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L03 FS: Unification Unification o Two major operations needed on feature structures - Merging contents of two feature structures - Rejecting incompatible structures. Unification provides both. o Unification of two simple feature structures (F1 U F2 = F3) + Ex. Failure to unify: [CAT v] U [CAT n] [NUMBER sg] [PERSON 3] where U stands for unification Above fails to unify, as the value of attribute CAT is different in both. o Unification of two simple feature structures (F1 U F2 = F3) + Ex. Successful unification: [CAT n] U [CAT n] = [CAT n ] [NUMBER sg] [PERSON 3] [NUMBER sg] [PERSON 3 ] where U stands for unification * Construct F3 as follows: - Take union of attributes in F1 and F2 * They are made the attributes of F3 - For an attribute A that occurs in both F1, F2 * Values of attribute A in F1 and F2 should be equal (Note: Values are atomic in simple FSs) * If not equal, reject. (Cannot combine incompatible info.) * If equal, value of A in F3 copied from F1 or F2 + Ex. Value of CAT in F3 - For an attribute A that occurs in one of F1, F2 but not in both * Value of A is copied from F1 or F2, into F3 (as value of A in F3). + Ex. Value of NUMBER and PERSON are copied in output F3 from F1, F2, respectively. + Ex.: [NUMBER sg] U [NUMBER Pl] Unification fails + Ex.: [NUMBER sg] U [PERSON 3] = [NUMBER sg] [PERSON 3] o Use of FS with lexicon and grammar + FS associated with 'child' in lexicon [CAT n] [NUMBER sg] [PERSON 3] + FS associated with 'a' in lexicon [SPEC indef ] [NUMBER sg ] [PERSON 3 ] + Example CF rule with constraint + NP -> det n + Constraint: (FS of NP) = (FS of det) U (FS of n) + Resulting FS (of NP) [CAT n ] [SPEC indef] [NUMBER sg ] [PERSON 3 ] o Unification of Complex feature strucutres (F1 U F2 = F3) * Do same as unification of simple FSs except - (When an attribute A has values in F1 and F2) AND (Values of A in F1 (or F2) is a feature structure) Do the following in such a case: - If value of A is feature structure in one, atomic in the other: * Reject. (F1 and F2 incompatible) - If value of A is FS in both: * Unify value of A in F1 and value of A2 in F2 - If reject, then return reject - If accept, then resulting FS is made value of A in F3 A(F3) = A(F1) U A(F2) + Ex. [ CAT n ] [ CAT n ] [ AGRMNT [NUMBER sg] ] U [ AGRMNT [PERSON 3] ] [ CAT n ] = [ AGRMNT [NUMBER sg] ] [ [PERSON 3] ] + Ex. [ CAT n ] [ CAT n ] [ AGRMNT [NUMBER sg] ] U [ AGRMNT [NUMBER pl] ] Reject. Incompatible structures. Because in trying to unify structures associated with attribute AGRMNT: [NUMBER sg] and [NUMBER pl] The values of NUMBER attribute are incompatible. o Subsumption relation between two FS F1 =< F2 %% To define relation and expand explanation. o Summary: - FS allows partial information to be kept - Unification allows us to integrate information from two different sources (two different FSs)...........................................NEXT PREVIOUS INDEX