Complexities of Proof-Theoretical Reductions

The present thesis is a contribution to a project that is carried out by Michael Rathjen and Andreas Weiermann to give a general method to study the proof-complexity of Pi_2 sentences. This general method uses the generalised ordinal-analysis that was given by Buchholz, Rueede and Strahm as well as the generalised characterisation of provable-recursive functions of PA with axioms for transfinite induction that was given by Weiermann. The present thesis links these two methods by giving an explicit elementary bound, for the proof-complexity increment that occurs after the transition from the theory that was used by Rueede and Strahm, to PA with axioms for transfinite induction, which was analysed by Weiermann

Making scenarios more worthwhile: orienting to design story work

Increased complexity in contemporary design work has led designers to place greater dependence on the use of story and narrative. Though many consider story and narrative a fundamental part of design, use continues to present challenges and efficacy is poorly understood. With regards to use, challenges stem from a lack of support in directing strategic conversations towards getting the right stories and to getting stories right. With regards to efficacy, poor understanding stems from a lack of research and a corresponding lack of unifying theory. Scenario research represents the largest body of knowledge on the use and efficacy of story and narrative in design. Yet, scenarios are characteristically narrow in scope and their descriptions typically thin. Scenario research is in decline, and what theory exists is neither extensive nor extensible. Nevertheless, scenarios serve as a starting point for this research, with questions posed about how designers work with story and narrative, and how, in turn, story and narrative work for designers. To explore these questions epistemological, philosophical and theoretical positions are taken up and these underpin a Research into/through/for Design methodology. A series of self-reflective experiments lead to the creation of novel narrative resources and approaches, which empirical studies expose to a range of increasingly challenging settings. Findings from these studies show that narrative resources coupled with resource-based approaches provide targeted support for cognitively challenging aspects of story work. Furthermore, outcomes from a programme of critical analysis provide insights into how story, narrative and narrative resources work for designers. Contributions to knowledge are made in three areas: first, in the area of design practice in relation to narrative resources and approaches to story work; second, in the area of design theory in relation to realistic approaches to method innovation; and third, in the area of research practice in relation to aids to visual analysis

Creative metaphor production in a first and second language and the role of creativity

The study of metaphor is an interdisciplinary endeavor crossing such fields as cognitive linguistics, psychology, and creativity studies. Two important conclusions on the nature of metaphor have been drawn to date: (1) the ability to use metaphor is a normal human cognitive ability and widespread in language; (2) metaphor is not a unitary construct and varies greatly from the highly familiar and conventional to the creative. Viewing metaphor as lying along a continuum, this thesis narrows the concept of metaphoric competence to creative metaphoric competence, which looks at this ability from a creativity perspective. In this thesis, it is hypothesized that creative metaphoric competence is an underlying competency, which is related to a more general creative competence, and therefore is projected onto both the L1 (Japanese) and L2 (English). In order to test this hypothesis, data from creative metaphor production tasks were collected in both languages. In addition, a number of creativity measurements were also developed with the aim of measuring the multifaceted nature of creativity. Relationships between these variables were investigated. Findings suggest that creative metaphoric competence is an individual difference variable, which could be described as a disposition towards novelty and is related to other measurements of creativity