Coalition Formability Semantics with Conflict-Eliminable Sets of Arguments

Abstract: We consider abstract-argumentation-theoretic coalition formability in this work. Taking a model from political alliance among political parties, we will contemplate profitability, and then formability, of a coalition. As is commonly understood, a group forms a coalition with another group for a greater good, the goodness measured against some criteria. As is also commonly understood, however, a coalition may deliver benefits to a group X at the sacrifice of something that X was able to do before coalition formation, which X may be no longer able to do under the coalition. Use of the typical conflict-free sets of arguments is not very fitting for accommodating this aspect of coalition, which prompts us to turn to a weaker notion, conflict-eliminability, as a property that a set of arguments should primarily satisfy. We require numerical quantification of attack strengths as well as of argument strengths for its characterisation. We will first analyse semantics of profitability of a given conflict-eliminable set forming a coalition with another conflict-eliminable set, and will then provide four coalition formability semantics, each of which formalises certain utility postulate(s) taking the coalition profitability into account.