## 7 Evaluation
### Discussion
#### 7.4.2 Semantic Consistency  
Here, we discuss the multilingual semantic consistency of MParser between English and Chinese. In MParser, a sentence is a concept tree, consisting of simple sentences defined by a sequential list _SiS_, where each atomic concept _iid_ is a _low-level concept llc_\(\in\)LLC in the step of human semantic input (HSI), and compound concept _eid_\(\in\)EIID is a _high-level concept hlc_\(\in\)HLC generated in MParser, acting as a sentence constituent in the step of sentence computerization (SC). Given two sentences, _SiS_, which is an English sentence, and _SiS_, which is a Chinese sentence, if low-level concept equivalence and high-level concept equivalence are equal such that _SiS_\({}_{i}=_{m}\)_SiS_\({}_{j}\) (=\({}_{m}\) indicates semantic equivalence), then they are semantically consistent. As low-level concept equivalence is semantic consistency of terms, or word-based, high-level concept equivalence is sentence-based semantic consistency.  
**1. _Low-level concept equivalence:_**_SiS_\({}_{i}\) and SiS_\({}_{j}\) are equivalent if and only if:_  
1. \(\forall\)_LLC_\({}_{i}\)\(\subset\)_IID_\({}_{i}\)\(\subset\)_CoDic_
2. \(\forall\)_LLC_\({}_{j}\)\(\subset\)_IID_\({}_{j}\)\(\subset\)_CoDic_
3. _Mapping relationship:_LLC_\({}_{i}\)\(\leftrightarrow\)_LLC_\({}_{j}\)_  
This guarantees that two heterogeneous single concepts are semantically consistent, as two sentences share a common _iid_\(\in\)_CoDic_.  
**2. _High-level concept equivalence:_**_SiS_\({}_{i}\) and SiS_\({}_{j}\) are equivalent if and only if:_  
1. \(\forall\)_HLC_\({}_{i}\)\(\subset\)EIID_\({}_{i}\)__
2. \(\forall\)_HLC_\({}_{j}\)\(\subset\)_EIID_\({}_{j}\)__
3. _Mapping relationship:_HLC_\({}_{i}\)\(\leftrightarrow\)_HLC_\({}_{j}\)__  
HLC achieves complex concept consistency by converging all heterogeneous structures onto an isomorphic grammatical structure through MParser.  
**3. _LLC_\(\Leftrightarrow\)**_HLC:_**_LLC and HLC are equivalent if and only if:_  
1. _Mapping relationship:_IID_\(\leftrightarrow\)_EIID, which is iid in Def. 4 mapped to eid in Def. 5 Thus, if and only if the following mapping path exists for semantic equivalence:  
_SiS_\({}_{i}\) (_local concept_) \(\leftrightarrow\)_LLC_\({}_{i}\) (_local concept_, _IID_\({}_{i}\)) \(\leftrightarrow\)_Map (_IID_\({}_{i}\), _Common concept_) \(\leftrightarrow\)_HLC_\({}_{i}\) (_Common concept_, _EIID_\({}_{i}\)) \(\leftrightarrow\)_HLC_\({}_{j}\) (_EIID_\({}_{j}\), _Common concept_) \(\leftrightarrow\)_Map (Common concept_, _IID_\({}_{j}\)) \(\leftrightarrow\)_LLC_\({}_{j}\) (_IID_\({}_{j}\), _local concept_) \(\leftrightarrow\)_SiS_\({}_{j}\) (_local concept_)  
It is obvious that if all three conditions are met, then _SiS_\({}_{i}=_{m}\)_SiS_\({}_{j}\). Figure 12 illustrates that languages \(i\) and \(j\) are semantically consistent as they share common tree concepts in cross languages through the unique _iid_ and _eid_ in MParser.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{_Intra-Annotator_} & \multicolumn{10}{c}{**MR (N = 505)**} \\ \cline{2-13} \multicolumn{2}{c}{**(Expert, MParser)**} & **NOM** & **PRE** & **ACC** & **DAT** & **GEN** & **LIN** & **ADV** & **COM** & **COMw** & **COMn** & **COMall** & **Avg.** \\ \hline _(Expert 1, MParser)_ & _0.684_ & _0.979_ & _0.804_ & _0.647_ & _0.958_ & _0.756_ & _0.840_ & _0.682_ & _0.649_ & _0.690_ & _0.916_ & _0.782_ \\ _(Expert 2, MParser)_ & _0.706_ & \(1\) & _0.847_ & _0.684_ & _0.973_ & _0.807_ & _0.891_ & _0.639_ & _0.711_ & _0.687_ & _0.907_ & _0.805_ \\ _(Expert 3, MParser)_ & _0.715_ & _0.979_ & _0.828_ & _0.749_ & _0.947_ & _0.784_ & _0.874_ & _0.662_ & _0.684_ & _0.648_ & _0.938_ & _0.801_ \\ _Avg._ & _0.702_ & _0.986_ & _0.826_ & _0.693_ & _0.959_ & _0.782_ & _0.868_ & _0.661_ & _0.681_ & _0.675_ & _0.920_ & \\ \hline \hline \end{tabular}
\end{table}
Table 10: Case Match Rate (MR) between Experts and MParser outputs.