"You can't get spoiled if you do your own ironing." – Meryl Streep

In the afternoon, we had a meeting to discuss the part of evaluation for our paper. We have some conclusions:

1. The evaluation in our paper will focus on the exploration of qualities of assertions and path instances. 

Matrix could be used in the computation of these qualities, and eigenvalue and eigenvector of the matrix are keys to illustrate relationships among assertions and path instances if eigenvalue does exist. 

However, if no eigenvalue exists, what does that mean? The iteration to calculate the qualities can not converge, one explanation might be that we can not get the qualities by using the assertions and the user's query. Right?

Then when such eigenvalues don't exist at all, what should we do???

I discussed with Candan in the morning. I didn't get the final decision yet, but we thought it's better to get a general idea about what others are doing with this subject. 

2. The definition of compatibility of assertions. The basic idea used for the definition is that at least one reasonable explanation should exist according to any pair of compatible assertions.  

Particularly, three rules could be exploited below:

Given two assertions, a_1 = {id_1, tag_1, pid_1} and a_2 = {id_2, tag_2, pid_2}.

(1) - if both id_1 and id_2 are singular and same, then tag_1^ tag_2 != null and pid_1 ^ pid_2 != null;

     - if both tag_1 and tag_2 are singular and same, then id_1^ id_2 != null and pid_1 ^ pid_2 != null;

     - if both pid_1 and pid_2 are singular and same, then tag_1^ tag_2 != null and id_1 ^ id_2 != null;

(2) - if id_1, id_2, pid_1 and pid_2 are singular, and id_1 = pid_2, then id_2 != pid_1;

     - if id_1, id_2, pid_1 and pid_2 are singular, and id_2 = pid_1, then id_1 != pid_2;

Please note that two assertions <{1, 2},{t1, ...},{1, 2}> and <{1, 2},{t2, ...},{1, 2}>, are contradict in nature, but they could be compatible based on the definition (2). 

Therefore, other methods should be used to define  the assertion compatibility. 

(3) when a_1 is a positive assertion, a_2 is a negative assertion, the condition of a_1 ~ a_2 is that there exists one way to decide nodes illustrated by them without any contradiction. 

Note the question: is it possible to distinguish the compatibility of a_1 and a_2 based on the number of correct explanations upon the concurrence of both assertions. 

The other choice: the compatibility of assertions can be defined as the possibility to explain them in a consistent way. 

For example,