The preservation of coherence
The authors introduce axiomatically a level function \(\ell\) for sets of modal propositional formulas. In the prime example \(\ell (\Sigma)\) is the least number n, such that \(\Sigma\) may be partitioned into n consistent subsets. Furthermore, generalized frames for modal logic are introduced, where the binary accessibility relation between possible worlds is replaced by n-ary relations. The level of a frame \({\mathcal F}\) is \(\ell (\{a:\) \(\square a\) is valid in \({\mathcal F}\})\). The main result is an axiomatic characterization of the class of frames of level 1. It would have been preferable if the authors had found a way to avoid the irrelevant and unfortunate introductory remarks.
scientific article; zbMATH DE number 3957054