Hypothetical Knowledge and Counterfactual Reasoning

: Salmetintroduced a notion of hypothetical knowledge and showed how it could be used to capture the type of counterfactual reasoning necessary to force the backwards induction solution in a game of perfect information. He argued that while hypotheticalknowledgeand the extended information structures used to model it bear someresemblanceto the way philosophershave used conditional logic to model counterfactuals, hypotheticalknowledgecannot be reduced to conditional logic together with epistemic logic. Here it is shown that in fact hypothetical knowledge can be captured using the standard counterfactual operator ">" and the knowledgeoperator "K", provided that some assumptions are made regarding the interaction between the two. It is argued, however, that these assumptions are unreasonable in general, as are the axioms that follow from them. Some implications for game theory are discussed.

• Type: Conference
• Year: 1998
• Where: TARK
• Authors: Joseph Y. Halpern
• Keywords: Automated Reasoning, Backwards Induction Solution, Conditional Logic, Hypothetical Knowledge, TARK 1998