EXTENDED RELATIONAL ALGEBRA FOR REDUCTION OF NATURAL QUANTIFIER EXPRESSIONS

Abstract

An extended relational algebra has been developed. This extended algebra is suitable for reduction of expressions written in the natural quantifier language COOL. The algebra consists of conventional operations plus a group select, a subgroup select and possibility join operation. The group select operation selects each group of related tuples where a quantity of the group obeys a condition. The subgroup-select operation selects each group of related tuples where a quantity of a subgroup of the group obeys a condition. The possibility join of relation R1 with relation R2 regenerates relation R1 but with each tuple having a logical attribute p concatenated, with p true where the R1 tuple could have been joined to an R2 tuple, otherwise p false. Generalized algebra routines for generalized COOL expressions are presented.