Automatic Semantic Generation and Arabic Translation of Mathematical Expressions on the Web

1. Introduction

Mathematical notations are used in mathematics, physics, engineering, and economics. These notations include symbolic representation, such as numbers, function symbols (e.g., sin, tan….), operators (e.g., +, *…..), conceptual symbols and variables (e.g., lim, dy/dx). These notations form a mathematical expression.

MathML is a standard XML-based encoding for mathematical structures (Carlisle et al., 2003b). The MathML elements can be embedded inside XHTML documents. All popular web browsers can display MathML equations. As XML supports Unicode, there are no difficulties with using Arabic letters in MathML. MathML is intended to provide a clear presentation of mathematics instead of using images of the expressions as these images are difficult to see, read, and search (Eddahibi et al., 2004). MathML allow the mathematical contents to be rendered, received, and processed on the web in a way similar to HTML.

A large number of learners are concerned about the availability Arabic mathematical contents online (Banouni et al., 2004; Lazrek et al., 2006). Large number of websites resources use Latin notation to present mathematical contents. The users who cannot understand English use online translation services to convert the contents in these learning resources into Arabic language. Unfortunately, the mathematical equations are not translated into the Arabic equivalent mathematical notation.

Processing mathematical expressions on the web is not an easy work (Su et al., 2008), since these expressions have special requirements like providing correct visual appearance of expressions on the web and encoding their semantic. Encoding the semantic of mathematical expressions means the encoding of the general structure of the expression, which is used in many applications to obtain the actual expression or to search for math contents (Carlisle et al., 2003).

Wang et al. (2003) presented a work about semantic of mathematics on the web called Web for Mathematical Education (WME). Another work is EditMath presented by Su et al. (2008) which provide online framework to present mathematics, and support the use of semantic features to encode and process mathematical expressions.

Searching for mathematical equations has many problems as the structure of equations may have different representations such as the coefficient notations (e.g., and _nC^k). Understanding the meaning of mathematical expressions will support the searching of these expressions. For example, the equation describes the distance between two points.

As described in Kohlhase and Sucan (2006), there are many difficulties when searching of mathematical expressions: first, the same mathematical symbols can be used in different forms to denote the same expression (e.g., and _nC^k denotes the same concept but in different forms). Second, the same mathematical expression has many different interpretations (e.g., can refer to a Rieman Integral or a Lebesgue Integral). Third, an expression contains a set of variables maybe replicated by just renaming the variables (e.g., has the same meaning as).

The Arabic language is the official language for the countries in the Middle East and North Africa. The Arabic script is used in extended version by other major languages. For example, Urdu (Pakistan), Persian and Farsi (Iran, India), Berber (North Africa), Sindhi (India), Uyghur, Kirgiz (Central Asia), Pashtun (Afghanistan), Kurdish, Jawi, Baluchi, and several African languages.