Abstract Plausible reasoning concerns situations that have an inherent lack of precision, which is not quantified; that is, there are no degrees or levels of precision, and hence no use of numbers like probabilities. A hopefully comprehensive set of principles that clarifies what it means for a formal logic to do plausible reasoning is presented. Several important plausible-reasoning examples that guide the development of some of the principles are also given. Versions of these principles and examples have appeared in Billington (2017) and chapter 4 of Billington (2019). Each principle in this article is the same as, or an improvement on, the corresponding principle in chapter 4 of Billington (2019); for a detailed comparison, see the Appendix. A propositional plausible logic that satisfies all these principles appears in Billington (2017, 2019). This shows that all the principles together are consistent.

Defeasible reasoning is a computationally simple nonmonotonic reasoning approach that has attracted significant theoretical and practical attention. It comprises a family of logics that capture different intuitions, among them ambiguity propagation versus ambiguity blocking, and the adoption or rejection of team defeat. This article provides a compact presentation of the defeasible logic variants, and derives an inclusion theorem which shows that different notions of provability in defeasible logic form a chain of levels of proof.

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.

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 modelling 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. There are several reasons for the significance of this work: (a) establishing links between formal systems leads to a better understanding and cross-fertilization, in particular our work sheds light on the argumentation-theoretic features of defeasible logic; (b) we provide the first ambiguity blocking Dung-like argumentation system; (c) defeasible reasoning may provide an efficient implementation platform for systems of argumentation; and (d) argumentation-based semantics support a deeper understanding of defeasible reasoning, especially in the context of the intended applications.

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.

For many years, the non-monotonic reasoning community has focussed on highly expressive logics. Such logics have turned out to be computationally expensive, and have given little support to the practical use of non-monotonic reasoning. In this work we discuss defeasible logic, a less-expressive but more efficient non-monotonic logic. We report on two new implemented systems for defeasible logic: a query answering system employing a backward chaining approach, and a forward-chaining implementation that computes all conclusions. Our experimental evaluation demonstrates that the systems can deal with large theories (up to hundreds of thousands of rules). We show that defeasible logic has linear complexity, which contrasts markedly with most other non-monotonic logics and helps to explain the impressive experimental results. We believe that defeasible logic, with its efficiency and simplicity is a good candidate to be used as a modelling language for practical applications, including modelling of regulations and business rules.

Although humans seem adept at drawing nonmonotonic conclusions, the nonmonotonic reasoning systems that researchers develop are complex and do not function with such ease. This paper explores people's reasoning processes in nonmonotonic problems. To avoid the problem of people's conclusions being based on knowledge rather than on some reasoning process, we developed a scenario about life on another planet. Problems were chosen to allow the systematic study of people's understanding of strict and nonstrict rules and their interactions. We found that people had great difficulty reasoning and we identified a number of negative factors influencing their reasoning. We also identified three positive factors which, if used consistently, would yield rational and coherent reasoning—but no subject achieved total consistency. (Another possible positive factor, specificity, was considered but we found no evidence for its use.) It is concluded that nonmonotonic reasoning is hard. When people need to reason in a domain where they have no preconceived ideas, the foundation for their reasoning is neither coherent nor rational. They do not use a nonmonotonic reasoning system that would work regardless of content. Thus, nonmonotonic reasoning systems that researchers develop are expected to do more reasoning than humans actually do!

Abstract Given a loop invariant, I , and an assignment, α , which decreases the variant, we define a constructive function, cg, called the co-invariant generator, which has the property that I Λ cg ( α, I ) ⇒ wp ( α, I ), where wp ( α, I ) is the weakest precondition for α to establish I. Several results about the co-invariant generator are proved, important special cases are considered, and a non-trivial example of its use in deriving the body of a loop is given. We also define a function which performs a related constructive action on terms formed from binary operations. The coinvariant generator makes a useful contribution to formalising and automating a key step in program derivation.

We define, and give some of the intuition behind the definition of, a nonmonotonic logic called defeasible logic. Results are proved which enable us to see how well the definition captures our intuitions. These results indicate that defeasible logic is well behaved. Section 3 considers, among other things, what happens when a defeasible logic is inconsistent. The next two sections are concerned with stability, that is, the property of being undisturbed by the addition or deletion of redundant information. In Section 4 we consider redundant rules, and in Section 5 we consider lemma addition. That is the adding of a proved result to the ‘axioms’ of the logic.

The sceptical inheritance nets introduced in Horty et al. [Proceedings of AAAI-87 (1987):358-363] are translated into a version of Nute's defeasible logic. Moreover this translation is modular in the sense of Thomason and Horty [Non-Monotonic Reasoning. Springer-Verlag (1989):234]. Apart from the importance of relating two nonmonotonic reasoning formalisms, this result shows that the reasoning mechanisms underlying defeasible logic and defeasible nets are the same. Yet they were invented independently and set in totally different contexts. This is perhaps some evidence that the underlying nonmonotonic reasoning mechanism is mainly correct. We also observe that since defeasible logics can contain both absolute and defeasible rules, they provided a uniform setting for considering nets which contain both strict and defeasible arcs.