Defeasible Theories Research Articles

Embedding defeasible logic into logic programming

Defeasible reasoning is a simple but efficient approach to nonmonotonic reasoning that has recently attracted considerable interest and that has found various applications. Defeasible logic and its variants are an important family of defeasible reasoning methods. So far no relationship has been established between defeasible logic and mainstream nonmonotonic reasoning approaches. In this paper we establish close links to known semantics of logic programs. In particular, we give a translation of a defeasible theory , instead.

Abductive inference in defeasible reasoning: a model for research programmes

Abduction is regarded as the inference process that goes from observations to explanations within a more general context or theoretical framework. There are good characterizations of abduction of surprising observations in monotonic theories. Also, in normal logic programs there are a tight relation among SLDNF and the abduction of negative literals. However, a problem that faces abduction is the explanation of anomalous observations, i.e., observations that are contradictory with respect to the current theory. For this reason, in this work we will consider the problem of embedding abduction of surprising and anomalous observations in defeasible (nonmonotonic) theories. We discuss some issues arising the pragmatic acceptance of abductive inferences in defeasible theories, and how to accommodate anomalous observations and characterize all the possible outcomes that a defeasible theory may face when confronted with new evidence. We explore the use of partial structures approach as a semantic foundation for our system. Finally, we discuss an application of our system as a formal device for representing the methodology of scientific research programmes. In this representation, a programme is regarded as a defeasible theory that draws predictions. When confronted with surprising or anomalous observations, the programme protects itself by means of heuristic procedures, which are represented in our system as abductive inference procedures.

On the relation between vector annotated logic programs and defeasible theories

In this paper, we propose an annotated logic program called a VALPSN (Vector Annotated Logic Program with Strong Negation) to deal with defeasible reasoning. We propose a translation from Billington’s defeasible theory into VALPSN and clarify the relation between them based on the translation.

A Theory of Legal Doctrine

Legal doctrine in Continental European law (scientia iuris) consists of professional legal writings, e.g., handbooks, monographs, etc., whose task is to systematize and interpret valid law. By production of general and defeasible theories, legal doctrine aims to present the law as a coherent net of principles, rules, meta‐rules, and exceptions, at different levels of abstraction, connected by support relations. The argumentation used to achieve coherence involves not only description and logic but also evaluative (normative) steps. However, sceptics criticise juristic doctrine for its normative character, ontological obscurity, vagueness, fragmentation, and locality. The author answers this criticism pointing out the following. Normative reason is possible. Liberal ontology, admitting such entities as morally justified law, is possible as well. The vagueness of legal doctrine can be construed as defeasibility. Defeasibility is inevitable in the law and in human thinking in general. Fragmentation of legal doctrine is not absolute. Its theories are linked to overarching moral theories. Finally, locality is not absolute either. Though sometimes restricted to a given state, theories of legal doctrine display relevant similarities to corresponding theories in other states.

Scientia Iuris - An Unsolved Philosophical Problem

Legal dogmatics in Continental European law (scientia iuris, Rechtswissenschaft) consists of professional legal writings whose task is to systematize and interpret valid law. Legal dogmatics pursues knowledge of the existing law, yet in many cases it leads to a change of the law. Among general theories of legal dogmatics, one may mention the theories of negligence, intent, adequate causation and ownership. The theories produce principles and they also produce defeasible rules. By means of production of general and defeasible theories, legal dogmatics aims at obtaining a system of law that is both internally coherent and harmonized with its background in morality and (political) philosophy. Legal dogmatics is necessary in the context of constitutional constraints on the majority rule. Only if the courts act on the basis of Reason they can be a legitimate counterpart of the majority rule. And Reason cannot be exhausted by particular decision making. It also needs a more abstract deliberation, given by expert jurists. However, legal dogmatics has been a target of several kinds of criticism: empirical, morally-political, epistemological, logical, and ontological. The position taken in this article is to answer such criticism by mutually adjusting philosophy and the practices of the law.

Defeasible logic graphs: II. Implementation

We propose development of an argument based decision support system utilizing defeasible or nonmonotonic reasoning. Defeasible logic graphs (d-graphs) represent the knowledge contained in a defeasible theory. A method for propagating labels through d-graphs is developed as a means for reasoning about the theory from which the d-graph is generated. This method is proven to be sound with respect to Nute's defeasible logic and complete for finite, consistent theories with acyclic d-graphs.

Defeasible logic graphs: I. Theory

We propose development of an argument-based decision support system utilizing defeasible or nonmonotonic reasoning. Defeasible logic graphs (d-graphs) represent the knowledge contained in a defeasible theory. A method for propagating labels through a d-graph is developed as a means for reasoning about the theory from which the d-graph is generated. This method is proven to be sound with respect to Nute's defeasible logic and complete for finite, consistent theories with acyclic d-graphs.

Ordered logic: defeasible reasoning for multiple agents

Our goal is to provide a theoretical foundation for knowledge based applications which support nonmonotonic or defeasible reasoning and which incorporate the knowledge of multiple experts in a principled way. We present a generalized proof theory for defeasible reasoning and briefly explain the relationship of this system to other nonmonotonic formalisms. Then we present a proof theory and semantics for a logic that allows us to explicitly model internal perspectives or multiple agents. This ordered logic properly extends defeasible logic by allowing more complex precedence structure on rules. It provides a mechanism for resolving conflicts between competing perspectives without obscuring the opinions of those perspectives. We show which defeasible theories can be transformed into an equivalent theory in the new logic for multiagent reasoning and how a theory in the logic for multiagent reasoning can be transformed into an equivalent set of defeasible theories, one for each perspective or agent. We present a proof theory for quantified ordered logic and introduce the concept of a curtain which shields the cognitive resources of one agent from another agent. Finally, we consider some examples and discuss how it is possible to specify the relative superiority of some experts over others in a natural way using ordered logic.

A Problem for Defeasibility Theories

A Problem for Defeasibility Theories

Defeasibility Theories of Knowledge

There have been many attempts of late to formulate a satisfactory theory of knowledge with which to replace the traditional justified true belief analysis. Almost all agree that it must be the case that in order for S to know that p; i.) p be true, and ii.) S believe that p. Although many argue that there must be a condition stating that S has adequate evidence for p, requirements other than i.) and ii.) are controversial. The most popular approach taken, however, is the addition of a requirement to the effect that for S to know that p there must be no other evidence against p strong enough to undermine S's belief that p, should this evidence come to S's attention. I shall call such a requirement a “defeasibility condition” and any theory containing such a requirement a defeasibility theory.Defeasibility theories are quite effective in handling a certain kind of difficulty to which theories of knowledge are subject, namely problems dealing with what Harman has termed the social aspect of knowledge.