Abstraction in Non-Monotonic Reasoning

Abstraction emerges as a valuable method across diverse domains of Artificial Intelligence (AI), particularly in the field of knowledge representation and reasoning. Intuitively, abstraction maps a complicated structure to a simpler version of it. That reduces the computational complexity of the task being considered, as it provides us with the ability to focus on the parts of the problem that are relevant to the solution. In our view, such a tool can also have potential in the field of non-monotonic reasoning. Non-monotonicity is a crucial notion as it is very common when reasoning over defeasible knowledge. Adding new entries to our current knowledge, oftentimes results in restricting the conclusions that we can draw. For this form of reasoning we use certain formalisms, such as computational argumentation and Logic Programming (LP), that help us capture non-monotonicity. However, interpreting these formalisms faces hardships due to the large structures that might occur when representing the problem in question. Hence, coming up with ways to manage these structures easier is necessary. Recently, abstraction was shown to be a promising tool when dealing with Argumentation Frameworks (AFs) as well as with LP. AFs are frameworks with graph-like structure, whose nodes represent arguments with no internal structure, while edges stand for conflicts among the arguments. In our research we focus on continuing in this direction by employing structured frameworks such as Assumption-Based Argumentation Frameworks (ABAFs). Subsequently, we will extend our research to similar formalisms such as LP.