Related papers: Embedding Default Logic in Propositional Argumenta…

Default logic can be regarded as a mechanism to represent families of belief sets of a reasoning agent. As such, it is inherently second-order. In this paper, we study the problem of representability of a family of theories as the set of…

This article describes the first implementation of the GADEL system : a Genetic Algorithm for Default Logic. The goal of GADEL is to compute extensions in Reiter's default logic. It accepts every kind of finite propositional default…

We endow prioritised default logic (PDL) with argumentation semantics using the ASPIC+ framework for structured argumentation, and prove that the conclusions of the justified arguments are exactly the prioritised default extensions.…

In default reasoning, usually not all possible ways of resolving conflicts between default rules are acceptable. Criteria expressing acceptable ways of resolving the conflicts may be hardwired in the inference mechanism, for example…

A fact apparently not observed earlier in the literature of nonmonotonic reasoning is that Reiter, in his default logic paper, did not directly formalize informal defaults. Instead, he translated a default into a certain natural language…

Reiter's original definition of default logic allows for the application of a default that contradicts a previously applied one. We call failure this condition. The possibility of generating failures has been in the past considered as a…

The lexicographic closure of any given finite set D of normal defaults is defined. A conditional assertion "if a then b" is in this lexicographic closure if, given the defaults D and the fact a, one would conclude b. The lexicographic…

A default theory can be characterized by its sets of plausible conclusions, called its extensions. But, due to the theoretical complexity of Default Logic (Sigma_2p-complete), the problem of finding such an extension is very difficult if…

We use the theory of defaults and their meaning of [GS16] to develop (the outline of a) new theory of argumentation.

This paper studies axioms for nonmonotonic consequences from a semantics-based point of view, focusing on a class of mathematical structures for reasoning about partial information without a predefined syntax/logic. This structure is called…

In inductive learning of a broad concept, an algorithm should be able to distinguish concept examples from exceptions and noisy data. An approach through recursively finding patterns in exceptions turns out to correspond to the problem of…

We consider the question of extending propositional logic to a logic of plausible reasoning, and posit four requirements that any such extension should satisfy. Each is a requirement that some property of classical propositional logic be…

Various structured argumentation frameworks utilize preferences as part of their standard inference procedure to enable reasoning with preferences. In this paper, we consider an inverse of the standard reasoning problem, seeking to identify…

We present an extension-based approach for computing and verifying preferences in an abstract argumentation system. Although numerous argumentation semantics have been developed previously for identifying acceptable sets of arguments from…

Many writers have observed that default logics appear to contain the "lottery paradox" of probability theory. This arises when a default "proof by contradiction" lets us conclude that a typical X is not a Y where Y is an unusual subclass of…

There is a generic way to add any new feature to a system. It involves 1) identifying the basic units which build up the system and 2) introducing the new feature to each of these basic units. In the case where the system is argumentation…

Within classical propositional logic, assigning probabilities to formulas is shown to be equivalent to assigning probabilities to valuations. A novel notion of probabilistic entailment enjoying desirable properties of logical consequence is…

We express Brewka's prioritised default logic (PDL) as argumentation using ASPIC+. By representing PDL as argumentation and designing an argument preference relation that takes the argument structure into account, we prove that the…

In the present paper, the existence and multiplicity problems of extensions are addressed. The focus is on extension of the stable type. The main result of the paper is an elegant characterization of the existence and multiplicity of…

We study a conservative extension of classical propositional logic distinguishing between four modes of statement: a proposition may be affirmed or denied, and it may be strong or classical. Proofs of strong propositions must be…