Sven Ove Hansson

Specified meet contraction is the operation defined by the identity where ∼ is full meet contraction and f is a sentential selector, a function from sentences to sentences. With suitable conditions on the sentential selector, specified meet contraction coincides with the partial meet contractions that yield a finite-based contraction outcome if the original belief set is finite-based. In terms of cognitive realism, specified meet contraction has an advantage over partial meet contraction in that the selection mechanism operates on sentences rather than on temporary infinite structures (remainders) that are cognitively inaccessible. Specified meet contraction provides a versatile framework in which other types of contraction, such as severe withdrawal and base-generated contraction, can be expressed with suitably chosen properties of the sentential selector.

Real-life decision-making often begins with a disorderly decision problem that has to be clarified and systematized before a decision can be made. This is the process of decision structuring that has largely been ignored both in decision theory and applied decision analysis. In this contribution, ten major components of decision structuring are identified, namely the determination of its scope, subdivision, agency, timing, options, control ascriptions, framing, horizon, criteria and restructuring. Four of these components, namely the scope, subdivision, options, and horizon of a decision, are subjected to a more detailed analysis.

In order to avoid the paradoxes of standard deontic logic, we have to give up the semantic construction that identifies obligatory status with presence in all elements of a subset of the set of possible worlds. It is proposed that deontic logic should instead be based on a preference relation, according to the principle that whatever is better than something permitted is itself permitted. Close connections hold between the logical properties of a preference relation and those of the deontic logics that are derived from it in this way. The paradoxes of SDL can be avoided with this construction, but it is still an open question what type of preference relation is best suited to be used as a basis for deontic logic.

Situationist deontic logic is a model of that fraction of normative discourse which refers to only one situation and one set of alternatives. As we can see from a whole series of well-known paradoxes, standard deontic logic (SDL) is seriously mistaken even at the situationist level. In this paper it is shown how a more realistic deontic logic can be based on the assumption that prescriptive predicates satisfy the property of contranegativity. A satisfactory account of situation-specific norms is a necessary prerequisite for a successful treatment of more complex normative structures

By replacement is meant an operation that replaces one sentence by another in a belief set. Replacement can be used as a kind of Sheffer stroke for belief change, since contraction, revision, and expansion can all be defined in terms of it. Replacement can also be defined either in terms of contraction or in terms of revision. Close connections are shown to hold between axioms for replacement and axioms for contraction and revision. Partial meet replacement is axiomatically characterized. It is shown that this operation can have outcomes that are not obtainable through either partial meet contraction or partial meet revision.