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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....@ucl.ac.uk), Alexandra (alexandra.si...@ucl.ac.uk), or Simon
(simon.docherty...@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.
--
Professor of Information, Logic, and Security
Head of Programming Principles, Logic, and Verification
University College London
Turing Fellow, The Alan Turing Institute, London
d....@ucl.ac.uk
www.cs.ucl.ac.uk/people/D.Pym.html
www.cs.ucl.ac.uk/staff/D.Pym/
Assistant: Julia Savage, j.sav...@ucl.ac.uk, +44 (0)20 7679 0327
