### TABLE I RESOLTS OF THE SEMANTIC MATCHING BASED COMPETENCY (%)

### Table 1. Degrees of hybrid semantic matching of WSMO service and goal derivatives

"... In PAGE 2: ... The degree of fuzzy similarity refers to a non-logic based semantic match such as syntactic similarity, while the degree neutral stands for neither match nor fail, hence declares the toler- ance of matching failure. The set-theoretic semantics of the hybrid matching degrees are given in Table1 based on the relations between the maximum possible instance sets of the derivatives DG and DW , denoted by G and W. Since we use the heuristic relative query containment for the con- straint matching, these sets are restricted to instances in the matchmaker knowledge base which satisfy the constraints.... ..."

### Table 2: Transformation rules for semantic matching with left-linear or non-

"... In PAGE 9: ...artelli et al., 1989; Gallier and Snyder, 1990; Dershowitz et al.,1990#5D, and #5BJouannaud and Kirchner, 1991#5D, whichisasurvey of uni#0Ccation. If we restrict ourselves to convergent rewrite systems that are, addition- ally, either non-erasing or left-linear, then the non-deterministic transforma- tion rules of Table2 constitutes a complete set for the matching problem: Theorem 3 #28Completeness#29. Let R be either a left-linear or a non-erasing convergent rewrite system.... In PAGE 9: ...roof. See Appendix. In fact, for non-erasing systems, Bind can be further simpli#0Ced, as shown in #5BMitra, 1994#5D. The system of Table2 , however, is incomplete for general uni#0Ccation: For example, if wehave the goals s ! ? x; t ! ? x, for terms s and t and variable x, such that both s and t have a constructor at the root position, then none of the transformation rules apply #28Eliminate or Bind doesn apos;t apply, since s and t are non-variable terms; furthermore, we cannot mutate, since the root symbols are constructors, and we cannot decompose since the... In PAGE 10: ...Table 2: Transformation rules for semantic matching with left-linear or non- erasing convergent systems right-hand sides are variables#29. However,ifwe augment the transformation rules of Table2 with those of Table 3, the resulting system is su#0Ecient for generating a complete set of uni#0Cers in theories de#0Cned byconvergent rewrite systems #5BMitra, 1994#5D. In fact, Imitate is the only new transformation rule that we need, since Apply is used for matching whenever bindings take place #28see the proof of Theorem 3#29.... In PAGE 22: ...At other times, we will always have a subgoal with a ground right-hand side, whichwe select #28if there are several such subgoals, we do not care as to which one is picked#29. The rest of the proof is as follows: Once we pick a subgoal #28say s ! ? t#29 using the selection strategy above, we apply the non-deterministic transfor- mation rules from Table2 . For example, if s #11 x; x being a variable, then one of Eliminate or Bind would apply.... In PAGE 24: ... Notice that the major di#0Berence between the transformation rules for semantic uni#0Ccation #28i.e, the collective rules from Tables 2 and 3#29 and those for matching in left-linear systems #28those from Table2 alone#29 is that the latter does not have the rule for imitation. However, by Lemma 15, whenever the right-hand side of a goal is a variable, that goal is trivially solvable.... In PAGE 25: ... Wenow state a proof of Theorem 5: Proof. Since wehave a left-linear system, it su#0Eces to consider transfor- mation rules from Table2 alone, that is, wedonothave to consider Apply and Imitate. Furthermore, due to left-linearity,we only need to solvegoals of the form s ! ? t, where anyvariable x in t is linear in t and does not occur in the right-hand side of any other subgoal #28this is true because wehave directed goals, and terms on the right-hand sides of goals could either be left-hand sides of #28left-linear#29 rules from previous mutations, or subterms of the ground term N, when solving for a initial goal of the form s 0 ! ? N;see Lemma 14#29.... ..."

### TABLE I N-TRIPLE FACTS CONSIDERED IN THE SEMANTIC MATCHING PROCESS.

### Table 3. Semantic Structure Matching on the XMethods collection

2003

Cited by 11

### Table 6: Matching Analysis of Semantic Enrichment

"... In PAGE 36: ... Thus the number of concepts that relate to their categories as attributes is slightly higher than one third. Relations ACC Ontology STS Ontology IS-A 68 91 IS-A (Prefix) 14 38 IS-A (Postfix) 3 8 Attribute-of 54 88 Instance-of 1 20 Ambiguous Category 2 3 Total 142 248 Table 5: Statistics of Concept-Category Relationships Table6 shows that about 10% of the STS concepts match UMLS concepts exactly, and 90% match UMLS concepts with various levels of approximation. For a few cases, a domain expert apos;s involvement was required to select a semantic type.... In PAGE 36: ... There are 284 semantic type assignments even though there are only 244 concepts, because some STS concepts match UMLS concepts which have several semantic types. For 244 concepts and 9 categories ( Table6 ) we found semantic type assignments directly, by matching them against the UMLS. For 41 concepts we found additional assignments because they inherit them from 5 categories.... ..."

### Table 1: Transformation rules for semantic matching with left-linear or non-erasing convergent systems

"... In PAGE 4: ... See #5BJouannaud and Kirchner, 1991#5D for a survey of uni#0Ccation. If we restrict ourselves to convergent rewrite systems that are, additionally, either non-erasing or left- linear, then the non-deterministic transformation rules of Table1 constitute a complete set for the matching problem: Theorem 2 #28Completeness#29. Let R be either a left-linear or a non-erasing convergent rewrite system.... ..."

### Table 3.9:Transformation rules for semantic matching with non-erasing systems

1994

Cited by 7

### Table 3.10:Transformation rules for semantic matching with left-linear systems

1994

Cited by 7

### Table 3: Requested and advertised Flow Simulation service capabilities with semantic matching of their parameters.

2004