Substructural logics for limited resources. This project aims to develop logical tools for managing reasoning and computation under conditions of bounded resources: fixed limits on the amount of time, memory, or other resources that can be allocated to a particular course of reasoning or computation. By drawing on both philosophical and computational approaches to logic, the project will develop new logical systems aimed at capturing these limitations. The expected outcome is new logical methods ....Substructural logics for limited resources. This project aims to develop logical tools for managing reasoning and computation under conditions of bounded resources: fixed limits on the amount of time, memory, or other resources that can be allocated to a particular course of reasoning or computation. By drawing on both philosophical and computational approaches to logic, the project will develop new logical systems aimed at capturing these limitations. The expected outcome is new logical methods for managing limited resources, as well as boosting interdisciplinary capacity. Anticipated benefits include developing a new programming language that will enable programmers to issue strong guarantees about the resources their programs will use.Read moreRead less
A Buddhist challenge to Western conceptions of logic. This project aims to advance and defend a theory about the nature of logic and rationality. The project will draw on Buddhist logic texts and demonstrate their relevance to contemporary Western debates about the nature of logic. It seeks to show that a Buddhist theory of logic can challenge widely-entrenched but unexamined Western conceptions of the nature of logic. The project is expected to advance intellectual engagement between Buddhist a ....A Buddhist challenge to Western conceptions of logic. This project aims to advance and defend a theory about the nature of logic and rationality. The project will draw on Buddhist logic texts and demonstrate their relevance to contemporary Western debates about the nature of logic. It seeks to show that a Buddhist theory of logic can challenge widely-entrenched but unexamined Western conceptions of the nature of logic. The project is expected to advance intellectual engagement between Buddhist and Western philosophers, bring attention to texts and theories not currently available to the Western philosophical world, and demonstrate the importance of a collaborative, interdisciplinary approach to global philosophy.Read moreRead less
Quasi-subtractive varieties: a unified framework for substructural, modal and quantum logic. An algebraic theory is proposed that provides a common umbrella for a plethora of non-classical logics. At the same time, it identifies a core that these logics share with classical algebras.
Structure of relations: algebra and applications. Relations and relational structures form the fundamental mathematical essence required for studying computational problems and computational systems. This project will provide new algebraic methods for solving old problems in the theory of relations, informing our understanding of computational complexity and the nature of computing.
Mathematical explanation. The best mathematical proofs tell us why some mathematical fact holds, not simply that it holds. However to understand how one piece of mathematics explains another piece of mathematics is poorly understood. This project will develop a philosophical account of mathematical explanation. In particular, it will show how mathematics can explain further mathematics as well as how it can explain physical phenomena.
Qualitative models of rationality: Philosophical foundations and applications. This project aims to establish the qualitative approach to rationality as a viable and attractive choice. Mathematical models of rationality, which aim to formalise the rules of good reasoning and decision making, traditionally assume that beliefs and desires are always given in precise, quantifiable degrees of confidence and value. This assumption is implausibly strong, and alternative, qualitative frameworks have be ....Qualitative models of rationality: Philosophical foundations and applications. This project aims to establish the qualitative approach to rationality as a viable and attractive choice. Mathematical models of rationality, which aim to formalise the rules of good reasoning and decision making, traditionally assume that beliefs and desires are always given in precise, quantifiable degrees of confidence and value. This assumption is implausibly strong, and alternative, qualitative frameworks have been developed to handle the frequent situations in which it fails. These, however, remain incomplete and their foundations poorly understood. The project will address their omissions, secure their conceptual underpinnings and use them to clarify and resolve long-standing philosophical problems.Read moreRead less
Algebraic categories and categorical algebra. Algebra is the study of operations, such as addition and multiplication, and the relationships between these operations. This project will study two exciting new branches of algebra, quantum algebra and postmodern algebra, which will lead to important advances in physics, geometry, and computing.
Reasoning about, and stepwise development of, quantum programs: a predicate transformer semantics approach. The project will provide a framework to reason about, and stepwise develop, quantum programs by rigorous predicate transformer semantics, and generate breakthrough theory and frontier techniques for quantum software engineering.