The interplay of logic and argumentation has a long history, from (at least) Aristotle to very recent research in the field of knowledge representation and reasoning, and on formalisation of argumentation in artificial intelligence. This is a highly interdisciplinary research field, involving researchers from several fields including logic, philosophy, computer science, artificial intelligence, and law.
For this special issue of Journal of Applied Non-Classical Logic on Logic and Argumentation we invited original contributions in either area, and particularly encouraged submissions in the intersection between the two, in order to facilitate further cross-fertilisation.
One of the currently most active areas in that intersection is the emerging field of abstract argumentation, taking the abstract argumentation framework proposed by Phan Minh Dung as a starting point. As Yuming Xu and Claudette Cayrol say in their article in this issue, ‘Dung's abstract argumentation provides us with a general framework to deal with argumentation, non-monotonic reasoning and logic programming’. For example, formal logic is used to instantiate abstract argumentation frameworks, and to reason about them.
The special issue is a follow-up to the First Chinese Conference on Logic and Argumentation (CLAR 2016) that took place at Zhejiang University in May 2016. The goal of the CLAR conferences is to promote communication between researchers in the field of logic and argumentation within and outside China. The CLAR 2016 conference was a truly international conference, with participants from several countries including France, Japan, Luxembourg, the Netherlands and Norway.
The articles submitted to the special issue were peer reviewed by at least two referees each. The six you find in this special issue are the result of a selection based on their recommendations, giving a glimpse of the current state of the art in the intersection of logic and argumentation. Most of them are related to Dung's abstract argumentation framework in some way.
In Beliefs supported by binary arguments, Chenwei Shi, Sonja Smets and Fernando R. Velázques-Quesada build connections between logic and argumentation in both directions. They use an abstract argumentation framework to provide the basis for a logic of belief, as well as providing a formal sound and complete logic for reasoning about a certain kind of arguments (binary arguments).
Gabriella Pigozzi and Leendert van der Torre, in Arguing about constitutive and regulative norms, study normative arguments, and explores connections between abstract argumentation frameworks and deontic logic.
Chiaki Sakama formulates and studies a notion of abduction in abstract argumentation frameworks, in Abduction in argumentation frameworks, and in particular shows how it can be computed using logic programming.
In On the measure of conflicts: An argumentation based framework by Badran Raddaoui, formal argumentation is used to study logic, instead of the other way around. The article employs deductive argumentation theory to provide a new measure of inconsistency in propositional knowledge bases.
In Initial sets in abstract argumentation frameworks, Yuming Xu and Claudette Cayrol propose and study two new extension-based semantics into Dung's abstract argumentation framework.
Finally, in A game-theoretic analysis on the use of indirect speech acts Mengyuan Zhao develops a game-theoretic model if indirect speech acts, and uses it to study non-conventional speech acts such as ironical requests and implicit bribery.
We would like to thank all the authors who submitted contributions, the referees for this special issue as well as the program committee of CLAR 2016, for their hard work on the frontiers of logic and argumentation.