Simple conceptual graphs are considered as the kernel of most knowledge representation formalisms built upon $owa's model. Reasoning in this model can be expressed by a graph homomorphism called projection, whose semantics is usually given in terms of positive, conjunctive, existential FOL. We present here a family of extensions of this model, based on rules and constraints, keeping graph homomorphism as the basic operation. We focus on the formal definitions of the different models obtained, including their operational semantics and relationships with FOL, and we analyze the decidability and complexity of the associated problems (consistency and deduction). As soon as rules are involved in reasonings, these problems are not decidable, but we exhibit a condition under which they fall in the polynomial hierarchy. These results extend and complete the ones already published by the authors. Moreover we systematically study the complexity of some particular cases obtained by restricting the form of constraints and/or rules.

Abductive logic programming (ALP) and disjunctive logic programming (DLP) are two di#erent extensions of logic programming. This paper investigates the relationship between ALP and DLP from the program transformation viewpoint. It is shown that the belief set semantics of an abductive program is expressed by the answer set semantics and the possible model semantics of a disjunctive program. In converse, the possible model semantics of a disjunctive program is equivalently expressed by the belief set semantics of an abductive program, while such a transformation is generally impossible for the answer set semantics. Moreover, it is shown that abductive disjunctive programs are always reducible to disjunctive programs both under the answer set semantics and the possible model semantics. These transformations are verified from the complexity viewpoint. The results of this paper turn out that ALP and DLP are just di#erent ways of looking at the same problem if we choose an appropriate seman...

this paper, we propose a computational mechanism for extended abduction. When a background theory is written in a normal logic program, we introduce its transaction program for computing extended abduction. A transaction program is a set of non-deterministic production rules that declaratively specify addition and deletion of abductive hypotheses. Abductive explanations are then computed by the fixpoint of a transaction program using a bottom-up model generation procedure. The correctness of the proposed procedure is shown for the class of acyclic covered abductive logic programs. In the context of deductive databases, a transaction program provides a declarative specification of database update. Keywords: abduction, nonmonotonic reasoning, database update 1. Introduction 1.1. Motivation and background Abduction is inference to best explanations, and has recently been recognized as a very important form of reasoning in both AI [2

this paper is to provide a discussion of some issues appertaining to the potential of abduction in Artificial Intelligence, set against a background which is on the one hand philosphical, but justified by means of mathematical formalization of its primary arguments concerning abduction, and on the other hand driven by practical application of the theory to for example machine learning or the development of robust, communicative agents.

this paper is to provide a discussion of some issues appertaining to the potential of abduction in Artificial Intelligence, set against a background which is on the one hand philosphical, but justified by means of mathematical formalization of its primary arguments concerning abduction, and on the other hand driven by practical application of the theory to for example machine learning or the development of robust, communicative agents.

los, no por ello pierden su importancia como formas de inferir informaci'on en otras ciencias y en las humanidades. Tal es caso del razonamiento explicativo, de la abduccion. A continuaci'on motivamos este tipo de razonamiento y presentamos algunos ejemplos. 1.1 Qu'e es la abducci'on? Un tema central en el estudio del razonamiento humano es el de la construcci 'on de las explicaciones que nos dan entendimiento del mundo en que vivimos. En un sentido muy amplio, la abducci'on es el proceso de razonamiento para explicar observaciones sorprendentes. Un ejemplo t'ipico se encuentra en el 'area de diagn'ostico m'edico. Cuando una doctora observa un s'intoma en un paciente, ella construye una hip'otesis sobre las posibles causas, bas'andose en su conocimiento de las relaciones causales entre enfermedades y s'intomas. La abducci'on tambi'en se manifiesta en el razonamiento de sentido com'un que hacemos a diario. Si nos levantamos una ma~nana y vemos que el patio est'a mojado, podemos explic