A Mathematical Conceptualization of Bundle Sets in Defeasible Logic Programming

Defeasible Logic Programming (DeLP) is a formalism for structured argumentation-based reasoning that is founded on a dialectical procedure that relies on trees to compute answers to queries, which return the so-called warrant statuses of the literals involved. In this work, we propose a novel, more general, and minimal structure (understanding it as the minimum information necessary to warrant a statement) than the concept of dialectical tree, which we call parsimonious bundle set. This structure is significant for a line of research that we are carrying out in which we are studying the theoretical foundations of DeLP toward the definition of model-theoretic semantics, a contribution that, in turn, will allow us to analyze the formalism from a different perspective, focusing on theoretical aspects, and also to eventually generalize the query language from literals to formulas built from Boolean connectives. Therefore, in this first step, we focus on developing the basic tools required to provide an alternative to the operational semantics of DeLP that is centered on declarative definitions.