[FOM] PhD Studentship at UCL: A Coalgebraic framework for reductive logic and proof-search

[Pym, David]

PhD Studentship: A Coalgebraic framework for reductive logic and proof-search

We are seeking to appoint a PhD student in UCL?sProgramming Principles, Logic, and Verification (PPLV, http://pplv.cs.ucl.ac.uk/welcome/) group,to work alongside the EPSRC-funded project ?A coalgebraic framework for reductive logic and proof-search (ReLiC)?.

See https://gow.epsrc.ukri.org/NGBOViewGrant.aspx?GrantRef=EP/S013008/1

The project is led by David Pym (PI), Alexandra Silva, and Simon Docherty (Co-Is). Facebook (Peter O?Hearn) is a partner in the project.

The position is available from 23 September 2019 for 4 years. The starting stipend will be approximately £17,280, with an approximate annual uplift of 3%.

We are looking for a talented, highly motivated student interested in working on some aspects of the project. Here is a description of the project.

The traditional treatment of logic is that of a deductive science: from axioms, conclusions are deduced according to formal proof rules. However, in practice many applications of logic and mathematical reasoning proceed in the opposite direction: from a putative conclusion, one finds sufficient axioms from which it may be concluded. This proceeds not by a step-by-step application of proof rules, but instead by the systematic reduction of the space of possible (deductive) proofs. We call this the reductive approach to logic. Archetypal examples of reductive reasoning in computer science include automated theorem proving, logic programming languages such as PROLOG, and precondition inference in program verification.

The ReLiC project aims to produce a uniform mathematical foundation for reductive logic via the framework of coalgebra and coinduction. Coalgebra can fruitfully be seen as a unifying formalism for stateful systems, while coinduction is a closely connected proof principle based on the reduction of goals into subgoals. In doing so we aim to

(1) deepen the theoretical understanding of reductive logic, facilitating a broadening of the applicability of such techniques;

(2) implement prototype provers and automated reasoning support based on a clear, principled semantics;

(3) interface with state-of-the-art coalgebraic and category theoretic approaches to the semantics of programs and probabilistic inference to understand and export shared features of key applications of reductive reasoning like Facebook?s program verification tool Infer and the machine-learning paradigm inductive logic programming.

We are looking for a student with an excellent first degree in mathematics, computer science, philosophy, or another mathematical discipline, who has a strong background and interest in logic. Ideally, candidates will also have an excellent, relevant Master?s degree and strong programming skills.

For an informal discussion of the position, please contact David (d.pym at ucl.ac.uk<mailto:d.pym at ucl.ac.uk>), Alexandra (alexandra.silva at ucl.ac.uk<mailto:alexandra.silva at ucl.ac.uk>), or Simon (simon.docherty.14 at ucl.ac.uk<mailto:simon.docherty.14 at ucl.ac.uk>).

To apply, please follow the instructions at


http://www.cs.ucl.ac.uk/prospective_students/phd_programme/funded_scholarships/

and indicate clearly on your application that you are applying for this Scholarship ("A Coalgebraic framework for reductive logic and proof-search") under the scholarships section, or in your personal statement.--
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--
Professor of Information, Logic, and Security
Head of Programming Principles, Logic, and Verification
University College London

Turing Fellow, The Alan Turing Institute, London

d.pym at ucl.ac.uk<mailto:d.pym at ucl.ac.uk>
www.cs.ucl.ac.uk/people/D.Pym.html
www.cs.ucl.ac.uk/staff/D.Pym/

Assistant: Julia Savage, j.savage at ucl.ac.uk<mailto:j.savage at ucl.ac.uk>, +44 (0)20 7679 0327

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