Serokell at AiML 2020
Advances in Modal Logic is one of the most popular conferences on modal logic. AiML covers the whole landscape of modal logic and its current state of affairs. Topics are not restricted to only abstract questions of modal logic but also includes the aspects related to artificial intelligence, philosophy, topology, algebra, etc. This year, the conference was online due to the pandemic – the University of Helsinki did a great job in organising it via Zoom.
The AiML talks were split into three categories. The first category was plenary talks. This year, invited speakers were Bahareh Afshari (the University of Amsterdam), Nick Bezhanishvili (the University of Amsterdam), Melvin Fitting (City University of New York), and Nina Gierasimczuk (Technical University of Denmark), all great talks indeed.
Out of those, I would like to emphasise the talk by Nick Bezhanishvili called ‘Filtrations, Canonical Formulas, and Axiomatisations of Superintuitionistic and Modal Logics’. The talk was quite close to my current research on model-theoretic aspects of Boolean algebras with operators.
There were also talks based on full papers. Topics of those papers represent a variety of trends in modal logic that include technical, applied, philosophical, and historical problems. Moreover, this conference is my debut as a paper reviewer. One of the accepted papers has been approved by myself as well.
My talk was the short one and is based on a short five-page abstract (see pp. 81 – 86). It’s called ‘Canonical extensions for the distributive full Lambek calculus with modal operators’.
Briefly, this talk provides an algebraic approach for Stone-style representation for bounded distributive lattices with modal operators to characterise the class of canonical logics. Canonical logics, in their turn, are adequate with respect to relational Kripke semantics if their algebras ‘respect’ such an algebraic representation called canonical extension. The result of this talk extends some of the results by Mai Gehrke, Yde Venema, and Hideo Nagahashi.