The process for building the BaseOntology is depicted in Fig. 2, which is based on the Ushold and King method. Given that the data source for building the ontology is fixed content from a textbook with limited knowledge, we employ a manual approach to construct the ontology following the steps outlined in this section. First, we digitized the document, followed by word segmentation and term identification. Next, we built and revised the ontology with input from a high school physics teacher. Details of this process are illustrated in Fig. 3. While our approach is time-consuming, it allows for thoroughly examining the domain knowledge and provides opportunities for refining and improving the ontology. We anticipate that our approach will have implications for developing ontologies in other domains with similar characteristics. The following is a detailed description of the BaseOntology development process.

(1) Detecting and cataloging words: The chosen data source is the physics textbook, as the system aims to support high school learning, and the content should be textbook-based. In order to make the content more accessible to students, concepts are named after physics terms listed in the textbook. Through manual analysis of popular physics textbooks, a total of 1528 terms are discovered. Before utilizing these terms for various purposes in the system, they are reviewed and verified by a physics teacher at Nguyen Thi Minh Khai High School in Soc Trang Province, Vietnam. The core terms are then included in the BaseOntology to facilitate the process of data expansion and to support the word separation algorithm (since the conventional method cannot be used due to the different corpus). Some of the terms in the BaseOntology are listed in Table 1.

(2) Defining the BaseOntology classes and properties: The terms identified in Table 1 are used to define classes and properties in the BaseOntology, as shown in Table 2. Each term is mapped to a corresponding class or property based on its meaning and context in the physics domain. The classes and properties were defined according to the Uschold and King method, which involves identifying the kinds of things in the domain and their relationships.

The base ontology contains Grade, Chapter, Lesson, Concept, Document, and Index classes. In addition, sub-classes of the above classes are also identified, such as Phenomenon, Equation, Device, Measurement Unit, Quantity, Law, etc., which are sub-classes of Concept.

Properties represent relationships between concepts in an ontology. They are essential components of an ontology as they represent the relationships between concepts and provide a structured representation of information. There are two types of properties: object property and data property. An object property represents relationships between objects (instances), while a data property represents relationships between objects and specific values. Some properties in the BaseOntology are described in Table 3.

To ensure that the whole meaning of the terms from the textbook is conveyed, it is essential to identify classes and attributes that capture the essence of each term. Entities are grouped into classes and are related to other entities through attributes. The following examples illustrate entities from the class Lesson and Quantity. For instance, consider the lesson “Rotational motion of a solid around a fixed axis” (“Chuyển động quay của vật rắn quanh một trục cố định” in Vietnamese). The content of this lesson is represented using terms and properties defined in the BaseOntology as shown in Table 4, such as title, page number, main content, concepts involved, etc. Another example is the description of the concept (quantity) “angular acceleration” (“Gia tốc góc” in Vietnamese) shown in Table 5. This is a concept from the lesson “Rotational motion of a rigid body about a fixed axis”; its unit is radian/s², etc. The above examples show that the developed ontology can basically represent the concepts in physics.

(3) Building the BaseOntology using Protégé: The ontology was built using the software Protégé. First, the identified classes and properties are created (called the ontology TBox). The statistical results of the ontology are shown in Fig. 4. As shown in Fig. 4, the number of classes created is 14, the number of Object properties is 29, and the Data property is 17. Then, the instances are added to the ontology (ABox). The number of instances (individuals) is 292, and the number of relationships created between entities through properties is 567.

Overall, BaseOntology provides a framework for representing the concepts and relationships in the domain of high school physics education. The classes and properties defined in the ontology serve as a foundation for the system’s semantic search and data expansion functionalities and future extensions and refinements of the ontology.

Typically, developing an ontology for a specific domain requires significant time and effort, necessitating the development of automatic or semi-automatic methods to expedite the extension process while ensuring comprehensive ontology coverage. This research employs the semi-automatic approach for ontology extension based on BaseOntology. Specifically, we use a pattern-based approach that emphasizes the relationships between terms and the semantic descriptions in the ontology. The following example illustrates how patterns can be used to identify and establish relationships for ontology expansion. In the sentence “The unit of work is Joule, denoted by J” (“Đơn vị của công là Jun, kí hiệu là J”), for example, it cannot be concluded that “work” is equivalent (“is”) to joule. Rather, a relationship between “joule” and “unit” must be established in the context of a physical quantity, where joule is the unit symbol for work.

The initial step in extending the ontology is to select the appropriate data sources. The data source materials for ontology expansion are chosen from the high school teaching materials based on the following criteria: they are rich in knowledge, clearly demonstrate the relationships between terms, and have a uniform presentation style. The ontology expansion process follows the diagram in Fig. 5. Next, pattern analysis is conducted by examining the entire selected document to identify common features in the text presentation that can be used to form patterns in the identification process. These patterns are then tested to determine their effectiveness before being applied to extend the ontology.

Based on the criteria above for selecting data sources for ontology expansion, the terms from Hung and Khiet (2015) are selected as the corpus for the BaseOntology expansion in this study. As shown in Fig. 6, the content of each concept is presented within its respective category, and a consistent presentation method is used for all knowledge. The content of each document has been digitized and organized into multiple documents, each representing a particular concept, theorem, law, or piece of knowledge.

Based on the criteria above for selecting data sources for ontology expansion, the terms from (Hung and Khiet, 2015) are selected as the corpus for the BaseOntology expansion in this study.

As shown in Fig. 6, the content of each concept is presented within its respective category, and a consistent presentation method is used for all knowledge. The content of each document has been digitized and organized into multiple documents, each representing a particular concept, theorem, law, or piece of knowledge.

A pattern in this study refers to a string of characters that conforms to the syntax of the Regular Expression language. Regular expression, also called Regex, is a powerful tool for advanced string processing, using expressions that follow rules. These rules include conventions for groups, wildcards, and other elements. For example, consider the sentence “The unit of work is Joule, denoted by J” (Đơn vị của công là Jun, kí hiệu là J). This sentence defines two terms: “energy” and “Joule”, with the symbol value “J”. Furthermore, we can establish two relationships between these terms and values using two attributes: “unit of” (đơn vị của) and “denoted as” (ký hiệu là). The regular expression that defines the pattern for the above relations is:

r’( unit of )(.+?)( is )(.+?)( denoted by )(.+?)’

Given an input sentence, the result of the above Regex is a list of 5 items with the following structure:

$\bullet$ result[3] (Concept) is a “unit of” (property) result[1] (Unit), and

$\bullet$ result[1] (Unit) is “denoted by” (property) result[5] (string literal).

For example, applying the above pattern to the sentence “The unit of work is Joule, denoted by J” yields the following result: [“unit of”, “work”, “is”, “Joule”, “denoted by”, “J”]. Similar analyses are conducted to define other Regex patterns in this study to extend the ontology, as shown in Table 6.

In Vietnamese, words are the same as in English and are not separated by spaces in other languages. Instead, words are combined into a string, making it difficult for computers to identify individual words. This can lead to problems in natural language processing, such as text classification, sentiment analysis, and information retrieval. Word segmentation or tokenization is the division of a string of characters into individual words or tokens. Many tools, such as Pivy and Underthesea, support word segmentation in Vietnamese. However, they can only segment common words or those from specific domains such as business and banking. Therefore, a special segmentation algorithm must be developed to meet the need for word segmentation in physics for indexing operations.

There are several methods for word segmentation in Vietnamese, including rule-based, dictionary-based, statistical, and machine learning-based approaches. This study proposes the PhyTokenizer segmentation algorithm based on a dictionary-based segmentation method. Our corpus is too small and does not contain enough data (only 1.500 concepts) to support machine learning-based word segmentation. This segmentation algorithm is based on a dictionary-based segmentation method that tries all words that can occur in the dictionary (a list of physical concepts). To speed up the processing, a binary search method is applied to check the presence of potential concepts in the dictionary. Algorithm 1 presents the main idea of PhyTokenizer, where ViTokenizer is a Vietnamese general-purpose tokenizer (Nguyen and Tran, 2024).

The first step in building the semantic search engine is to collect data (documents) from various sources. This study’s resources were obtained mainly from high school physics teachers’ materials. Additionally, various sources available on the internet were used to enrich the evaluation data. The collected data were used for both ontology development and search engine construction. The materials were saved in .doc or .pdf formats and sorted by topic, such as mechanics, electricity, etc., to facilitate indexing. Primary sources of the collected materials include the website of physics teachers at Nguyen Thi Minh Khai High School in Soc Trang province, Vietnam (http://thuvienvatly.com), as well as other reputable websites with physics content, such as https://vatlypt.com and https://vatly247.com. These websites are well-known in Vietnam for providing practical physics knowledge for teaching and learning.

Text data from the selected resources were collected and saved to the database using the BeautifulSoup library (https://pypi.org/project/beautifulsoup4/). The Hyper Text Markup Language (HTML) structure of the website was analyzed to identify the tags in which the article’s main content is located, along with the associated ID or class. Furthermore, links to other articles on the website were collected to automatically expand the collection of documents to other pages within the same website and to ensure that the content is not duplicated.

Fig. 7 shows the document collection process.

$\bullet$ Step 1. Collect documents from the Internet: The BeautifulSoup library selects and extracts text from HTML files downloaded from the Internet. It is necessary to ensure that each document is associated with a unique path in this step.

$\bullet$ Step 2. Normalization of data: This step involves the removal of documents that do not contain the expected content, special characters, and numbers and the standardization of the Vietnamese accent to ensure homogeneity.

$\bullet$ Step 3. Tokenization of the collected documents: The PhyTokenizer algorithm is used to tokenize the selected documents, and the extracted words are then stored in a database.

The cosine similarity calculation based on TF-IDF is implemented using the scikit-learn library to facilitate the document vectorization and the similarity calculation between the query and documents of the search engine. First, the TfidfVectorizer function from the scikit-learn library is used to vectorize the documents and calculate the TF and IDF matrix. Then, the cosine similarity function is used to evaluate the similarity between the query and the indexed documents. Finally, the similarity is used to rank the search results. The appropriate parameters for these functions are determined based on thorough experiments.

The primary goal of this step is to create the index for the search data (documents). The input of this step is the PhyOntology and the list of the list words tokenized by the PhyTokenizer, and the output is the indexed terms of the documents. The index creation involved two steps. First, the terms are sorted and traversed to count their frequency of occurrence. Then, each term and its frequency are added to the result list. Then, the result list is added to the PhyOntology using the workflow described in Fig. 8. Two classes, “Document” and “Index” store the index in the PhyOntology.

Based on the standard cosine similarity score calculation (Salton, 1989), which is commonly used to evaluate the similarity between two documents’ vectors with the same representation, this study introduces an extension of this calculation to accommodate the use of ontology. The cosine similarity between two documents based on TD-IDF is given in Eqn. 1.

(1)$$\begin{array}{c}\hfill \mathrm{CosineSimilarity}(A,B)=\frac{A\cdot B}{\parallel A\parallel \parallel B\parallel }=\hfill \\ \hfill \frac{{\sum }_{i=1}^n{A}_i{B}_i}{\sqrt{{\sum }_{i=1}^n{A}_i^2}\cdot \sqrt{{\sum }_{i=1}^n{B}_i^2}}\hfill \end{array}$$

Where:

- A, B: TF-IDF vectors of the two documents for which we want to calculate the similarity.

- $A\cdot B$: the dot product of the two vectors.

- $A_i$, $B_i$: the TF-IDF values for term i in documents A and B.

- $\parallel A\parallel$, $\parallel B\parallel$: the magnitudes (norms) of vectors A and B.

To compute the similarity between the input query and the documents with semantic information, we first extend the concepts in the input using PhyOntology. Then, the similarity score between a query Q and a document d is calculated using Eqn. 2 as follows:

(2)$$\mathrm{Score}(Q,d)=\frac{{\sum }_i{W}_{Q_i}{W}_{d_i}}{\sqrt{{\sum }_i{\left(W_{Q_i}\right)}^2}\sqrt{{\sum }_i{\left(W_{d_i}\right)}^2}}$$

This calculation is based on the idea of the cosine similarity. However, instead of computing the cosine similarity using the TF-IDF of the original query and the document, we add the semantics for the terms in the query and the document before calculating. In addition, the algorithm also includes a parameter that allows the adjustment of the importance level of a concept. Typically, the concepts in the query are considered more important than the extended concepts to ensure that documents related to the concepts in the query are ranked higher than those related to the extended concepts. Therefore, $W_{Q_i}$ and $W_{d_i}$ are defined in Eqn. 3 as follows:

(3)$$W_{D_i}=tf\left(Q_i\right)\cdot id{f}_{\text{owl}}\left(Q_i\right)$$ $$W_{d_i}=tf\left(d_i\right)\cdot id{f}_{\text{owl}}\left(d_i\right)$$

In which,

(4)$$id{f}_{owl}(q)=\frac{{\sum }_{i=1}^{len(Q)}{m}_{i}idf\left(Q_i\right)}{{\sum }_{i=1}^{len(Q)}{m}_i}$$

Parameter m in Eqn. 4 is the important level of the term $Q_i$ mentioned above.

The proposed method for measuring the similarity between a query and a document is presented in Algorithm 2.

In Algorithm 2, the document’s score value obtained represents the degree of relevance of the document to the search query, with higher scores indicating higher relevance. Documents with a score greater than 0 are ranked and returned as the result of the query.

Expanding related concepts based on PhyOntology, as mentioned in the previous sections, helps learners save time in searching for documents related to a specific knowledge domain. It is crucial to provide learners with a comprehensive overview of the structure of the knowledge block they are studying, which helps them to systematize their knowledge. Therefore, in addition to expanding the search results with related keywords as presented, this study classified the keywords based on PhyOntology. The search results are expanded based on keyword categories. Based on the structure of PhyOntology, a search keyword is classified into one of the following three categories:

1. Type 1 — The keyword is the chapter’s name: The search results are supplemented with the names of the lessons that belong to this chapter (using the attribute “belongs to chapter”).

2. Type 2 — The keyword is the name of a lesson: The search results are supplemented with the chapter’s name containing this lesson and other lessons of the same chapter. Also, the concepts in the lesson are added to the search results.

3. Type 3 — The keyword is a concept, law, theorem, or physical quantity: Depending on the case’s specifics, the corresponding knowledge is added to the search results. For example, if it is physical quantities, the name of the quantity, the unit of measurement, the symbol of the quantity, etc., will be added to the search results.

In test case 1, the keyword “sóng cơ” (“mechanical waves” in English) was entered. This is the title of a chapter in the Year 12 General Physics program, and the search engine correctly recognized it. Therefore, as described in Section 3.2, the “Chapter: Mechanical Waves” and its summary were given priority to be displayed first in the search results, as shown in Fig. 12.

Furthermore, the search result also included additional information about this keyword obtained by expanding the search keyword using PhyOntology. This information included the level of knowledge (year 12), a list of lessons within the chapter (five lessons) associated with the lesson number, and its page number. In addition, expanding the search keyword, its hypernyms (e.g., “wave phenomenon”, “physical phenomenon”) and related concepts (e.g., “amplitude”, “wavelength”, “frequency”, “wave propagation velocity”, etc.) were also displayed in the search results.

In this test case, we entered the keyword “phương trình sóng” (“wave equation” in English), which is the name of a lesson. As in Test case 1, the keyword was correctly classified as a lesson name, and the lesson’s number, name, and page number were displayed first. Then, the concepts contained in the lesson were listed, which are the main content of the lesson. In addition, based on the PhyOntology, the hypernym (Chapter “mechanical waves”) and the hyponyms (a list of related concepts, e.g., “amplitude”) were also included in the result. The result of this test case is shown in Fig. 13.

In this test case, we entered the keyword “chu kỳ” (“cycle” in English). This is a physical quantity, and as designed, the search engine is expected to return the related concepts and related knowledge of the cycle. Fig. 14 shows the result of the search engine. First, the search term was recognized as a physical quantity. Therefore, the related information about this quantity is displayed, such as the notation, unit, formula, and definition. In addition, the related knowledge to cycle was also returned, such as “mechanical waves”, “motor oscillations”, and “oscillation systems”. With each piece of knowledge returned in the search result, a link to that knowledge was also provided so that the users could click on the link to navigate to the desired content.

Test cases 1, 2, and 3 have shown different semantic search results and provided discussions to explain the search results and their benefits. This evaluation uses the precision @10 metric to compare the semantic search based on ontology and the typical search method using TF-IDF combined with cosine similarity (TF-IDF method). Table 7 compares these two methods.

Based on the precision @10 results for the ten keywords in Table 7, it can be seen that the proposed semantic search method outperformed the traditional TF-IDF method using the cosine similarity method. The precision @10 for the semantic search ranges from 0.8 to 1.0 with an average of 94%, while the precision and recall @10 for the TF-IDF method ranges from 0.6 to 1.0 with an average of 77%.

The results indicate that the semantic search method better understands the meaning of the query and the documents in the physics domain, which leads to more relevant results. In contrast, the TF-IDF method relies on the frequency of occurrence of the search terms in the documents and may not capture the subtle relationship between the terms. Overall, the proposed semantic search method shows promise in improving the accuracy of search results in the physics domain. Further studies with larger datasets and diverse queries may provide more insight into the method’s effectiveness.

Table 8 shows the ten documents with the highest similarity score found by the semantic search method for the keyword “chu kỳ” (cycle). These documents were evaluated by the high school physics teachers at Nguyen Thi Minh Khai High School, Soc Trang Province, Vietnam, and all of them are relevant to the search term. Table 9 shows the search result for the same search term using the TF-IDF method, which yielded only 2 of 10 relevant documents. Of the remaining documents, one was related to astrophysics, and the remaining seven were related to chemistry and physics.