The logic of reusable propositional output with the fulfilment constraint (Q2701987)

Input/output logics are abstract structures reflecting the mathematical behaviour of conditional obligations, goals, etc. They were introduced by the author and the reviewer in a paper with that name in J. Philos. Log. 29, 383-408 (2000; Zbl 0964.03002).NEWLINENEWLINENEWLINETo handle contrary-to-duty obligations adequately, input/output systems need to be limited by consistency constraints. The paper under review begins a study of such constraints. It focuses on a particular one, called the fulfilment constraint, where the fulfilment of a conditional object is the conjunction of its body and head. This constraint is applied to a specific input/output system (basic reusable output) approached in terms of derivations. The author shows the equivalence of three ways of formulating the constraint: (1) as a global requirement on the derivation tree, requiring the joint consistency of the fulfilments of the nodes in each `dependency subtree'; (2) as a local requirement on the label of each node in the same tree, under an appropriate labelling system; (3) more surprisingly, as a local requirement on each (unlabelled) node of the same tree, accompanied by a `phasing condition', i.e. a condition imposing a fixed order on the application of derivation rules.NEWLINENEWLINENEWLINEReviewer's comments: The fulfilment constraint is the most severe in a family of four natural restrictions, called the fulfilment, head, materialization, and output constraints. A subsequent paper of the author and reviewer [``Constraints for input/output logics'', J. Philos. Log. 30, 155-185 (2001)] studies the mildest of the family (the output constraint), with also some comparisons between the four. The fulfilment constraint is the only one for which a characterization of the kind (3) above is known.NEWLINENEWLINEFor the entire collection see [Zbl 0940.00024].