A Theory of Conditionals Based on Hierarchies of Situations

We present an approach to the semantics of subjunctive conditionals based on the situation semantics notion of a constraint, in which the connection between antecedent A and consequent B of a conditional ‘if A were the case, B would be’ is an informational relation between types of situations. We also argue that the information contained in a hierarchy of planning schemas as commonly used in Artificial Intelligence enables an agent to represent the semantic objects involved in evaluating conditionals and thus to understand a subclass of subjunctive conditionals. A logic of situations based on modelling situations as sets of possible worlds is given; then a logic of conditionals based on hierarchies of situations is presented. The bridge between the logic and the planning representation is an explicit construction showing how a hierarchy of situations suitable for evaluating conditionals can be generated from a collection of planning schemas. We conclude with a discussion of the theory, including the paradoxes of conditional implication, the difference between truth conditions and assertibility conditions for subjunctive conditionals, the relationship between subjunctive and indicative conditionals, conditionals and explanation, competing conditionals and the conditional excluded middle, and ‘might’ conditionals.