BOEMIE Workshop 02/12/2008Giorgos Flouris1 Formalizing the Evolution Process Institute of Computer Science Foundation for Research and Technology – Hellas Heraklion, Greece Giorgos Flouris George Konstantinidis

BOEMIE Workshop 02/12/2008Giorgos Flouris2 Introduction  Change management is a critical process in knowledge- intensive applications  Lots of research on the subject  Several fields dealing with change management  Several change algorithms and tools have emerged for different contexts  Dedicated events (e.g., IWOD yearly series)  We define change (evolution) as the process of adapting (revising) a corpus of knowledge based on new information

BOEMIE Workshop 02/12/2008Giorgos Flouris3 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 idea  Similarity offers an opportunity for abstraction  Study change at a more fundamental level  Apply this study to practical problems

BOEMIE Workshop 02/12/2008Giorgos Flouris4 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

BOEMIE Workshop 02/12/2008Giorgos Flouris5 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

BOEMIE Workshop 02/12/2008Giorgos Flouris6 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)

BOEMIE Workshop 02/12/2008Giorgos Flouris7 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

BOEMIE Workshop 02/12/2008Giorgos Flouris8 Parameters of Change  Change algorithms follow the same general scheme, but:  Are applicable to very different contexts  Give different results (select different side-effects to apply)  There must be some parameters hidden in the algorithmic scheme, which affect algorithms’ behaviour  Language  Domain of application  Validity model  Inference model  Minimality model  An algorithm’s expected result and behaviour is determined by the values of these five parameters

BOEMIE Workshop 02/12/2008Giorgos Flouris9  The language  Determines the pool of elements for the KBs and updates  The domain of application  Determines the supported pairs  Inference model  Determines the inference mechanism  Validity model  Determines the valid KBs  Selection process  Selects one of the possible sets of side-effects  Determines the minimality model List of Parameters

BOEMIE Workshop 02/12/2008Giorgos Flouris10 All updates (side-effects) Effect of Parameters  Language 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 Infeasible updates Minimal?

BOEMIE Workshop 02/12/2008Giorgos Flouris11 Levels of Abstraction (1/2)  The values of the parameters determine:  The working hypotheses and context of the change algorithm  The expected result of the change algorithm  Did not specify  Possible values of the parameters  How 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

BOEMIE Workshop 02/12/2008Giorgos Flouris12 Levels of Abstraction (2/2) Level 1 Meta-algorithm Most general; applicable in any context; framework; no implementation hints Level 2 General-purpose algorithm Quite general; widely applicable, parameters range over a family of possibilities; implementation hints; special case of level 1 Level 3 RDF-specific algorithm Specific; usable only for RDF/S; directly implementable; proof of concept; special case of level 2 GeneralityCovered Contexts ImplementabilitySpecificityPractical Applicability

BOEMIE Workshop 02/12/2008Giorgos Flouris13 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)

BOEMIE Workshop 02/12/2008Giorgos Flouris14 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 fact  Only relational ground facts in L (no operands like ¬, , ,  )  Directly representable in a database  Examples: Q(x), R(x,y), …  The original language may be of a different form  Provide a mapping

BOEMIE Workshop 02/12/2008Giorgos Flouris15 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

BOEMIE Workshop 02/12/2008Giorgos Flouris16 Setting the Domain of Application  Level 1: a non-empty set D of pairs  Level 2: some restrictions apply  KB must be valid  Update must not be infeasible  Level 3: the same for the RDF/S context  D={ | K: valid, U: not infeasible}

BOEMIE Workshop 02/12/2008Giorgos Flouris17 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 rules  The set V consists of the KBs that satisfy the validity rules  Validity 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

BOEMIE Workshop 02/12/2008Giorgos Flouris18 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 KB  Inference 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

BOEMIE Workshop 02/12/2008Giorgos Flouris19 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

BOEMIE Workshop 02/12/2008Giorgos Flouris20 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-effects  Determines (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

BOEMIE Workshop 02/12/2008Giorgos Flouris21 Need for an Algorithm All updates (side-effects) Satisfying validity Satisfying success Minimal  Knowing the expected result is not the same as being able to produce it algorithmically  No algorithm to determine the candidate side-effects  The 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

BOEMIE Workshop 02/12/2008Giorgos Flouris22 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 filtered  Some paths lead to infeasible solutions (rejected)  Tree-like search space (rooted in U) All updates (side-effects) Satisfying validity Satisfying success U

BOEMIE Workshop 02/12/2008Giorgos Flouris23 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,…  Q 1 (x,y,…)  Q 2 (x,y,…)  ∃ z,w,…Q 3 (x,y,…,z,w,…)  …  Each branch represents one way to restore a violated rule  Each node represents one violated rule that is restored

BOEMIE Workshop 02/12/2008Giorgos Flouris24 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

BOEMIE Workshop 02/12/2008Giorgos Flouris25 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

BOEMIE Workshop 02/12/2008Giorgos Flouris26 Algorithm Summary (Levels 2 and 3)  Level 2:  The presented algorithm identifies the updates to compare  The minimality relation is used to compare them  Correctness is guaranteed  Termination is not guaranteed (for some parameters)  Level 3:  Uses the general-purpose algorithm — Applied for the particular parameters of level 3  Correctness is guaranteed  Termination is guaranteed (for the specific parameters)

BOEMIE Workshop 02/12/2008Giorgos Flouris27 Comparison With Related Work  Pattern (algorithmic scheme) is followed, in general  Side-effects decided, per-case, during design time  Decisions hard-coded in the algorithm  Our approach takes the related decisions at run-time  Avoids error-prone checking for all possible cases at design-time  Easier to guarantee “global policy” towards updates  Easier to prove formal properties of the algorithm  Can support an infinite number of different updates  Allows experimentation with certain parameters, even as part of user’s input  Less efficient — Special-purpose algorithms can be developed — Heuristics and application-specific optimizations can be used

BOEMIE Workshop 02/12/2008Giorgos Flouris28 Contributions (Level 1)  Uncovers fundamental properties of change algorithms  Easier understanding of existing algorithms  Aids the development of new algorithms  Modularizes 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

BOEMIE Workshop 02/12/2008Giorgos Flouris29 Contributions (Level 2)  Allows the design of a general-purpose algorithm  Returns the expected result, per its parameters  Provides formal guarantees (correctness, consistent policy etc)  Applicable in several different contexts  Specific contexts are simple applications of the general algorithm  Algorithm design can be reduced to the setting of the parameters  Designer 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

BOEMIE Workshop 02/12/2008Giorgos Flouris30 Contributions (Level 3)  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)  Heuristics  Special-purpose algorithms  Very specific, only applicable for the RDF/S context

BOEMIE Workshop 02/12/2008Giorgos Flouris31 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:  Future work  Detailed experimental performance evaluation of RDF-specific algorithm  Optimizations, heuristics  Applications to ontology debugging

BOEMIE Workshop 02/12/2008Giorgos Flouris32 Thank You References: 1. George Konstantinidis. Belief Change in Semantic Web Environments. Master Thesis, Computer Science Department, University of Crete, George Konstantinidis, Giorgos Flouris, Grigoris Antoniou and Vassilis Christophides. “A Formal Approach for RDF/S Ontology Evolution”. In Proceedings of the 18 th European Conference on Artificial Intelligence (ECAI-08), pages , SWKM web site:

BOEMIE Workshop 02/12/2008Giorgos Flouris33 EXTRA SLIDES

BOEMIE Workshop 02/12/2008Giorgos Flouris34 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

BOEMIE Workshop 02/12/2008Giorgos Flouris35 Summary  Set some principles for rational updates  Expected update result is determined by five parameters:  Language  Domain of Application  Inference Model  Validity Model  Selection 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