VU @ D2.1.1 Part 1: Approximation Reasoning method Knowledge - - PDF document

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Dec 02, 2023 315 likes •392 views

VU @ D2.1.1 Part 1: Approximation Reasoning method Knowledge Knowledge base Base A-Box (UoM) and T-Box Reasoning Input Output Method Input 1 Guidelines for Reasoning Methods Semantically well-founded providing a

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1

VU @ D2.1.1

Part 1: Approximation

Reasoning method Knowledge base

A-Box (UoM) and T-Box

Input

Input Output Reasoning Method Knowledge Base

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2

Guidelines for Reasoning Methods

Semantically well-founded

providing a clear answer to the problem

Computationally attractive

resulting in an easier computation of approximate answers

Improvable approximate

answers

Dual sound and complete Flexible to apply to different

problems

Input Output Reasoning Method Knowledge Base

Reasoning Methods: Anytime Algorithms

Measurable Quality of the

approximate result

Recognizable Quality can be

determined at run time

Monotonicity over time and

input quality

Consistency Diminishing returns with

more improvements in the beginning

Interuptibility at any time Preemptability ensures

algorithm can be suspended and resumed

0.2 0.4 0.6 0.8 1 1 2 3 4 5 6 7 Quality Algorithm step Quality of algorithm

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Anytime Algorithms for logical entailment

Boolean Constraint Propagation (BCP) sound but incomplete

Clausal BCP (restricted to clauses)

CNF-BCP Prime-BCP (intractable)

Formula BCP (intractable) Fact Propagation

S1-/S3-entailment sound and complete semantic approach

S L

x ¬x

S1 S3 false true ? false

Approximation for knowledge bases

“Compile”

a knowledge base into another one with better computational

properties

Possibilities

Translate A-Box into a

role-free ABox

Knowledge compilation

Input Output Reasoning Method Knowledge Base

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Approximation on A-Boxes

Normal A-Box Role-Free A-Box

Querying in Role-Free A-Boxes

Query Instances contained in the query Instances to be tested if contained

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Compiling the knowledgebase

Exact Knowledge Compilation Approximate Knowledge Compilation

Input Output Reasoning Method Knowledge Base Input Output Reasoning Method

Knowledge Base++

Pre-Compile = Offline Reasoning

Exact Knowledge Compilation

Prime implicants D Σ

and Prime implicates Σ C

Con-/Disjunction of Literals How to compute

Directly Derviable by unit

resolution

W.r.t. a tractable theory

Theory Σ v v v v v v = =

Implicants D Implicats C

= =

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Approximate Knowledge Compilation

Classical approaches

Language Restriction

(c.f. Role-Free A-Boxes)

Theory Approximation

(TA)

Methods for TA:

Upper bound:

if UP Q then Σ Q

Lower bound:

if LB Q then Σ Q

Theory Σ

Upper Bound Lower Bound

= = ≠ ≠

UB Q

LB Q

≠ yes no No ≈ don’t care Yes ≈ don’t care

Anytime Variants of Exact Methods

Theory Σ v v v v v v

Implicants D Implicats C

Theory Σ

Upper Bound Lower Bound