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.

While propositional Answer Set Programming (ASP) is already NP-hard and therefore powerful enough to express many challenging problems, their specification can be tedious and complicated. Further, there are relevant problems that require higher expressivity or reasoning over data that changes with time. This and the practical usage of ASP gave rise to a need for a simpler, more expressive, and more concise specification language [1, 11]. Thus, ASP was extended in multiple directions. We focus on the following ones: 1. Time Domain (TD): In [5] ASP-semantics were combined with a temporal context resulting in the Logic-based framework for Analytic Reasoning over Streams (LARS). Here, interpretations assign possibly different sets of facts to time points. Accordingly, the input language was extended with operators like, corresponding to existential quantification over time points. Another temporal extension of ASP is Temporal Equilibrium Logic (TEL) [9].