LAUSR

Dear editor, In 2008, the SPARQL query language was the official world wide web consortium (W3C) recommendation for a resource description framework (RDF) query language [1], which is a database query language that can retrieve and manipulate data stored in the RDF format. SPARQL allows a query to have triple patterns, conjunctions (AND), disjunctions (UNION), optional patterns (OPT) and built-in conditions (constraints) that can be filtered (FILTER). The official semantics of SPARQL recommended by the W3C is a three-valued semantics in the built-in conditions [1], wherein each mapping is assigned to true, false or error, and error is assigned to mappings that do not contain all of the variables occurring in the constraints [2]. The two-valued semantics of SPARQL, called the two-valued semantics, were introduced by [3] in 2006 wherein each mapping was assigned to either true or false. As a traditional and important problem, the expressivity of SPARQL has attracted considerable attention ever since SPARQL was released. Although the expressivity of SPARQL under the two-valued semantics is the same as the expressivity of SPARQL under the three-valued semantics [4], it is interesting to differentiate the three-valued semantics and two-valued semantics of SPARQL patterns; i.e., the two semantics of a given pattern. Moreover, the primitivity of operators in SPARQL 1.0 has been previously investigated [4]. Although AND is expressed by OPT and FILTER, it is still interesting to distinguish OPT from the other operators, such as AND, under the two semantics. Moreover, although the expressivity of non-monotonic operators in SPARQL 1.1 such as MINUS, BIND, and VALUES have been investigated [5], the expressivity of the nonmonotonic fragments persists to be an-open problem, especially with regards to the further classification of the non-monotonic fragments. In this study, we investigated the expressivity of different operators in SPARQL 1.0, by conducting a comparison among the expressivity of AND, OPT, OPT from well-designed patterns, under the two-valued and three-valued semantics via constraints, monotonicity, weak monotonicity, and non-optionally monotonicity. We summarize the main contributions of this study as follows. • To differentiate between the two patterns semantics, we present two constraints, namely, the positive and bound constraints. Subsequently, we introduce two kinds of fragments with the corresponding constraints, namely, the positive SPARQL fragment (denoted by SPARQL) and the bound SPARQL fragment (denoted by SPARQLb). We demonstrate that the two semantics are equivalent in SPARQL, while the three-valued semantics are slightly stronger than the two-valued semantics in SPARQLb.