Editing Rete algorithm (section)

=== Existential and universal quantifications ===
Conditional tests are most commonly used to perform selections and joins on individual tuples.   However, by implementing additional beta node types, it is possible for Rete networks to perform [[Quantification (logic)|quantification]]s.    [[Existential quantification]] involves testing for the existence of at least one set of matching WMEs in working memory.   [[Universal quantification]] involves testing that an entire set of WMEs in working memory meets a given condition.    A variation of universal quantification might test that a given number of WMEs, drawn from a set of WMEs, meets given criteria.   This might be in terms of testing for either an exact number or a minimum number of matches.

Quantification is not universally implemented in Rete engines, and, where it is supported, several variations exist.   A variant of existential quantification referred to as ''negation'' is widely, though not universally, supported, and is described in seminal documents.   Existentially negated conditions and conjunctions involve the use of specialised beta nodes that test for non-existence of matching WMEs or sets of WMEs.   These nodes propagate WME lists only when no match is found.   The exact implementation of negation varies.   In one approach,  the node maintains a simple count on each WME list it receives from its left input.   The count specifies the number of matches found with WMEs received from the right input.   The node only propagates WME lists whose count is zero.   In another approach, the node maintains an additional memory on each WME list received from the left input.   These memories are a form of beta memory, and store WME lists for each match with WMEs received on the right input.   If a WME list does not have any WME lists in its memory, it is propagated down the network.   In this approach, negation nodes generally activate further beta nodes directly, rather than storing their output in an additional beta memory.   Negation nodes provide a form of '[[negation as failure]]'.

When changes are made to working memory, a WME list that previously matched no WMEs may now match newly asserted WMEs.   In this case, the propagated WME list and all its extended copies need to be retracted from beta memories further down the network.   The second approach described above is often used to support efficient mechanisms for removal of WME lists.   When WME lists are removed, any corresponding production instances are de-activated and removed from the agenda.

Existential quantification can be performed by combining two negation beta nodes.   This represents the semantics of [[double negation]] (e.g., "If NOT NOT any matching WMEs, then...").   This is a common approach taken by several production systems.