A parameterised hierarchy of argumentation semantics for extended logic programming and its application to the well-founded semantics

Abstract

Argumentation has proved a useful tool in defining formal semantics for assumption-based reasoning by viewing a proof as a process in which proponents and opponents attack each others arguments by undercuts (attack to an argument's premise) and rebuts (attack to an argument's conclusion). In this paper, we formulate a variety of notions of attack for extended logic programs from combinations of undercuts and rebuts and define a general hierarchy of argumentation semantics parameterised by the notions of attack chosen by proponent and opponent. We prove the equivalence and subset relationships between the semantics and examine some essential properties concerning consistency and the coherence principle, which relates default negation and explicit negation. Most significantly, we place existing semantics put forward in the literature in our hierarchy and identify a particular argumentation semantics for which we prove equivalence to the paraconsistent well-founded semantics with explicit negation, WFSXp. Finally, we present a general proof theory, based on dialogue trees, and show that it is sound and complete with respect to the argumentation semantics.

The State of the Art in the Development of a Versatile Argumentation System based on the Logic of Multiple-valued Argumentation

“…Argument in EALP and LMA EALP (Extended Annotated Logic Programming) is an extended version of the Annotated Logic Programming (ALP) (Schweimeier and Schroeder, 2005) by introducing the extra negations below. Suppose the followings are knowledge bases that agent A and B have for argumentation respectively.…”

“…In LMA, whether an agenda of argumentation is justified or not is judged based on the grounded semantics in Dungean semantics (Dung, 1995). In particular, the results of argumentation are displayed as dialogue trees based on the dialectical proof theory that corresponds to the grounded semantics (Schweimeier and Schroeder, 2005). A dialogue tree is a tree in which the node of the tree represents an argument and the branch of the tree represents an attack relation (Takahashi and .…”

An encompassing framework for Paraconsistent Logic Programs

“…In this work, we will generalize to some extent this property involving the detection of information support on inconsistency, in order to make it applicable in complete bilattices of truth-values. For a recent characterization of WFSX p in terms of argumentation semantics, the reader is referred to [29].…”