Logic List Mailing Archive

PhD student position on coalgebra and logic, London (England)

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@ucl.ac.uk), Alexandra (alexandra.silva@ucl.ac.uk), or Simon 
(simon.docherty.14@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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