Logical Theory and Sentence Composition -- A General and Comparative Study of the Principal Sentential Connectives. The aims are to get clear about the semantic and logical properties of
the basic sentence connectives, and to adjudicate several debates on
these matters. The significance is that the logic of sentence
connectives is fundamental for the whole of logic. The expected aim is a large book - probably to be called *The Connectives* - in which all of this is set out.
Rules in Logic. Logic is a foundational discipline which supports work in philosophy and other intellectual fields. Communities and nations are enriched by research in logic even if there are no direct economic benefits. But, in Australia, which has been a world-leader in philosophical logic for the past thirty years, there are also more direct benefits. Continued foundational research in logic attracts international students to Australia, and enhances the international reputation of Australian ....Rules in Logic. Logic is a foundational discipline which supports work in philosophy and other intellectual fields. Communities and nations are enriched by research in logic even if there are no direct economic benefits. But, in Australia, which has been a world-leader in philosophical logic for the past thirty years, there are also more direct benefits. Continued foundational research in logic attracts international students to Australia, and enhances the international reputation of Australian universities. This research will contribute significantly to Australia's reputation for fundamental logical research.Read moreRead less
Options For Proofs: New Perspectives on Propositional Logic. Philosophers and logicians recognise that proof is important, but they do not agree on what proofs are. Recent research in logic has greatly expanded our notion of proof, but this research is not unified. We need a coherent, general and applicable concept of proof. This project will unify the literature on proof and bring these insights to bear in the philosophy of language. It will show how proof can help analyse many features of ....Options For Proofs: New Perspectives on Propositional Logic. Philosophers and logicians recognise that proof is important, but they do not agree on what proofs are. Recent research in logic has greatly expanded our notion of proof, but this research is not unified. We need a coherent, general and applicable concept of proof. This project will unify the literature on proof and bring these insights to bear in the philosophy of language. It will show how proof can help analyse many features of language (more than just logical constants) but that the role of inference does not justify one kind of proof in preference to others.Read moreRead less
The One and the Many - the Path Through Contradiction. Australia has a major presence on the international philosophical world out of all proportion to its size (comparable to that which it has in sport). It is known for its development of radical new ideas and forthright approaches. One area in which this is particularly the case is logic and its philosophical applications. The present project is a high profile example of this, and will further enhance Australia's international intellectual p ....The One and the Many - the Path Through Contradiction. Australia has a major presence on the international philosophical world out of all proportion to its size (comparable to that which it has in sport). It is known for its development of radical new ideas and forthright approaches. One area in which this is particularly the case is logic and its philosophical applications. The present project is a high profile example of this, and will further enhance Australia's international intellectual profile.Read moreRead less
Complexity in Algebra and Algebra in Complexity: the role of finite semigroups and general algebra. Algebra and logic form the mathematical framework for expressing and analysing algorithms and their difficulty. We can then scientifically analyse what makes some tasks more difficult than others. This project unifies parallel areas of algebra to focus on two key topics at this interface between algebra and computational complexity. As a flow on, our work can uncover new algorithms for solving ....Complexity in Algebra and Algebra in Complexity: the role of finite semigroups and general algebra. Algebra and logic form the mathematical framework for expressing and analysing algorithms and their difficulty. We can then scientifically analyse what makes some tasks more difficult than others. This project unifies parallel areas of algebra to focus on two key topics at this interface between algebra and computational complexity. As a flow on, our work can uncover new algorithms for solving constraint problems and for the study of formal languages.
With a team of top international researchers developing new interactions between mathematics and the study of algorithms, the project will foster a culture of innovation and bring Australia into the play in this internationally competitive area.Read moreRead less
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
Paraconsistent Foundations of Mathematics. In the English-speaking world, Australia is already the most prominent centre for paraconsistent research, known for development of radical new ideas advanced here in the last few decades. The program is ready to mature into its next phase, making important and lasting contributions to logic, philosophy, and mathematics. The Australian academy will derive international recognition for impressive new mathematics, and innovative philosophical explanations ....Paraconsistent Foundations of Mathematics. In the English-speaking world, Australia is already the most prominent centre for paraconsistent research, known for development of radical new ideas advanced here in the last few decades. The program is ready to mature into its next phase, making important and lasting contributions to logic, philosophy, and mathematics. The Australian academy will derive international recognition for impressive new mathematics, and innovative philosophical explanations of truth and proof. Read moreRead less
Permanents, permutations and polynomials. The benefits to Australia of fundamental research in core disciplines such as mathematics are well documented. Discrete mathematics and combinatorics are boom disciplines of the computer age and this project seeks new knowledge concerning basic building blocks of combinatorial mathematics. The outcomes will be of interest to theoreticians around the world, enhancing Australia's already high research profile in this crucial area. Importantly, the project ....Permanents, permutations and polynomials. The benefits to Australia of fundamental research in core disciplines such as mathematics are well documented. Discrete mathematics and combinatorics are boom disciplines of the computer age and this project seeks new knowledge concerning basic building blocks of combinatorial mathematics. The outcomes will be of interest to theoreticians around the world, enhancing Australia's already high research profile in this crucial area. Importantly, the project also offers substantial postgraduate training in mathematics, an area in which Australia has an identified skill shortage.Read moreRead less
An Exploration of the Ramifications of the Re-conceptualization of Entailment. By revamping the field of deductive logic, the project will enhance the already solid international reputation Australia has in this area. The level of innovation in the work would set an example to other researchers and help to promote innovation in Australia. The project will provide more meaningful and accurate applications of logic in computer science, philosophy and mathematics, and engender smarter use of inform ....An Exploration of the Ramifications of the Re-conceptualization of Entailment. By revamping the field of deductive logic, the project will enhance the already solid international reputation Australia has in this area. The level of innovation in the work would set an example to other researchers and help to promote innovation in Australia. The project will provide more meaningful and accurate applications of logic in computer science, philosophy and mathematics, and engender smarter use of information. There would also be benefits to the teaching of logic in Australia, with the development of sharper analytical skills in students, and the project would lay the groundwork for a textbook on the new logic.Read moreRead less