boemie workshop 02/12/2008giorgos flouris1 formalizing the evolution process institute of computer...

BOEMIE Workshop

02/12/2008 Giorgos Flouris 1

Formalizing the Evolution Process

Institute of Computer Science Foundation for Research and Technology – Hellas

Heraklion, Greece

Giorgos FlourisGeorge Konstantinidis

{fgeo,gconstan}@ics.forth.gr

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Introduction

Change management is a critical process in knowledge-intensive applications

Lots of research on the subject Several fields dealing with change managementSeveral change algorithms and tools have emerged for different

contextsDedicated events (e.g., IWOD yearly series)

We define change (evolution) as the process of adapting (revising) a corpus of knowledge based on new information

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Motivation

Original motivation

Create “yet another” change algorithm (for RDF/S ontologies)

But, in the process…

Uncovered a “pattern of change”Change algorithms can be viewed as different manifestations of

the same general ideaSimilarity offers an opportunity for abstraction

Study change at a more fundamental level

Apply this study to practical problems

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Basic Notions

Consider a pool of elements L (the language)

A Knowledge Base (KB) K is any set of elements from L (subset of L)

An update is a request to add and remove elements from K

U=(U+,U-)U+: the elements to add (subset of L)U-: the elements to remove (subset of L)

Update operation: K●U

A function, that returns a KB given a KB and an update

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Change Principles

General principles (inspired by research on belief revision)

Principle of Algorithmic Adequacy:well-defined and deterministic operation; the output is a KB

Principle of Irrelevance of Syntax:semantical considerations only (syntax is not important)

Principle of Validity:output is valid

Principle of Success:update takes precedence over existing knowledge

Principle of Minimal Change:protect existing knowledge (no unnecessary changes)

Principles are widely applicable, but not in all contexts (exceptions exist); here, we adopt these principles

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Change Process (Intuition and Problems)

KB(set of elements)

Update (request for element

additions and removals)

But KBs are not just sets of elements(must be valid –

Principle of Validity)

KB(set of elements)

Main Challenge

To determine the minimal set of side-effects that guarantee success and

validity, taking into account only semantical

considerations, in the presence of inference, and apply the side-effects (and

the update) upon the original KB

KB

Apply the update(must be successful – Principle of Success)

Validity Model

Inference Model

Side-effects

Minimality Model

Apply side-effects(to guarantee validity

and success – Principle of Validity

Principle of Success)

But KBs are not just sets of elements

(inference applies – Principle of Validity,

Principle of Success)But there may be several different options for the

side-effects(minimality considerations – Principle of Minimal Change)

Determine the minimal side-effects

(to guarantee minimality – Principle of Minimal Change)

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Hard part

Easy part

Algorithmic Scheme (Meta-algorithm)

Input:KB K

Update U

Apply U upon K

Valid and successful?

No side-effects

Determine the side-effects; result must be successful,

valid and minimal

Apply U and the side-effects upon K;

return the result

YES

NO

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Parameters of Change

Change algorithms follow the same general scheme, but:

Are applicable to very different contextsGive different results (select different side-effects to apply)

There must be some parameters hidden in the algorithmic scheme, which affect algorithms’ behaviour

LanguageDomain of applicationValidity modelInference modelMinimality model

An algorithm’s expected result and behaviour is determined by the values of these five parameters

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The language

Determines the pool of elements for the KBs and updates

The domain of application

Determines the supported <KB, update> pairs

Inference model

Determines the inference mechanism

Validity model

Determines the valid KBs

Selection process

Selects one of the possible sets of side-effectsDetermines the minimality model

List of Parameters

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All updates (side-effects)

Effect of ParametersLanguage determines the pool of elements (for the KB and the update)

Domain of application determines the acceptable input of the algorithm

Validity determines the side-effects that satisfy validity

Inference affects the side-effects that satisfy validity and success

Selection mechanism determines the side-effects to apply (and, consequently, the expected result of the algorithm)

Satisfying validity

Satisfying success

Minimal

Infeasibleupdates

Input:KB K

Update U

Apply U upon K


No side-effects


valid and minimal


return the result

YES

NO

Input:KB K

Update U

Apply U upon K


No side-effects


valid and minimal


return the result

YES

NO

Minimal?

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Levels of Abstraction (1/2)

The values of the parameters determine:

The working hypotheses and context of the change algorithmThe expected result of the change algorithm

Did not specify

Possible values of the parametersHow to implement an algorithm returning the expected result

We study these questions at different abstraction levels

Parameters can be specific, or range over a vast pool of possibilities

This affects our ability to develop (design) an algorithm returning the expected result

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Levels of Abstraction (2/2)Level 1Meta-algorithm

Most general; applicable in any context; framework; no implementation hints

Level 2General-purpose algorithm

Quite general; widely applicable, parameters range over a family of possibilities; implementation hints; special case of level 1

Level 3RDF-specific algorithm

Specific; usable only for RDF/S; directly implementable; proof of concept; special case of level 2

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Introduction to RDF, RDFS

RDF: triple-based representation

(s, p, o): s (subject) has property p (predicate) with value o (object)(myCar, hasColor, Red)Triples connect resources (anything with a URI)

RDFS: semantics to RDF

Added special resources (e.g., property rdfs:subClassOf)(Car, rdfs:subClassOf, Vehicle)Added semantics to these resources (e.g., rdfs:subClassOf

denotes the subsumption relationship, so it is transitive)

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Setting the Language (1/2)

Level 1: a non-empty set

Level 2: based on a finite set of predicates P and a set of constants Σ

The ground fact Q(x) represents some factOnly relational ground facts in L (no operands like ¬, , , )Directly representable in a databaseExamples: Q(x), R(x,y), …

The original language may be of a different form

Provide a mapping

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Setting the Language (2/2)

Example (RDF/S)

Subclass relationship (rdfs:subClassOf) denoted by C_IsA(Car, rdfs:subClassOf, Vehicle) mapped into C_IsA(Car, Vehicle)This allows mapping sets of triples (KBs in RDF) to sets of

relational ground facts (KBs in L)

Level 3: a particular set of predicates P and constants Σ and the respective mapping

See (Konstantinidis, 2008) for details

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Setting the Domain of Application

Level 1: a non-empty set D of <KB, update> pairs

Level 2: some restrictions apply

KB must be validUpdate must not be infeasible

Level 3: the same for the RDF/S context

D={<K,U> | K: valid, U: not infeasible}

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Setting the Validity Model

Level 1: a set V of valid KBs

Level 2: validity decided through a set of validity rules

A KB is valid if and only if it satisfies the validity rulesThe set V consists of the KBs that satisfy the validity rulesValidity rules are disjunctive embedded dependencies (DEDs),

which is a general class of first-order logic axioms

Level 3: a particular set of validity rules (DEDs), suitable for the RDF/S context

See (Konstantinidis, 2008) for a full list

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Setting the Inference Model (1/2)

Level 1: a function Cn from KBs to KBs

Level 2: unusual handling

Inference rules (DEDs) determine the implications of a KBInference rules are included in the validity rules, not in the Cn

function

No inference as such

If a KB is valid, then it is also “closed” with respect to “inference”For a KB K, Cn(K)=K (no inference)No implicit information, in the strict sense

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Setting the Inference Model (2/2)

Practical implications

No implicit information, so validity and success checks need not take inference into account

—Simplifies algorithm design

—Simplifies the definition of the validity rules

Guarantees satisfaction of the Principle of Irrelevance of Syntax—Equivalent (and valid) KBs are equal

Level 3: a particular set of inference rules, applicable for the RDFS context, added to the validity rules

See (Konstantinidis, 2008) for a full list

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Setting the Selection Mechanism

Level 1: a function σ that selects one update out of a set of updates

Level 2: a relation (<) comparing the different updates

Compares sets of effects plus side-effectsDetermines (i.e., selects) the minimal update (must be unique)Relation assumed to satisfy certain properties (conflict sensitivity,

totality, partial antisymmetry, monotonicity, transitivity)

Level 3: via a particular relation, suitable for the application at hand (RDF/S)

See (Konstantinidis, 2008) for details

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Need for an Algorithm


Satisfying validity

Satisfying success

Minimal

Input:KB K

Update U

Apply U upon K


No side-effects


valid and minimal


return the result

YES

NO

Input:KB K

Update U

Apply U upon K


No side-effects


valid and minimal


return the result

YES

NO

Knowing the expected result is not the same as being able to produce it algorithmically

No algorithm to determine the candidate side-effectsThe candidates may be infinite

Designing an algorithm is only possible for levels 2 and 3

RDF-specific algorithm is an application of the general-purpose one

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General-Purpose Algorithm

Starting with U, we enhance it (add side-effects) in an effort to guarantee both validity and success

Possible solutions are compared (using <) and filteredSome paths lead to infeasible solutions (rejected)Tree-like search space (rooted in U)


Satisfying validity

Satisfying success

U

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Algorithm: Determining the Paths

If validity is not satisfied, then at least one rule is violated

Path determination is based on the violated rule(s)

x,y,… Q1(x,y,…) Q2(x,y,…) ∃z,w,…Q3(x,y,…,z,w,…) …

Each branch represents one way to restore a violated rule

Each node represents one violated rule that is restored


Satisfying validity

Satisfying success

U


Satisfying validity

Satisfying success

U

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Algorithm: Correctness

The nature of the algorithm, the properties of < and our hypotheses (language, validity rules etc) guarantee that:

The algorithm will always converge to a valid and successful set of side-effects

—Unless the update is infeasible, in which case infeasibility will be detected

The minimal set of side-effects will be discovered (i.e., at least one path will lead to that)

The result will satisfy all the principles

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Algorithm: Termination

Unfortunately, we cannot, in general, guarantee that:

There is a finite number of paths Each path will converge in a finite number of steps

For some selections of the parameters, the algorithm may not terminate

Applying the algorithm for specific contexts presupposes careful selection of the parameters

For the parameters used for level 3, termination is guaranteed

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Algorithm Summary (Levels 2 and 3)

Level 2:

The presented algorithm identifies the updates to compareThe minimality relation is used to compare themCorrectness is guaranteedTermination is not guaranteed (for some parameters)

Level 3:

Uses the general-purpose algorithm —Applied for the particular parameters of level 3

Correctness is guaranteedTermination is guaranteed (for the specific parameters)

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Comparison With Related Work

Pattern (algorithmic scheme) is followed, in general

Side-effects decided, per-case, during design timeDecisions hard-coded in the algorithm

Our approach takes the related decisions at run-time

Avoids error-prone checking for all possible cases at design-timeEasier to guarantee “global policy” towards updatesEasier to prove formal properties of the algorithmCan support an infinite number of different updatesAllows experimentation with certain parameters, even as part of

user’s inputLess efficient

—Special-purpose algorithms can be developed

—Heuristics and application-specific optimizations can be used

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Contributions (Level 1)

Uncovers fundamental properties of change algorithms

Easier understanding of existing algorithmsAids the development of new algorithmsModularizes the development of new algorithms

Allows the understanding of change at a fundamental level

When you understand how you do changes in you mind, it is easier to encode and implement them

Abstracts away from the peculiarities of each application

Not implementable

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Allows the design of a general-purpose algorithm

Returns the expected result, per its parametersProvides formal guarantees (correctness, consistent policy etc)Applicable in several different contextsSpecific contexts are simple applications of the general algorithmAlgorithm design can be reduced to the setting of the parametersDesigner only has to determine the correct parameters

Delegates all the hard work at run-time

Algorithm (partly) orthogonal to the context

Application-specific optimizations necessary for efficiency

Termination is not guaranteed for all possible parameters

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Implemented algorithm for changing RDF/S ontologies

An application of the general-purpose algorithm for some specific set of parameters, suitable for RDF/S

Proof of concept

Enjoys all the nice formal properties and guarantees of the general-purpose algorithm (e.g., correctness)

Termination (for the particular parameterization)

Optimizations possible (application-specific)

HeuristicsSpecial-purpose algorithms

Very specific, only applicable for the RDF/S context

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Conclusions and Future Work

RDF-specific algorithm implemented in the SWKM (Semantic Web Knowledge Middleware) platform

Large scale real-time system based on web services, developed in FORTH

SWKM web site: http://athena.ics.forth.gr:9090/SWKM/

Future work

Detailed experimental performance evaluation of RDF-specific algorithm

Optimizations, heuristicsApplications to ontology debugging

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Thank You

References:

1. George Konstantinidis. Belief Change in Semantic Web Environments. Master Thesis, Computer Science Department, University of Crete, 2008.

2. George Konstantinidis, Giorgos Flouris, Grigoris Antoniou and Vassilis Christophides. “A Formal Approach for RDF/S Ontology Evolution”. In Proceedings of the 18th European Conference on Artificial Intelligence (ECAI-08), pages 405-409, 2008.

3. SWKM web site: http://athena.ics.forth.gr:9090/SWKM/

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EXTRA SLIDES

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Rules and Language: Semantics

The language contains only relational atoms

No inference rules (only validity rules)

The language assumes closed-world semantics

Q(x) implied by K if and only if Q(x)∈K (explicitly)Q(x) implied by K if and only if Q(x)∉K (explicitly)

Checking the validity of a rule becomes simple:

x,y C_IsA(x,y)→C_IsA(y,x) satisfied by K if and only if for all x,y, it holds that C_IsA(y,x)∉K whenever C_IsA(x,y)∈K

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Summary

Set some principles for rational updates

Expected update result is determined by five parameters:

LanguageDomain of ApplicationInference ModelValidity ModelSelection Mechanism

Implementing an algorithm returning the expected result is a different thing

Three levels of abstraction

Different restrictions on parameters’ values and different opportunities for algorithm design

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