Propositional Abduction

Reasoning can be defined as the process of applying existing knowledge in order to produce new knowledge. In logic, there are at least two fundamentally different sorts of reasoning: the deductive and the abductive. Deductive reasoning (or simply deduction) is the process of deriving consequences from what is known or assumed to be true. On the other hand, abductive reasoning (or simply abduction) infers what needs to be assumed to derive a given consequence. Thus, deduction and abduction differ in the direction in which a rule has been used for inference. In this work, we present a calculus to generate abductive explanations for propositional theories. The formalism is based on propositional resolution with Set-Of-Support strategy. Furthermore, we investigate an extension of this calculus dealing with orderings