A family of defeasible reasoning logics and its implementation

Proceedings of the 2008 ACM symposium on Applied computing - SAC '08, 2008

Defeasible logic is a simple and efficient rule-based nonmonotonic reasoning approach, that has been shown useful for various applications areas. Recently defeasible logic has been used in applications to the Semantic Web.

Annals of Mathematics and Artificial Intelligence, 2005

In this paper, we establish a formal semantics for Pollock’s [23] theory of defeasible reasoning. As a notion of argument or argumentation has never been formalised in this theory, it is important that such a formal account be introduced to couple with the algorithmic description of the theory. In particular, it makes Pollock’s theory become more comparable to other related frameworks as shown in the paper. In also enforces a well-defined semantical account for Pollock’s theory of defeasible reasoning based on the argumentation-theoretic approach proposed by Dung and Bondarenko et al. [1,5]. Our formalisation thus enables further studies to the meta-theoretic properties of Pollock’s defeasible reasoning system.

The work reported here introduces Defeasible Logic Programming (DeLP), a formalism that combines results of Logic Programming and Defeasible Argumentation. DeLP provides the possibility of representing information in the form of weak rules in a declarative manner, and a defeasible argumentation inference mechanism for warranting the entailed conclusions. In DeLP an argumentation formalism will be used for deciding between contradictory goals. Queries will be supported by arguments that could be defeated by other arguments. A query q will succeed when there is an argument A for q that is warranted, i. e. the argument A that supports q is found undefeated by a warrant procedure that implements a dialectical analysis. The defeasible argumentation basis of DeLP allows to build applications that deal with incomplete and contradictory information in dynamic domains. Thus, the resulting approach is suitable for representing agent's knowledge and for providing an argumentation based reasoning mechanism to agents.

Theory and Practice …, 2006

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.

Theory and Practice of Logic Programming, 2020

Recent technological advances have led to unprecedented amounts of generated data that originate from the Web, sensor networks, and social media. Analytics in terms of defeasible reasoning – for example, for decision making – could provide richer knowledge of the underlying domain. Traditionally, defeasible reasoning has focused on complex knowledge structures over small to medium amounts of data, but recent research efforts have attempted to parallelize the reasoning process over theories with large numbers of facts. Such work has shown that traditional defeasible logics come with overheads that limit scalability. In this work, we design a new logic for defeasible reasoning, thus ensuring scalability by design. We establish several properties of the logic, including its relation to existing defeasible logics. Our experimental results indicate that our approach is indeed scalable and defeasible reasoning can be applied to billions of facts.

Argument & Computation, 2014

Argumentation represents a way of reasoning over a knowledge base containing possibly incomplete and/or inconsistent information, to obtain useful conclusions. As a reasoning mechanism, the way an argumentation reasoning engine reaches these conclusions resembles the cognitive process that humans follow to analyse their beliefs; thus, unlike other computationally reasoning systems, argumentation offers an intellectually friendly alternative to other defeasible reasoning systems. Logic Programming is a computational paradigm that has produced computationally attractive systems with remarkable success in many applications. Merging ideas from both areas, Defeasible Logic Programming offers a computational reasoning system that uses an argumentation engine to obtain answers from a knowledge base represented using a logic programming language extended with defeasible rules. This combination of ideas brings about a computationally effective system together with a human-like reasoning model facilitating its use in applications.

Journal of Logic and …, 2004

Defeasible reasoning is a simple but efficient rule-based approach to nonmonotonic reasoning. It has powerful implementations and shows promise to be applied in the areas of legal reasoning and the modeling of business rules. This paper establishes significant links between defeasible reasoning and argumentation. In particular, Dung-like argumentation semantics is provided for two key defeasible logics, of which one is ambiguity propagating and the other ambiguity blocking.

… , 2008. WI-IAT'08. …, 2008

Modal logic deals with necessity and possibility, exhibiting defeasibility; thus, it is possible to combine defeasible logic with modal operators. This paper reports on the extension of the DR-DEVICE defeasible reasoner with modal and deontic logic operators. The aim is a practical defeasible reasoner that will take advantage of the expressiveness of modal logics and the flexibility to define diverse agent types and behaviors.

ACM Transactions on …, 2001

The importance of transformations and normal forms in logic programming, and generally in computer science, is well documented. This paper investigates transformations and normal forms in the context of Defeasible Logic, a simple but efficient formalism for nonmonotonic reasoning based on rules and priorities. The transformations described in this paper have two main benefits: on one hand they can be used as a theoretical tool that leads to a deeper understanding of the formalism, and on the other hand they have been used in the development of an efficient implementation of defeasible logic.

Theory and practice of logic programming, 2004

The work reported here introduces Defeasible Logic Programming (DeLP), a formalism that combines results of Logic Programming and Defeasible Argumentation. DeLP provides the possibility of representing information in the form of weak rules in a declarative manner, and a defeasible argumentation inference mechanism for warranting the entailed conclusions.