On Indicative Conditionals

In this paper we present a new approach to evaluate indicative conditionals with respect to some background information specified by a logic program. Because the weak completion of a logic program admits a least model under the three-valued Lukasiewicz semantics and this semantics has been successfully applied to other human reasoning tasks, conditionals are evaluated under these least L-models. If such a model maps the condition of a conditional to unknown, then abduction and revision are applied in order to satisfy the condition. Different strategies in applying abduction and revision might lead to different evaluations of a given conditional. Based on these findings we outline an experiment to better understand how humans handle those cases. 1 Indicative Conditionals Conditionals are statements of the form if condition then consequence. In the literature the condition is also called if part, if clause or protasis, whereas the consequence is called then part, then clause or apodosis. Conditions as well as consequences are assumed to be finite sets (or conjunctions) of ground literals. Indicative conditionals are conditionals whose condition may or may not be true and, consequently, whose consequence also may or may not be true; however, the consequence is asserted to be true if the condition is true. Examples for indicative conditionals are the following: If it is raining, then he is inside. (1) If Kennedy is dead and Oswald did not shoot him, then someone else did. (2) If rifleman A did not shoot, then the prisoner is alive. (3) If the prisoner is alive, then the captain did not signal. (4) If rifleman A shot, then rifleman B shot as well. (5) If the captain gave no signal and rifleman A decides to shoot, then the prisoner will die and rifleman B will not shoot. (6) Conditionals may or may not be true in a given scenario. For example, if we are told that a particular person is living in a prison cell, then most people are ? The authors are mentioned in alphabetical order.