Selected Topics from Contemporary Logics

As used by professional logicians today, is the name of their chosen subject

singular or plural, "logic" or "logics"? This is a special case of a more general

question. For instance, an algebraist might write a book entitled "Algebra", which

is about algebras. Though many mathematicians are not aware of it, logic today

most decidedly has its plural aspect. Indeed, it always did. Classical logic, which

mathematicians often tend to identify with the entirety of logic, was in place

roughly by the beginning of the twentieth century. Since then a wide range of

so-called non-classical logics have been developed. But indeed, before the creation

of classical logic, there were multiple versions of logic, some of them more-or-less

formalized. The current growing interest in medieval and ancient European and

Asian logics has brought much of this back to modern awareness. Perhaps a later

volume in this series will look at the history from a contemporary viewpoint. But

that is not our task here.

This is the second volume in a series called Landscapes in Logic. The intention

of the series is to present reports illustrating the interplay between contemporary

work in logic and mainstream mathematics. Of course this is both vague and

overly ambitious, and must result in heterogeneous collections. The first volume

in the series, Contemporary Logic and Computing, appeared in 2020. The

contents divided plausibly into topics from contemporary logic, and from contemporary

computing. The present volume is more diverse, and includes articles

about both classical and non-classical logics, sometimes from the semantic side

and sometimes from the proof-theoretic side. Some articles are primarily technical,

often algebraic, while others are more philosophical in nature. Many fit into

multiple categories. This multiplicity should not be seen as a defect. The papers

here do not just explore logics house by house, but say something about their

general neighborhoods as well.