Concepts inLogical definability and query languages over ranked and unranked trees

Definable set

In mathematical logic, a definable set is an n-ary relation on the domain of a structure whose elements are precisely those elements satisfying some formula in the language of that structure. A set can be defined with or without parameters, which are elements of the domain that can be referenced in the formula defining the relation.  more from Wikipedia

Query language

Query languages are computer languages used to make queries into databases and information systems. Broadly, query languages can be classified according to whether they are database query languages or information retrieval query languages. The difference is that a database query language attempts to give factual answers to factual questions, while an information retrieval query language attempts to find documents containing information that is relevant to an area of inquiry. Examples include: .  more from Wikipedia

Category of relations

In mathematics, the category Rel has the class of sets as objects and binary relations as morphisms. A morphism (or arrow) R : A ¿ B in this category is a relation between the sets A and B, so R ¿ A × B. The composition of two relations R: A ¿ B and S: B ¿ C is given by: (a, c) ¿ S R if (and only if) for some b ¿ B, (a, b) ¿ R and (b, c) ¿ S.  more from Wikipedia

Binary relation

In mathematics, a binary relation on a set A is a collection of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A = A × A. More generally, a binary relation between two sets A and B is a subset of A × B. The terms dyadic relation and 2-place relation are synonyms for binary relations.  more from Wikipedia

Polynomial hierarchy

In computational complexity theory, the polynomial hierarchy is a hierarchy of complexity classes that generalize the classes P, NP and co-NP to oracle machines. It is a resource-bounded counterpart to the arithmetical hierarchy and analytical hierarchy from mathematical logic.  more from Wikipedia

First-order logic

First-order logic is a formal system used in mathematics, philosophy, linguistics, and computer science. It is also known as first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic (a less precise term). First-order logic is distinguished from propositional logic by its use of quantified variables.  more from Wikipedia

Structure (mathematical logic)

In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations which are defined on it. Universal algebra studies structures that generalize the algebraic structures such as groups, rings, fields and vector spaces. The term universal algebra is used for structures with no relation symbols.  more from Wikipedia

Classical logic

Classical logic identifies a class of formal logics that have been most intensively studied and most widely used. The class is sometimes called standard logic as well.  more from Wikipedia