Artificial Intelligence Technology Web Technology Knowledge Information Processing Technology Semantic Web Technology Ontology Technology Natural Language Processing Machine learning Ontology Matching Technology
In the previous article, we discussed the probabilistic Bayesian network model, Markov model, and Markov logic network approaches to calculate similarity. In this article, we will discuss semantic approaches.
The main feature of semantic approaches is that they use model-theoretic semantics to justify their results. Therefore, they are classified as deductive methods. Like other global methods, purely deductive methods do not work very well on their own for tasks that are inherently inductive, such as ontology matching. Therefore, an anchor is needed. That is, entities that are declared to be equivalent (based on name identity, external resources, or user input, for example). These anchors constitute the initial alignment for the application of deductive methods. The semantic method serves to amplify these seed alignments.
The basis of the semantic method is to infer new correspondences or to test the sufficiency of the alignments. This can be achieved by using a rear sonar that implements alignment semantics. There are several such systems, but the most commonly used method will be the one that uses reduced semantics (Meilicke et al. 2009; Meilicke and Stuckenschmidt 2009; Meilicke 2011).
In the following, we introduce a semantic method based on propositional and modal satisfiability, and a method based on description logic for inferring new correspondences. Methods for detecting and repairing alignment inconsistencies will be presented in the next chapter.
Propositional Techniques
The approach for applying propositional satisfiability (SAT) techniques to ontology matching is based on the following steps (Giunchiglia and Shvaiko 2003; Shvaiko 2006)
- For a given input ontology, a theory or domain knowledge (axioms) is constructed as a combination of available axioms. To construct the theory, we use the basic techniques described in the previous chapter, such as those based on WordNet or using external ontologies (Section.7.3).
- From both ontologies, we construct matching equations for each pair of classes c and c′. the criterion for determining whether a relation is established between two classes is whether the relation is supported by assumptions (theory). Therefore, a matching query is constructed as an expression of the form. [Axioms Rightarrow r(c,c’)] for each pair of classes c and c′ for which we want to test the relation r (in = c and c′ are sometimes called contexts; in = c and c′ are not contexts).
- Check the validity of the expression, i.e., that it is true for all truth assignments of all propositions. Check the validity of the expression. That is, check that it is true for all truth assignments of all propositional variables that occur in the expression. A propositional expression is valid only if its negation is unsatisfiable, which is checked using a satisfiability solver.
The SAT solver is the correct and complete decision procedure for determining the acceptability of a proposition, and can therefore be used to exhaustively check all possible correspondences. In a sense, these techniques compute the deductive closure of an initial arrangement.
An example of relational inference in propositional logic.
Step 1. Assume that the classes images and Europe belong to one ontology, and that another ontology has the classes pictures and Europe (as well). a matcher using WordNet can determine that images = pictures. Many other matchers can find that the class of Europe in both ontologies is identical, i.e., Europe = Europe. Next, converting the relations between the classes of interest into propositional connectives in an obvious way, we obtain the following axiom. [((imagesequiv pictures)∧(Europeequiv Europe))].
Step 2. Suppose that c is defined to be Europe ⊓ images, which intuitively represents the notion of European images, and c′ is defined to be pictures ⊓ Europe, which intuitively represents the notion of European pictures. And when we want to know if c is equivalent (≡) to c′. In the collation task, we need to construct the following equation [((imagesequiv pictures)∧(Europeequiv Europe)] Rightarrow\
((Europe∧images)equiv (Europe ∧ pictures))]
Step 3 The negation of this equation is found to be unsatisfactory, and hence the equivalence relation holds.
In addition to pruning out erroneous correspondences, this method can also infer new correspondences between complex concepts. In the example above, c is defined by combining (intersecting) atomic concepts such as Europe and images. The same is true for c′. These are simple examples of complex concepts that are within the expressive power of the propositional language. Relations between complex concepts such as (Europe ∧ images) and (Europe ∧ pictures) are not obtained after the first step, but are inferred by the reasoner.
This method can only be used for matching tree-like structures such as classifications or taxonomies, where properties and roles are not considered.Modal SAT can be used to extend methods related to propositional SAT to binary predicates, as proposed in (Shvaiko 2006). It can be
Methods of Description Logic
In description logic, alignment relations (=, ≤, ≥, ⊥, etc.) can be expressed with respect to subsets. Subsumption tests can be used to establish relations between classes in a purely semantic way. In fact, first merging two ontologies (after renaming them) and then testing subsumption of each pair of concepts and roles is sufficient to match terms with the same interpretation (or a subset of other interpretations) (Bouquet et al., 2009).
An example of reasoning about relations in description logic. Consider the minimal description logic ontology.
[Microcompany ≡ Company ⊓ ≤ 5 emploee] refers to a company with less than 5 employees.
[SME ≡ Firm ⊓ ≤ 10 associates] means that SME is a firm with at most 10 associates. The following initial placement mentoring (expressed in description logic syntax) will be as follows. [Company ≡ Firm\associate ⊑ employee] This means that Company is equivalent to Firm, and associate is a subproperty of employee. The conclusion from the above is as follows. [Microcompany ⊑ SME] That is, Microcompany is a subclass of SME.
ContentMap will be an interactive tool for diagnosing and repairing alignments. From the alignment, the results of the combined OWL ontology will be generated using a reasoning machine (Pellet). The results are then presented to the user, and the user can select the undesirable results. ContentMap can also provide a repair plan, a set of correspondences that are excluded from the alignment.
There are other uses of description logic techniques that are related to ontology matching. For example, in the scenario of spatio-temporal database integration proposed in (Parent and Spaccapietra 2000) and developed in (Sot- nykova et al. 2005), the correspondences between schemas are first proposed by the integration schema designer and then, together with the input schemas, are stored in ALCRP (S2⊕T) language to be encoded. Then, a description logic reasoning service is used to check the satisfiability of the two source schemas and the set of inter-schema correspondences. If any of them are not satisfactory, we need to reconsider the correspondences between the schemas.
Summary on Semantic Methods
Semantic methods can be very useful in generating correspondences to ensure the completeness and consistency of alignments. These two types of operations can, of course, be used together. Only a few of these techniques have been developed so far. However, with the improvement of deductive tools for handling Semantic Web languages, we expect to see more systems using semantic-based techniques. Semantic-based techniques are a good starting point for the development of more general approaches for alignment (Qi et al. 2009) and for revision and updating in networks of ontologies.
Conclusion
In this paper, we have described an approach for comparing ontologies and ontology entities globally, as opposed to the basic matchers introduced in the word-level similarity descriptions. Such techniques use the basic matcher to provide anchors and seed alignments, but require specific principles to develop the comparison globally. These are based on structural relationships, semantic interpretations, or probabilities.
As a result, the techniques presented can provide similarities or alignments. These can be combined with other similarities or alignments, or manipulated as in other matcher results. In the next article, we will examine various techniques for doing this, and discuss how to combine matchers into a coherent system.
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