A Causal Theory of Abduction

Representation theorems for explanatory reasoning based on cumulative models

“…This explains why the semantic for EM found by Flach does not use a preference relation between states. A similar comment is valid for the work of Bochman [4,5] who uses a rule called Weakening rule which corresponds to our full explanatory cut. In [20] two others (weaker) cut rules were introduced.…”

“…Despite the absent of a general definition of explanation, there have been several attempts to develop a logical account of explanatory reasoning [1][2][3][4][5]7,[10][11][12]20,22,23]. Some of these attempts have followed the so-called KLM methodology developed by Kraus, Lehmann and Magidor and many others for the study of consequence relations (see [16,18,19] and the references therein).…”

“…We will use the system of postulates introduced in [20,22]. Others systems for explanatory reasoning were studied by Flach [10,11], Bochman [4,5] and Walliser et al [23]. We make some comments about them later in this introduction.…”

Configurations for Inference Between Causal Statements

“…Some logics for causal reasoning (e.g., [4,7]) satisfy apparently much more properties than the formalism presented here. However, any comparison should keep in mind that here a new specific kind of "causal formulas" has been introduced by the way of the "causal atoms".…”

“…Since {} and {α, ¬α} ⊥ obviously hold, it looks like the predictive inference relation satisfies all the postulates of a causal production relation as defined in [4] and all the properties of a disjunctive causal relation [3]. It must be pointed out that our hypotheses are expressed here in terms of causal formulas while our conclusions pertain to classical logic.…”