Logics and reasoning for computational creativity

Computational creativity is a subdomain of artificial intelligence that explores the potential of computational systems to create original artefacts and ideas. Overlapping with the broader field of cognitive science, it encompasses "the philosophy, science and engineering of computational systems which ... exhibit behaviours that unbiased observers would deem to be creative". We study creativity from an algebraic point of view, showing how we can give a mathematical formalization of creative systems and their components. We start from the tenet that creativity can be seen in essence as the identification or location of new conceptual objects in a conceptual space. While most of the current research in computational creativity embraces a connectionist view on cognitive and, in particular, creative processes, our approach adheres to the symbolic computational theory of mind. We adopt the understanding of a concept as an algebraic specification, and develop our study based on Goguen and Burstall's theory of institutions. This allows us to use formal definitions for concept discovery, abstraction, concretization, and blending that enable reasoning about creative processes. We first define creative systems by means of specifications over many-valued logics and of abstract strategies for the discovery and evaluation of concepts using the notion of graded consequence. We then focus on a subclass of creative systems modelled as complex dynamic systems and investigate a new connection between improvisation processes and service-oriented architectures where concepts and concept discovery are regarded as modules and service discovery, respectively. In this context, we evaluate the usefulness of a concept through the mechanism of service selection, and recast concept blending in terms of service binding. This leads us to the implementation of a specification and programming language whose operational semantics extends the logic-programming semantics of services from the classical Boolean setting to one with multiple truth values, akin to fuzzy logic programming. As a case study, we model free jazz improvisations using notions and techniques from service-oriented computing. To that end, we study a suite of logics for describing music using soft constraints or specialized notations. We show how musical fragments can be captured by means of specifications of service modules, and we instantiate the service-oriented processes of discovery, selection and binding to simulate music improvisation.