Abstract
We explore systematic connections between weighted (semi-abstract) argumentation frames and t-norm-based fuzzy logics. To this aim we introduce the concept of argumentative immunity, as well as corresponding notions of argumentative soundness and completeness with respect to given sets of logical attack principles. For Gödel logic, a detailed proof of argumentative soundness and completeness with respect to appropriate principles is presented. For Łukasiewicz and product logic this is indicated more briefly, but with some hints on corresponding interpretations of the attack relation between (claims of) arguments. Moreover, the central axiom of prelinearity is analyzed from our argumentation-based perspective.
Highlights
In a seminal paper Dung (1995) demonstrated that various concepts of non-monotonic reasoning, logic programming, and game theory can be modeled via so-called abstract argumentation frameworks
The idea to connect the semantics of fuzzy logics to weighted attacks seems to be novel
We introduced the notion of argumentative immunity with respect to given collections of attack principles
Summary
In a seminal paper Dung (1995) demonstrated that various concepts of non-monotonic reasoning, logic programming, and game theory can be modeled via so-called abstract argumentation frameworks The latter are directed graphs, where the vertices are identified with arguments and the edges represent attacks between arguments. Our aim is to provide a detailed picture regarding the respective necessity and sufficiency of a fairly large set of different principles for characterizing various tnorm-based fuzzy logics Another possible misunderstanding that we want to address right away concerns the very nature of argumentation-based reasoning: shouldn’t any ‘logic of argumentation’ be non-monotonic? 2 we quickly review some basic concepts from Corsi and Fermüller (2017) regarding classical attack principles These notions and some of the principles are generalized to weighted (semi-abstract) argumentation frames in Sect. In the conclusion (Sect. 10) we briefly look back at what we have achieved and suggest several directions for further research
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
