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Dynamic Concept Spaces in Computational Creativity for Music

Part of the Studies in Applied Philosophy, Epistemology and Rational Ethics book series (SAPERE,volume 44)


I argue for a formal specification as a working understanding of ‘computational creativity’. Geraint A. Wiggins proposed a formalised framework for ‘computational creativity’, based on Margaret Boden’s view of ‘creativity’ defined as searches in concept spaces. I argue that the epistemological basis for delineated ‘concept spaces’ is problematic: instead of Wiggins’s bounded types or sets, such theoretical spaces can represent traces of creative output. To address this problem, I propose a revised specification which includes dynamic concept spaces, along with formalisations of memory and motivations, which allow iteration in a time-based framework that can be aligned with learning models (e.g., John Dewey’s experiential model). This supports the view of computational creativity as product of a learning process. My critical revision of the framework, applied to the case of computer systems that improvise music, achieves a more detailed specification and better understanding of potentials in computational creativity.


  • Computational Creativity
  • Conceptual Space
  • Creative Output
  • Time-based Framework
  • Experiential Learning Model

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  1. 1.

    The Universal Turing Machine was presented in (Turing 1936). ‘The [Universal] Turing Machine not only established the basic requirements for effective calculability but also identified limits: No computer or programming language known today is more powerful than the Turing Machine’ (Petzold 2008, p. 330). See Petzold’s (2008) book for an insightful interpretation and discussion of Turing’s 1936 article.

  2. 2.

    I use the term ‘trace’ in the sense of Jean-Jacques Nattiez where ‘the symbolic form [of the work] is embodied physically and materially in the form of a trace accessible to the five senses’ (Nattiez 1990, p. 12).

  3. 3.

    I have previously examined ‘co-creativity’ in the musical context (Mogensen 2017b).

  4. 4.

    Briefly, the Z schema notation includes a declarations part above the central horizontal line and predicates below the horizontal line. “The central horizontal line can be read ‘such that’.” The axiomatic predicates (below the line in Fig. 1) “appearing on separate lines are assumed to be conjoined together, that is to say, linked with the truth-functional connective \(\wedge \)” (Diller 1990, 6).

  5. 5.

    For a full narrative explanation of more details of Wiggins’s framework I refer the reader to his (2006a) paper.

  6. 6.

    Here I am representing \(\mathscr {M}_{1}\) and \(\mathscr {M}_{2}\) as arrays, rather than summing the individual motivation components as I did in (Mogensen 2017a); the array is a less reductive representation which I expect will be more useful for the framework development.

  7. 7.

    Oudeyer and Kaplan (2007) do not address issues of probability calculation and I will also defer such issues. The references on which they base their typology do include reports on implementations some of which may detail instances of probability calculations.

  8. 8.

    These component descriptions are adapted from Oudeyer and Kaplan (2007).

  9. 9.

    Arguably, in Fig. 5 and expression 1 the component \(\big ( c(p) \big )\) should be replaced by \(\big (\varDelta \mathscr {M}_{1} (p), \varDelta \mathscr {M}_{2} (p), c(p), \mathscr {W}(p-1) \big )\) if we want to include memory of motivations.

  10. 10.

    The term ‘poietic’ is from Nattiez (1990).

  11. 11.

    Kolb states that a characteristic of experiential learning models is that learning is best described as a process (Kolb 2015, 37).

  12. 12.

    Wiggins appears to interchange the term ‘artefact’ with the term ‘concept’ and examines the ‘conceptual space in which the artefact is found’ (Wiggins 2006b, p. 209). This seems to be a confusion of terms since ‘artefact’ refers to physical objects made in some way by humans, whereas ‘concepts’ exist in human consciousness. What the nature of the relations between concepts and artefacts is, is a question beyond the present scope, but I expect that the distinction between these terms would still hold when applied in the context of computational creativity.

  13. 13.

    One might question whether knowledge is ‘created’ and this becomes a questioning of the constructivist stance. Perhaps it is more accurate to say that knowledge is ‘attained’ or ‘arrived at’ since knowledge potentially exists regardless of our access to it? Resolving this question is beyond the present scope.


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Mogensen, R. (2018). Dynamic Concept Spaces in Computational Creativity for Music. In: Müller, V. (eds) Philosophy and Theory of Artificial Intelligence 2017. PT-AI 2017. Studies in Applied Philosophy, Epistemology and Rational Ethics, vol 44. Springer, Cham.

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