) pp 133–187
- ↑ Veale, Tony, O’Donoghue, Diarmuid (2007), Computation and Blending, Cognitive Linguistics, 11(3-4), special issue on Conceptual Blending
- ↑ Pereira, Francisco Câmara (2006), Creativity and Artificial Intelligence: A Conceptual Blending Approach, Applications of Cognitive Linguistics. Amsterdam: Mouton de Gruyter, http://eden.dei.uc.pt/~camara/AICreativity
- ↑ Meehan, James (1981), TALE-SPIN, Shank, R. C. and Riesbeck, C. K., (eds.), Inside Computer Understanding: Five Programs plus Miniatures. Hillsdale, NJ: Lawrence Erlbaum Associates
- ↑ Turner, S.R. (1994), The Creative Process: A Computer Model of Storytelling, Hillsdale, NJ: Lawrence Erlbaum Associates
- ↑ Bringsjord, S., Ferrucci, D. A. (2000), Artificial Intelligence and Literary Creativity. Inside the Mind of BRUTUS, a Storytelling Machine., Hillsdale NJ: Lawrence Erlbaum Associates
- ↑ Pérez y Pérez, Rafael, Sharples, Mike (2001), MEXICA: A computer model of a cognitive account of creative writing, Journal of Experimental and Theoretical Artificial Intelligence, 13, pp 119-139
- ↑ Martin, James (1990), A Computational Model of Metaphor Interpretation, Academic Press
- ↑ Barnden, John (1992), Belief in Metaphor: Taking Commonsense Psychology Seriously, Computational Intelligence 8, pp 520-552
- ↑ Veale, Tony, Hao, Yanfen (2007), Comprehending and Generating Apt Metaphors: A Web-driven, Case-based Approach to Figurative Language, Proceedings of AAAI 2007, the 22nd AAAI Conference on Artificial Intelligence. Vancouver, Canada
- ↑ Falkenhainer, Brian, Forbus, Ken and Gentner, Dedre (1989), The structure-mapping engine: Algorithm and examples, Artificial Intelligence, 20(41) pp 1–63, http://www.qrg.northwestern.edu/papers/Files/smeff2(searchable).pdf
- ↑ Veale, Tony, O’Donoghue, Diarmuid (2007), Computation and Blending, Cognitive Linguistics, 11(3-4), special issue on Conceptual Blending
- ↑ Binsted, K., Pain, H., and Ritchie, G. (1997), Children's evaluation of computer-generated punning riddles, Pragmatics and Cognition, 5(2), pp 309–358
- ↑ Stock, Oliviero, Strapparava, Carlo (2003), HAHAcronym: Humorous agents for humorous acronyms, Humor: International Journal of Humor Research, 16(3) pp 297–314
- ↑ Veale, Tony (2006), Tracking the Lexical Zeitgeist with Wikipedia and WordNet, Proceedings of ECAI’2006, the 17th European Conference on Artificial Intelligence
- ↑ Duch, Wlodzislaw (2007), Creativity and the Brain, In: A Handbook of Creativity for Teachers. Ed. Ai-Girl Tan, World Scientific Publishing, Singapore, pp 507–530
- ↑ Duch, Wlodzislaw (2007), Intuition, Insight, Imagination and Creativity, IEEE Computational Intelligence Magazine, 2(3) pp 40–52
- ↑ Pilichowski Maciej, Duch Wlodzislaw (2007), Experiments with computational creativity, Neural Information Processing – Letters and Reviews, 11(4-6) pp 123-133
- ↑ Gervás, Pablo (2001), An expert system for the composition of formal Spanish poetry, Journal of Knowledge-Based Systems 14(3-4) pp 181–188
- ↑ Cope, David (2006), Computer Models of Musical Creativity, Cambridge, MA: MIT Press
- ↑ http://www.npr.org/templates/story/story.php?storyId=121763193
- ↑ McCorduck, Pamela (1991), Aaron's Code., W.H. Freeman & Co., Ltd.
- ↑ Romero, Juan, Machado, Penousal (eds.) (2008), The Art of Artificial Evolution: A Handbook on Evolutionary Art and Music, Natural Computing Series. Berlin: Springer Verlag
- Algorithmic composition
- Algorithmic art
- Artificial Architecture
- Computer-generated music
- Computer-generated mathematics
- Computer art
- Generative systems
- Digital poetry
- Procedural generation
- Further reading
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- An Overview of Artificial Creativity on Think Artificial
- Cohen, H., "the further exploits of AARON, Painter", SEHR, volume 4, issue 2: Constructions of the Mind, 1995
- Artificial Creativity Blog
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- Gero, J. S. and Sosa, R. "Artificial Creativity in Communities of Design Agents", 2006
- LaDuke, B. "Knowledge Machine"
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- Applications and examples
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- Glot-Bot v2
- The Painting Fool
- Mambo invents novel words
- Transhypnagogia - computer hallucinations
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- generative art by Bogdan Soban
- CLAC - Software for Logical Composition
- The SWALE project
- jMapper - Java Library for Analogy/Metaphor Generation
- Aristotle - online metaphor generation and browsing system
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- Institutions and individuals
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- Margaret Boden
- Neurocognitive Computational Creativity, including Mambo server, Wlodek Duch lab
- The Creative Systems Area of the AI Group/CISUC
- notnot Creative Systems
- Stephen L. Thaler, Ph.D.
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