Adaptive Entailment of Equations over Rational Trees ?

Two variants of an incremental and adaptive entailment algorithm are presented. Both variants decide incrementally whether a xed conjunction of syntactical equations over the rational trees is entailed by another conjunction in rational solved form which may change dynamically. In the case of entailment, an extension of the rational solved form is computed which is equivalent to the conjunction of both considered conjunctions. Contrary to other incremental entailment algorithms, our approach uses a sim-pliied form of justiications used in truth maintenance systems to support solution adaptation after changes of the entailing rational solved form. In detail, previously made decisions and extensions are adapted after arbitrary additions and deletions of global variable bindings. An application domain of the adaptive entailment algorithm is dynamic constraint processing based on Fr uhwirth's Constraint Handling Rules, where head matching and guard entailment depends on the currently valid constraint store, especially on the contained variable bindings.