Having in essence the same initial idea of phrase structures and their context-free combining, the HPSG and several other new approaches within Chomskian mainstream select the general and very powerful mathematical conception of unification. The purpose of unification is to make easier the syntactic analysis of natural languages.
The unification algorithms are not linguistic proper. Rather they detect similarities between parts of mathematical structures (strings, trees, graphs, logical formulas) labeled with feature sets. A priori, it is known that some features are interrelated, i.e., they can be equal, or one of them covers the other. Thus, some feature combinations are considered compatible while met in analysis, whereas the rest are not. Two sets of features can be unified, if they are compatible. Then the information at an object admitting unification (i.e., at a constituent within a sentence to be parsed) combines the information brought by both sets of features.
Unification allows filtering out inappropriate feature options, while the unified feature combination characterizes the syntactic structure under analysis more precisely, leading to the true interpretation of the sentence.
As the first example of unification operations, let us compare feature sets of two Spanish words, el and muchacho, staying in a text side by side. Both words have the feature set [gender = masculine, number = singular], so that they are equivalent with respect to gender and number. Hence, the condition of unification is satisfied, and this pair of words can form a unifying constituent in syntactic analysis.
Another example is the adjacent Spanish words las estudiantes. The article las has the feature set [gender = feminine, number = plural]. As to the string estudiantes, this word can refer to both ‘he-student’ of masculine gender and ‘she-student’ of feminine gender, so that this word is not specified (is underspecified) with respect to gender. Thus, the word occurrence estudiantes taken separately has a broader feature set, namely, [number = plural], without any explicit indication of gender. Since these two feature sets are not contradictory, they are compatible and their unification [gender = feminine, number = plural] gives the unifying constraint set assigned to both words. Hence, this pair can form a unifying mother constituent las estudiantes, which inherits the feature set from the head daughter estudiantes. The gender of the particular word occurrence estudiantes is feminine, i.e., ‘she-students,’ and consequently the inherited gender of the noun phrase las estudiantes is also feminine.
As the third example, let us consider the words niño and quisiera in the Spanish sentence El niño quisiera pasar de año. The noun niño is labeled with the 3rd person value: [person = 3], whereas the verb quisiera exists in two variants labeled with the feature set [person = 1 or person = 3], correspondingly. Only the latter variant of the verb can be unified with the word niño. Therefore this particular word occurrence of quisiera is of the third person. The whole sentence inherits this value, since the verb is its head daughter.