# arity

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We introduce a fresh function symbol h of arity n + 1, with [Lambda](h, n + 1) if and only if t does not occur at an active position in r, and [Lambda](h, i) for i = 1, .

Consider an ordinary relational algebra query Q, with arity n, over a given database schema S.

They may be either CPs which can participate in relations or CPs denoting relations with fixed arity.

Note that if I contains a constant predicate symbol p of arity zero then the corresponding component in [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (I) is always (p, true), and if some predicate p is missing in I then the corresponding component in [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (I) is given by (p, false), since false = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

In these cases, we used a transformation similar to the one above, but now we maintain the old arguments of mutually recursive predicates as different arguments of the m predicate and add one extra argument to represent the old predicate symbol (as a functor of arity one).

Let MSO denote the fragment of second order logic in which all predicate variables have arity at most one,(4) and let REG denote the class of regular languages.

Query containment consists in determining, given a knowledge base and two queries of the same arity, whether the answer to one query is contained in the answer to the other one whenever all assertions of the knowledge base are satisfied.

struct wam [ struct code *P; /* program pointer */ struct code *L; /* continuation program pointer */ struct environment *E; /* current environment */ struct wam *B; /* current choice point */ struct valuecell **T; /* top of trail stack */ struct valuecell *H; /* top of heap */ struct valuecell A [m]; /* m argument registers */ ]; where m is a suitable number defining the arity limit of functors and predicates.

In examples, we write p/n to distinguish the predicate whose symbol is p and whose arity is n.

In Figure 7 we have allowed for a single kind of unlabeled directed hyperedge of arity between 2 and 3.

The number of extra reductions is 2 if u is a variable and 2 + a if u is a nonvariable and a is its arity.

The only difference is that set nodes do not have a fixed arity and the order of their children is not significant, whereas all functions in Courcelle [1983] do have a fixed arity.

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