Divergent Production of Music Pieces

This paper describes our model for the production of a variety of creative solutions. This is allowed by the mind ability of divergent production, which was claimed by Guilford as responsible for the construction of creative solutions, in opposition to the use of convergent production to construct ordinary solutions. Besides this Guilford influence, our approach to creativity is also inspired in the main problem solving models for the creative process, especially the Wallas’ model, in that we consider that creativity involves a sequence of four stages: preparation, incubation, illumination and verification The knowledge acquired in the preparation stage is represented by documented past experiences of plans. With the aim of achieving a flexible knowledge representation, we split cases into pieces, which are ill-related each other by links (explanations). Our system constructs a creative plan solution by establishing new associations (or new relations) between case pieces retrieved from past successful case solutions. Divergent production is achieved by guaranteeing that those associations are novel in each problem solving session. We treat music pieces as plans. Introduction Solving a problem in a creative way implies finding a good solution that is different from previous ones. This means creative solutions are undoubtedly mainly characterised by two properties: appropriateness and originality (Cabezas, 93; Moorman & Ram, 94). An appropriate solution is one that fulfils the goal(s) of the problem, i.e., it is useful by satisfying a need. A solution, to be appropriate, should also be coherent, without incompatibilities between its components, and be able to be executed as well (Macedo et al., 96b, 96c, 97). An original solution is one that is different from previous ones, i.e., it stands apart from the solutions that the individual or the other people have already produced. It is singular, novel and somehow unpredictable. Guilford (68) has claimed that the exploration of creative solutions is mainly due to the mind ability that he called divergent production (somehow similar to the concept of lateral thinking of De Bono (86)). This ability is related with the generation of a variety of solutions to the same problem. It is used in those kind of domains were creative solutions are required, which cannot be classified in an evaluation space of correctness. Instead, these solutions may be classified in an evaluation space about their originality and appropriateness. In contrast with divergent production, convergent production was considered as the ability to produce the right solution to a given problem that can only have correct or incorrect solutions. Although there are four mainly perspectives of creativity (the creative person, the creative environment, the creative product, and the creative process (Brown, 89)), the creative process and the creative product perspectives are the most addressed in the literature. Even if there are several explanation models for the creative process, we are interested in those entailed to problem solving (also called cognitive models). From the main predecessor problem solving models, Good Problem Solving, Creative Production, and Invention, proposed by Dewey (10), Wallas (26) and Rossman (31), respectively, Wallas' model has much acceptance in cognitive research community. He proposed that creativity involves four sequential steps: preparation, incubation, illumination (or insight) and verification. Ehereas the preparation involves the identification of a problem and the acquisition of the knowledge necessary to solve it, incubation consists of reassembling past knowledge into new knowledge structures. Illumination is the outcome of the incubation stage: the eureka. Verification is the assessment of the quality of the solution proposed about their creative properties. Case-Based Reasoning (CBR) (Kolodner, 93) allows to solve problems using past successful solutions. Usually, a CBR system searches through every case in memory, applies a similarity metric and returns the case or k cases with the past problem more similar to the new one. Kolodner (89) has considered that the most useful cases are those that can address the reasoner’s current goal, which means that they may not be the most similar ones. Particularly, this stands to reason when the goal is to achieve creative solutions. Considering cases as set of pieces (Barletta & Mark, 88; Kolodner, 88; Redmond, 90; Veloso, 92) instead of monolithic entities, the results of a system may be improved in that solutions of problems may result from the contribution of multiple cases. Furthermore, this allows a more flexible representation of knowledge, which is important to creativity. A plan is a specific sequence of steps (or actions) with the aim of a goal achievement. Case-Based Planning (CBP) systems (Veloso, 92) reuse past sequences of actions from past plans to construct new ones. Some systems like CELIA (Redmond, 90), JULIA (Kolodner, 89), PRODIGY/ANALOGY (Veloso, 92), etc., break up the goal into smaller sub-goals, enabling plan construction by composition of sub-plans. This leads to one of the most common structure for plan cases: the hierarchical representation of plan cases (Macedo et al., 96a). The case representation is similar to a tree where each node is a goal and its sons are the sub-goals, or at the latest level, the actions of the plan. Each goal (or action) depends on other goals. This is particularly evident in structured domains. In the last years there has been a variety of research on computational creativity. The research group of Georgia Institute of Technology has been taken an important role on that. Ashwin Ram et al. (94) defend that creativity is the result of mechanisms which are on a continuum with those used in ordinary thinking. They view creativity as an extraordinary outcome originated by the application of ordinary mechanisms, improved and applied with conscious strategic control. Particularly, Linda Wills and Janet Kolodner (94) proposed a model for creative design based on three steps: enumeration of several alternative solutions; re-description and elaboration of problem specifications; and evaluation of proposed solutions. Also in creative design, A. Goel, S. Bhatta and S. Prabhakar (94) has been working on IDEAL, a system that deals with knowledge with three features: behavior, functionality and structure. Ashwin Ram (93) addressed the matter of conceptual change distinguishing two types of creative processes involved: constructive conceptual change and extrapolative conceptual change. Keneth Moorman and also the same Ashwin Ram (94) proposed a model for creative understanding, which they separate from another form of creativity called creative invention or creative problem solving. This model was implemented in ISAAC, a system that models the creative reading of science fiction stories. Douglas Hofstadter (94) and Melanie Mitchel (93) worked on COPYCAT, a nondeterministic analogy-making system which intends to model not just human analogymaking but also creative analogy-making. Actually, analogy (Gentner & Stevens, 83; Keane, 88; Veloso, 92; Holyoak & Thagard, 95; Hofstadter, 94, Mitchell, 93) plays an important role in creativity. The systems mentioned above make use of it. It allows to use knowledge of a familiar problem (called source analog) to solve a problem (called target) which is analogous with the first. In this paper we present our model for the Creative Planning Process, which we called INSPIRER (ImagiNation taking as Source Past and Imperfectly RElated Reasonigs). There is an implementation of this model entailed to music composition in the system SICOM (a detailed explanation of this application may be found in Pereira et al. 97). Divergent production of creative music pieces (hierarchically represented) is achieved by assembling pieces from past music pieces, to which is applied a similarity metric with different parameter values in each problem solving session of a same problem, or establishing different degrees of originality for different hierarchical levels in each problem solving session of a same problem. Our model for the process of plan solution construction is presented in the next section. Section 3 illustrates the application in the music composition domain. The results obtained with divergent production in this domain are presented in section 4. Finally, a conclusion about our work is made in section 5. 2 A Computational Model for the Creative Planning Process In this section we describe our Creative Planning Process. It comprises the following steps: preparation, incubation, illumination and verification.