Conditionals are useful for modelling, but are not always sufficiently expressive for capturing information accurately. In this paper we make the case for a form of conditional that is situation-based. These conditionals are more expressive than classical conditionals, are general enough to be used in several application domains, and are able to distinguish, for example, between expectations and counterfactuals. Formally, they are shown to generalise the conditional setting in the style of Kraus, Lehmann, and Magidor. We show that situation-based conditionals can be described in terms of a set of rationality postulates. We then propose an intuitive semantics for these conditionals, and present a representation result which shows that our semantic construction corresponds exactly to the description in terms of postulates. With the semantics in place, we proceed to define a form of entailment for situated conditional knowledge bases, which we refer to as minimal closure. It is reminiscent of and, indeed, inspired by, the version of entailment for propositional conditional knowledge bases known as rational closure. Finally, we proceed to show that it is possible to reduce the computation of minimal closure to a series of propositional entailment and satisfiability checks. While this is also the case for rational closure, it is somewhat surprising that the result carries over to minimal closure.

翻译：条件句在建模中非常有用，但并非总能充分表达精确信息。本文提出了一种基于情境的条件句形式。这类条件句比经典条件句更具表达力，具有足够通用性可应用于多个领域，并能区分预期条件句与反事实条件句等不同类别。在形式上，我们证明它们可以推广至Kraus、Lehmann和Magidor所提出的条件推理框架。研究表明，基于情境的条件句可通过一组理性公设来描述。随后我们为这些条件句提出直观的语义解释，并给出表征性结论，证明该语义构建与公设描述完全对应。基于此语义，我们进一步定义了情境条件知识库的蕴含关系——最小封闭（minimal closure）。该概念令人联想到（实际上也受启发于）命题条件知识库的理性封闭（rational closure）蕴含机制。最后，我们证明可将最小封闭的推理过程简化为一系列命题蕴含与可满足性检测。尽管理性封闭也具有此特性，但该结论能推广至最小封闭却令人颇感意外。