An Axiomatic Study of the Evaluation of Enthymeme Decoding in Weighted Structured Argumentation

An argument can be seen as a pair consisting of a set of premises and a claim supported by them. Arguments used by humans are often enthymemes, i.e., some premises are implicit. To better understand, evaluate, and compare enthymemes, it is essential to decode them, i.e., to find the missing premisses. Many enthymeme decodings are possible. We need to distinguish between reasonable decodings and unreasonable ones. However, there is currently no research in the literature on "How to evaluate decodings?". To pave the way and achieve this goal, we introduce seven criteria related to decoding, based on different research areas. Then, we introduce the notion of criterion measure, the objective of which is to evaluate a decoding with regard to a certain criterion. Since such measures need to be validated, we introduce several desirable properties for them, called axioms. Another main contribution of the paper is the construction of certain criterion measures that are validated by our axioms. Such measures can be used to identify the best enthymemes decodings.

Understanding Enthymemes in Argument Maps: Bridging Argument Mining and Logic-based Argumentation

Argument mining is natural language processing technology aimed at identifying arguments in text. Furthermore, the approach is being developed to identify the premises and claims of those arguments, and to identify the relationships between arguments including support and attack relationships. In this paper, we assume that an argument map contains the premises and claims of arguments, and support and attack relationships between them, that have been identified by argument mining. So from a piece of text, we assume an argument map is obtained automatically by natural language processing. However, to understand and to automatically analyse that argument map, it would be desirable to instantiate that argument map with logical arguments. Once we have the logical representation of the arguments in an argument map, we can use automated reasoning to analyze the argumentation (e.g. check consistency of premises, check validity of claims, and check the labelling on each arc corresponds with thw logical arguments). We address this need by using classical logic for representing the explicit information in the text, and using default logic for representing the implicit information in the text. In order to investigate our proposal, we consider some specific options for instantiation.

Preferential and Preferential-discriminative Consequence relations

The present paper investigates consequence relations that are both non-monotonic and paraconsistent. More precisely, we put the focus on preferential consequence relations, i.e. those relations that can be defined by a binary preference relation on states labelled by valuations. We worked with a general notion of valuation that covers e.g. the classical valuations as well as certain kinds of many-valued valuations. In the many-valued cases, preferential consequence relations are paraconsistant (in addition to be non-monotonic), i.e. they are capable of drawing reasonable conclusions which contain contradictions. The first purpose of this paper is to provide in our general framework syntactic characterizations of several families of preferential relations. The second and main purpose is to provide, again in our general framework, characterizations of several families of preferential discriminative consequence relations. They are defined exactly as the plain version, but any conclusion such that its negation is also a conclusion is rejected (these relations bring something new essentially in the many-valued cases).