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The Identification of Missing Information Resources through the Query Difference Operator: 

The Identification of Missing Information Resources through the Query Difference Operator Michael Minock

Global Schema: 

Global Schema Virtual outer-join into single relation Agree on a non-cyclic set of equi-joins over a set of relations

Queries: 

Queries Simple queries have projection (entire relations) and selection Despite the similar appearance, this is not (exactly) relational algebra. Query super-imposition operator gives “union” over non-union compatible projections. Such queries are termed compound queries. A conjunction of simple conditions

The Query Difference Operator: 

The Query Difference Operator Theorem 1: May compute query intersection, subsumption, and equivalence. Theorem 2: Query Difference is distributive over compound queries

Query Simplification: 

Query Simplification Horizontal Merge Vertical Merge Absorption

Limitations: 

Limitations Caveat - take care in applying negation! Simplify when condition attribute is both: 1.) functionally dependent on the key of each relation in projection set 2.) not a proper subset of a primary key Schema Requires a non-cyclic set of equi-joins to be predetermined among a set of relations Queries Projections are (currently) entire relations No self-joins Implicit inclusion of predetermined schema equi-joins

Internet Distributed Conceptual Information Spaces: 

Internet Distributed Conceptual Information Spaces Global schema models domain (E.g. Movies, Social Events, Electronics, etc.) Data resources (agents) advertise their contents to Broker User’s asks conceptual query to Broker Broker agent knows schema B

Problems: 

Problems Complex Semantics of Global Schema Agreement Common Understanding Quality of Data Completeness Consistency Quality of Access Novice query construction Non-misleading answers (identification of missing resources, conceptual answers, etc.)

Approach: 

Approach Use the Query Difference Operator (defined here) : Valid only over a restricted class of schemas Defines a syntactic method of computing query (concept) difference Applied here to: Identify the exact portion of a user’s query that is not covered by any agent in the information space Relevant to other problems as well...

Movie Example: 

Movie Example Movie(title,year,type) Show(title, theater, time, city) Review(title,source,evaluation) ... “All films made after 1927”

Example Queries/Responses: 

Example Queries/Responses Query 1: “Give movie information and reviews for all dramas.” Response: “…, but no reviews for dramas made after 1983.” Query 3: “Give movie information for all films made in the thirties, forties, or fifties.” Query 2: “Give movie information and reviews for all dramas and documentaries made in the 1950’s.” Response: “…, but no movie information for non-drama and non-comedy films made between 1930and 1954. Also no movie information for non-drama, non-action, non-comedy and non-documentary films made between 1930 and 1959.” Response: “…, but no movie information or reviews for documentaries made between 1950 and 1954. Also no review information for documentaries made between 1955 and 1959. ”

Example Calculation(1 of 3): 

Example Calculation(1 of 3) Query’ = Query -Textbook “Give movie information and reviews for all dramas and documentaries made in the 1950’s.”

Example Calculation(2 of 3): 

Example Calculation(2 of 3) Query’ = Catalog = Query’’ = Query’ -Catalog

Example Calculation(3 of 3): 

Example Calculation(3 of 3) Query’’ = Via Horizontal Merge = “No movie information or reviews for documentaries made between 1950 and 1954. Also no review information for documentaries made between 1955 and 1959. ”

Prototype: 

Prototype Proof of concept in LISP Condition types: On PC calculates query plan over 1000 resources in <10 seconds On PC calculates query residual over 1000 resources in <30 seconds Worst case query lengths governed by number of attributes Planning a straight C (or JAVA) implementation.

Formal Extensions: 

Formal Extensions Materialized values, open and closed-world modifiers in language Mixed Intensional/Extensional responses Summarization Encompassing less-restrictive schemas and queries Inheritance, Cycles through Cliques Spatial and Temporal conditions Meta-schema (Meta-Meta-schema, …) Row types and Semi-structured Data (XML) Agents Knowledge and Belief Operators

Applications: 

Applications Conversational (mixed intensional/extensional) access to distributed information spaces ‘Perfect’ semantic caching over distributed agent systems Reasoning over contracts, access restrictions, and regulations for electronic commerce among competitive agents And more...

Conclusions: 

Conclusions The Query Difference Operator solves conceptual equations over schema of non-cyclic equi-joins Applied to the problem of identifying missing information resources Prototype proves concept and gives good performance Set of formal extensions and new application ideas proposed

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