Logical connections between some open problems concerning nil rings

Some Questions concerning Alternative Rings

Some problems and results related to nil and graded-nilpotent rings

Strongly nil-clean corner rings

We show that if $R$ is a ring with an arbitrary idempotent $e$ such that $eRe$ and $(1-e)R(1-e)$ are both strongly nil-clean rings‎, ‎then $R/J(R)$ is nil-clean‎. ‎In particular‎, ‎under certain additional circumstances‎, ‎$R$ is also nil-clean‎. ‎These results somewhat improves on achievements due to Diesl in J‎. ‎Algebra (2013) and to Koc{s}an-Wang-Zhou in J‎. ‎Pure Appl‎. ‎Algebra (2016)‎. ‎...

Some Ontological Problems concerning Predication

The Aristotelian double characterization of a primary substance exploits the difference between the part-whole relation and the non-linguistic relation of predication. A problem arises whether and how the second relation could be reduced to something else. Such a reduction is explicitly declared or at least implicitly assumed in all version of conceptualism and nominalism. The moderate realism ...

Open Problems in Logical Dynamics

In recent years, a number of 'dynamic epistemic logics' have been developed for dealing with information, communication, and interaction. This paper is a survey of conceptual issues and open mathematical problems emanating from this development. 1 Logical Dynamics The traditional paradigm of logic is drawing a conclusion from some given premises. But derivation from data already at our disposal...