A Logic for Hypothetical Reasoning

This paper shows that classical logic is inappropriate for hypothetical reasoning and develops an alternative logic for this purpose. The paper focuses on a form of hypothetical reasoning which appears computationally tractable. Specifically, Horn-clause logic is augmented with rules, called embedded implications, which can hypothetically add atomic formulas to a rulebase. By introducing the notion of ruZebuse independence, it is shown that these rules can express hypothetical queries which classical logic cannot. By adopting methods from modal logic, these rules are then shown to be intuitionistic. In particular, they form a subset of intuitionistic logic having semantic properties similar to those of Horn-clause logic.