Compiling Axioms from the Source Descriptions Craig Knoblock - - PowerPoint PPT Presentation

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Compiling Axioms from the Source Descriptions Craig Knoblock University of Southern California 4/4/2005 University of Southern California 1 Domain Modeling Language Domain model specified in a KL-ONE style knowledge representation system

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Compiling Axioms from the Source Descriptions

Craig Knoblock University of Southern California

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Domain Modeling Language

Domain model specified in a KL-ONE style knowledge representation system Unary relations (classes) used to represent classes of objects Binary relations used to describe attributes

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Domain and Source Model

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Query Processing

How do you determine which sources are relevant to a query? One approach: compile a set of axioms that are then used in the query processing Alternative approach: determine the relevant sources at run-time

Explored later in this class

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Axioms

Defines the set of sources that can be used to produce various classes of information Relevant axioms depend both on the class of information and the required attributes Example Axioms:

Large-seaport(pn) = s2(s2.pn) Large-seaport(cr gc pn) = s4(s4.cr s4.gc s4.pn) or s5(s5.cr s5.gc s5.pn)

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Inference Rules for Axiom Compilation

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Approach to Compiling Axioms

Like a production system, run to quiescence Consider each axiom generated to potentially activate later rules Allow potentially multiple applications of particular rule Only apply rules when they might generate something new

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Algorithm:

gen := 0; apply DIRECT rule producing axioms(gen); gen := 1; repeat

⌧new := 0; ⌧for each rule in {COVERING, DEFINITION, INHERIT, COMPOSE} ⌧for each activation of rule

if activation intersection axioms(gen-1) is not empty

– apply rule candidate axioms(gen); – add candidate axioms not already present; – new := #(added axioms); – gen := gen + 1

until new = 0;

transfer all axioms to lattice;

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Axioms from the Direct Rule

Seaport(cr gc pn) = s1(s1.cr s1.gc s1.pn)

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Axioms after Covering Rule

Large-seaport(cr gc pn) = s4(s4.cr s4.gc s4.pn) or s5(s5.cr s5.gc s5.pn)

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Axioms after Definition Rule

Small-seaport(cr gc pn) = s1(s1.cr s1.gc s1.pn) and s1.cr <=7

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Axioms after Inherit Rule

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Axioms after the Compose Rule

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Initial Axiom Lattice for Large-Seaport

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Large-Seaport Lattice with Supplementary Axioms

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Large-Seaport Lattice with Interstitial Axioms

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Domain and Source Model with Binding Patterns

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Large-Seaport Lattice with Binding Patterns

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Big Picture

Given a query

Find the appropriate axiom for each of the domain terms in the query Rewrite domain query into a source query Translate into a Theseus plan (with xwrapper, select, project join, etc) Execute the plan

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Discussion

Expression language for describing sources Efficient to build axioms as long as there are not many coverings Efficient to process queries Limitation: can’t describe sources as joins