Page 222 - Artificial Intelligence for the Internet of Everything

Accessing Validity of Argumentation of Agents of the Internet of Everything 203

A CDT can be represented by a vector V of integer counts of each sub-
tree type (without taking into account its ancestors):
V(T) ¼ (# of subtrees of type 1, …,# of subtrees of type I, …,# of subtrees of
type n). This representation results in a very high dimensionality since the
number of different sub-trees is exponential in size. Thus it is computationally
infeasible to directly use the feature vector Ø(T). To solve the computational
issue, a tree kernel function is introduced to calculate the dot product bet-
ween the previously mentioned high-dimensional vectors efficiently. Given
two tree segments CDT 1 and CDT 2 , the tree kernel function is defined:
P
i V(CDT 1 )[i],
K (CDT 1 , CDT 2 ) ¼ <V(CDT 1 ), V(CDT 2 ) > ¼
P P P
n1 n2 i I i (n 1 )* I i (n 2 ),
V(CDT 2 )[i] ¼
Where n 1 2N 1 , n 2 2N 2 and N 1 and N 2 are the sets of all nodes in CDT 1
and CDT 2 , respectively; I i (n) is the indicator function; and I i (n)¼{1 iff a
subtree of type i occurs with a root at a node; 0 otherwise}. Further details
for using TK for paragraph-level and discourse analysis are available in
Galitsky (2017).
Only the arcs of the same type of rhetoric relations (presentation relation,
such as antithesis, subject matter relation, such as condition, and multinuclear rela-
tion, such as List) can be matched when computing common sub-trees. We
use N for a nucleus or situations presented by this nucleus, and S for a satellite
or situations presented by this satellite. Situations are propositions, completed
actions or actions in progress, and communicative actions and states (includ-
ing beliefs, desires, approve, explain, reconcile, and others). Hence we have the
following expression for RST-based generalization “^” for two texts text 1
and text 2 :
text 1 ^text 2 ¼[ i,j (rstRelation 1i, (…,…) ^rstRelation 2j (…,…)),
where i 2 (RST relations in text 1 ) and j 2 (RST relations in text 2 ). Further,
for a pair of RST relations their generalization looks as follows:
rstRelation 1 (N 1 ,S 1 ) ^rstRelation 2 (N 2 , S 2 ) ¼ (rstRelation 1 ^rstRelation 2 )
(N 1 ^N 2 , S 1 ^S 2 ).
We define CA as a function of the form verb (agent, subject, cause), where
verb characterizes some type of interaction between involved agents (e.g.,
explain, confirm, remind, disagree, deny, etc.), subject refers to the information
transmitted or the object described, and cause refers to the motivation or
explanation for the subject. To handle the meaning of words expressing
the subjects of CAs, we apply word2vec models (Mikolov, Chen, Corrado,
& Dean, 2015).
To compute similarity between the subjects of CAs, we use the following
rule. If subject1¼subject2, then subject1^subject2 ¼ <subject1, POS(subject1), 1>.