Abductive Reasoning with Abstraction Axioms

ion Axioms ? Luca Console 1 and Daniele Theseider Dupr'e 2 1 Dipartimento di Matematica e Informatica, Universit`a di Udine Via Zanon 6, 33100 Udine, Italy 2 Dipartimento di Informatica, Universit`a di Torino, Corso Svizzera 185, 10149 Torino, Italy Abstract. This paper deals with abductive reasoning on knowledge bases that are expressed at different levels of abstraction, but are not necessarily organized as a set of increasingly more abstract models, each one giving a complete (even if abstracted) description of a domain. We claim that the search for abductive explanations in such a context and, in particular, the choice of the "right" level at which explanations have to be determined, should be driven by the available observations in such a way that explanations involving low-level phenomena are allowed only if there are specific observations related to them, or higher-level explanations cannot be found. We present formal definitions following this principle and we discuss ho..

The Different Roles of Abstraction in Abductive Reasoning

ion in Abductive Reasoning Daniele Theseider Dupr'e and Mauro Rossotto ? Dipartimento di Informatica -- Universit`a di Torino Corso Svizzera 185 -- 10149 Torino, Italy -- E-mail: [email protected] Abstract. The use of knowledge at different levels of abstraction can be proposed to make automated abduction more flexible. This paper analyzes several declarative and computational ways of exploiting abstractions in abduction, including the definition and implementation of preference criteria for explanations based on abstraction, and the use of abstractions to focus the explanation process. 1 Introduction An important challenge in knowledge representation and reasoning is the reproduction, at least to some extent, of the human capability of exploiting abstractions, i.e. of being able to deal with information at different levels of abstraction, and to shift from one level to another when necessary. The goal of this paper is to analyze the use of abstractions in abductive reasoning (i.e. rea..

On the Role of Abduction

point of view, this corresponds to the unsound inference concluding A from A ! B and B. Abduction is thus a form of non-classical inference whose properties (e.g., non-monotonicity) are similar to those of other non-classical logics proposed and studied in the AI literature. Given such premises, one would expect that abduction played a central role in the logical approaches to AI. In fact, however, many researchers are quite diffident about such a form of reasoning and some criticisms have arisen in the Appears in ACM Computing Surveys vol.27 n.3, 1995, pp 353-355. 2 last decade. We believe that abduction should gain its central role, that most of the criticisms are not justified and that the use of abduction has interesting properties that make it comparable and in some case preferable to other forms of non-monotonic reasoning. Let us start from the last point. In our view abduction is a quite simple form of inference, w

Ramifications in an Event-based Language

In the last couple of years, several high-level languages have been proposed for modeling actions and change, following the example of Gelfond and Lifschitz's A language and tackling increasingly complex issues. In this paper we present a narrative-based language ER with a linear time structure, which is designed to deal correctly with simultaneous actions as well as with general fluent and change dependencies, in particular ramifications. We argue that a combination of state constraints, causal laws and action preconditions is necessary to correctly represent all such dependencies. In particular, we introduce causal laws stating that a change is triggered by a change in truth value of a complex fluent formula; we show such laws to be useful for a compact representation of ramifications, in particular those of simultaneous actions. A semantics for such complex causal laws is provided based on the principle of inductive definitions. Moreover ER is able to deal in a very flexible way wi..