The Good, the Bad and the Right: Formal Reductions among Deontic Concepts

The present article provides a taxonomic analysis of bimodal logics of normative ideality and normative awfulness, two notions whose meaning is here explained in terms of the moral values pursued by a given community. Furthermore, the article addresses the problem of defining other relevant normative notions, such as obligation, explicit permission and Hohfeldian relations, in terms of ideality and awfulness. Some proposals formulated in the literature are improved and discussed with reference to the various logics introduced.

Non-finitely axiomatisable two-dimensional modal logics

We show the first examples of recursively enumerable (even decidable) two-dimensional products of finitely axiomatisable modal logics that are not finitely axiomatisable. In particular, we show that any axiomatisation of some bimodal logics that are determined by classes of product frames with linearly ordered first components must be infinite in two senses: It should contain infinitely many propositional variables, and formulas of arbitrarily large modal nesting-depth.