3.1.1. First-Order Predicate Logic (FOL)

Our category independent framework does not incorporate operations. Therefore, we examine many-sorted first-order predicate logic without functions. We consider manysorted signatures Σ = (*S*, *P*, *ar* : *P* → *S*∗) with *S* a set of sort symbols, *P* a set of predicate

symbols and a map *ar* : *P* → *S*<sup>∗</sup> assigning to each predicate symbol its arity. We may sometimes omit the word 'symbol' and simply refer to sort symbols as sorts and to predicate symbols as predicates. We show that any many-sorted signature can be represented quite naturally within our framework and therefore gives rise to different institutions of statements. We will demonstrate this by means of a sample signature.
