(To understand this concept I recommend you first refer to the following nodes 1, 2, 3, 4 and 5 and make sure you know what an interpretation function is. If there are any other nodes with good explanations of the language model relationship please /msg me.)

A relational structure is a kind of mathematical structure or model that only has relations (sometimes also referred to as a relational model, just be careful when talking to a modal logician since they mean something else by a model). I.e. it forms the semantics for a language that has no functional symbols (such a language is sometimes called a relational language). Therefore a relational structure would be some kind of set *S* with an interpretation function that interprets the relational symbols from the language as subsets of *S*.

Kripke models are a much used example of this. As an example we will consider a simple Kripke model viewed from an algebraic logician's perspective. This Kripke model will have two objects *W* and *R* where *W* is the set of worlds of the model and *R* is a binary relational symbol. We also need an interpretation function *I* that goes from the syntax of this model (which has variables and *R*) to subsets of *W*. In practice *I* will intrepret *R* in such a way as to show which worlds are reachable from other worlds. So let's say that a and b are worlds (i.e. a and b are elements of *W*) then a*R*b would mean that you can reach world b from world a. (Formally we would write *I*(*R*(a,b)) but that gets hard to read...)

Related mathematical subjects where these kind of structures get used include model theory, modal logic and formal methods.