15th Meeting of the Southern and Midlands Logic Seminar

15th Meeting of the Southern and Midlands Logic Seminar, UCL, London

The 15th meeting of the Southern and Midlands Logic Seminar will be held on the afternoon of Wednesday 24 June at University College London.

Talks will take place in Lecture Theatre Maths 505, 25 Gordon Street, WC1H 0AY, London.

Participants are encouraged to join the SMLS community on Discord, which is used for announcements and coordination. Please contact one of the SMLS organisers to be added.

The meeting is supported by a London Mathematical Society Joint Research Groups grant.

Programme

Travel bursaries

The seminar has a budget to cover travel costs for speakers and participants. The instructions on how to claim travel expenses will be sent out after the seminar.

Abstracts

"Quantitative Diagrammatic Axiomatisation of Relative Entropy" Ralph Sarkis, UCL
Relative entropy is a fundamental class of distances between probability distributions with widespread applications in probability theory, statistics, and machine learning. Following recent work of Paolo Perrone, we study relative entropy from a categorical perspective, viewing it as an enrichment of the category of stochastic matrices. We provide diagrammatic theories that axiomatise this category with three different enrichment with the Kullback--Leibler divergence, the more general Rényi divergence, and the Jensen--Shannon divergence. Our results are formulated within the framework of quantitative monoidal algebra, using a graphical language of string diagrams enriched with quantitative equations.

"From Phase Semantics to Base-extension Semantics (and back)" Katya Piotrovskaya, UCL
Linear logic admits a wide range of semantic presentations. One well-known example is phase semantics: an algebraic semantics in which formulas are interpreted in phase spaces, consisting of a commutative monoid and a fixed subset, with respect to which an orthogonality relation is defined. A rather different and much more recent approach is given by base-extension semantics, which defines validity by inductively extending a provability relation on a base -- a set of inference rules over atomic propositions. In this talk, we establish an equivalence between the two semantics by first defining bidirectional maps between bases and phase spaces, and then constructing an isomorphism between a phase space (resp. base) and its image under the composition of these maps.

"Counting Small Subhypergraphs" Madhumitha Krishnakumar, Queen Mary
TBA

"TBA" Paaras Padhiar, Birmingham
TBA

Organisers

Local Organiser