A Paraconsistent Approach to Vagueness. This project will utilise logical techniques that have been developed largely by Australian logicians. This techniques will be brought to bear on the problem of vagueness, one of the most important problems in the philosophy of logic. The project will thus greatly enhance Australia's already strong international reputation in logic and philosophical logic.
A Computational Solution to the Problem of Reference. This project will attack the core problem of philosophy of language by developing and applying tools from the theory of algorithmic complexity. Groundbreaking pure research at the intersection of logic, language, information and computation is the lifeblood of commercial research and development in information technology and telecommunications. The project will foster a cross-fertilisation of ideas between philosophy, computer science, math ....A Computational Solution to the Problem of Reference. This project will attack the core problem of philosophy of language by developing and applying tools from the theory of algorithmic complexity. Groundbreaking pure research at the intersection of logic, language, information and computation is the lifeblood of commercial research and development in information technology and telecommunications. The project will foster a cross-fertilisation of ideas between philosophy, computer science, mathematics, linguistics and psychology, and will provide students with skills and analytic techniques that will be valuable in future pure and applied research.Read moreRead less
Rationality and Resource Bounds in Logics for Intentional Attitudes. Formal philosophy is the discipline at the interface between traditional philosophy and modern mathematical logic. It has had a substantial impact in recent years and has benefited neighbouring disciplines, including computer science and artificial intelligence. It is a good example of how philosophical research can interact with more practical disciplines. This project will make substantial contributions to formal philosophy, ....Rationality and Resource Bounds in Logics for Intentional Attitudes. Formal philosophy is the discipline at the interface between traditional philosophy and modern mathematical logic. It has had a substantial impact in recent years and has benefited neighbouring disciplines, including computer science and artificial intelligence. It is a good example of how philosophical research can interact with more practical disciplines. This project will make substantial contributions to formal philosophy, which will in turn provide benefits in computer science and artificial intelligence, by providing a framework for logicians, computer scientists and researchers in artificial intelligence to discuss issues concerning knowledge, belief and rationality.Read moreRead less
Generalised topological spaces. Pure mathematics creates abstractions of real-world entities; one such is the idea of a 'topological space', which abstracts from geometric forms like cubes and toruses. But topological spaces fail to capture geometric structures arising in areas like quantum physics; and this project seeks to rectify this, by developing a new more general notion.
Design of dynamic visual signals. Models of the design of visual signals depend heavily upon analyses of static ornaments. Nothing is known about dynamic visual signals. We will use an array of new techniques to tackle this problem for the first time. Motion analyses will define the task faced by the visual system. Sensory limitations will be measured to identify constraints on signal evolution. Digital video playback studies will assess recognition and explain aspects of signal design. Results ....Design of dynamic visual signals. Models of the design of visual signals depend heavily upon analyses of static ornaments. Nothing is known about dynamic visual signals. We will use an array of new techniques to tackle this problem for the first time. Motion analyses will define the task faced by the visual system. Sensory limitations will be measured to identify constraints on signal evolution. Digital video playback studies will assess recognition and explain aspects of signal design. Results will test the generality of principles that have been developed in studies of female mate choice and extend these ideas to address intra-sexual selection operating through opponent assessment.Read moreRead less
RichProlog, a System for Deducing, Inducing and Learning in the Declarative Programming Paradigm. The aim of the project is to contribute to bridge the gap between learning and logic, theoretically and practically. Our purpose is to extend considerably the scope of the declarative programming paradigm, and build a system that can be used to solve learning or discovery problems as encountered in Artificial Intelligence. The system will enable rapid prototyping when applied to problems involving d ....RichProlog, a System for Deducing, Inducing and Learning in the Declarative Programming Paradigm. The aim of the project is to contribute to bridge the gap between learning and logic, theoretically and practically. Our purpose is to extend considerably the scope of the declarative programming paradigm, and build a system that can be used to solve learning or discovery problems as encountered in Artificial Intelligence. The system will enable rapid prototyping when applied to problems involving deduction, induction, and nonmonotonic reasoning. We intend the system to become a standard tool for tackling a broad range of applications, and the underlying theory to provide new insights on the logical foundations of Artificial Intelligence.
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Verification and analysis of quantum programs. This project aims to develop theoretical foundations and techniques, as well as efficient algorithms and effective tools, for the verification and analysis of quantum programs. This project will introduce new ideas and techniques to tackle the problem of verifying and analysing quantum programs and provide efficient algorithms and effective tools to help quantum program compilation and optimisation. Successful development of the outcomes and tools i ....Verification and analysis of quantum programs. This project aims to develop theoretical foundations and techniques, as well as efficient algorithms and effective tools, for the verification and analysis of quantum programs. This project will introduce new ideas and techniques to tackle the problem of verifying and analysing quantum programs and provide efficient algorithms and effective tools to help quantum program compilation and optimisation. Successful development of the outcomes and tools in this project will help Australian industries build frontier technologies for quantum software engineering and establish and preserve their competitive status in the era of quantum computing.Read moreRead less
The Logical Theories of Robert Kilwardby. The project is to produce a monograph on the logical theories of Robert Kilwardby (d. 1279) as they are expounded in his commentary on Aristotle's Prior Analytics, analyzing them from the perspective of modern logic. Kilwardby's commentary - which has not been critically edited, translated, or extensively studied - is remarkable for its fidelity to Aristotle's text, and its innovations in logical theory. This forms part of a larger project jointly with D ....The Logical Theories of Robert Kilwardby. The project is to produce a monograph on the logical theories of Robert Kilwardby (d. 1279) as they are expounded in his commentary on Aristotle's Prior Analytics, analyzing them from the perspective of modern logic. Kilwardby's commentary - which has not been critically edited, translated, or extensively studied - is remarkable for its fidelity to Aristotle's text, and its innovations in logical theory. This forms part of a larger project jointly with Dr Henrik Lagerlund (Uppsala University), to do a critical edition, historical introduction, and English translation of Kilwardby's commentary, together with the present logical analysis.Read moreRead less
Chromatic polynomials, random graphs, and error-correcting codes: a unified approach to graph colouring problems. Through a unified approach involving cutting-edge results on chromatic polynomials, random graphs, matroids, and error-correcting codes, this project will establish the foundations for a rigorous mathematical framework for attempting to provide a short, transparent and illuminating solution to the Four Colour Problem. The project will support developments in computer science and sta ....Chromatic polynomials, random graphs, and error-correcting codes: a unified approach to graph colouring problems. Through a unified approach involving cutting-edge results on chromatic polynomials, random graphs, matroids, and error-correcting codes, this project will establish the foundations for a rigorous mathematical framework for attempting to provide a short, transparent and illuminating solution to the Four Colour Problem. The project will support developments in computer science and statistical mechanics and is likely to have flow-on effects in real-world disciplines such as network communication. This project will also strengthen Australia's international presence in discrete mathematics and will further strengthen ties between Australian and international mathematicians.Read moreRead less
Analysis in the idealist tradition: the development of Leibniz's analytic method by Kant and Hegel and its implications for contemporary philosophy. This project investigates the development of the 'analytic' method in the idealist philosophies of Leibniz, Kant and Hegel, and compares it to 'analysis' as used in analytic philosophy. It thereby seeks to find a ground for dialogue between strands within contemporary philosophy that are usually thought to be opposed.