Logical Foundation of the Semantic Web Zhisheng Huang

语义网的逻辑基础 Logical Foundation of the Semantic Web 主讲： 黄智生 Zhisheng Huang Vrije University Amsterdam， The Netherlands huang@cs. vu. nl 助教： 胡伟 Wei Hu Southeast University whu@seu. edu. cn China 2009 1

课程时间表Schedule China 2009 2

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讲座 5：本体管理与推理(I) Lecture 5: Ontology Management and Reasoning (I) • 本体推理与管理(Reasoning and Management of Ontologies) • 不一致本体的推理（Reasoning with Inconsistent Ontologies) • 多版本本体的推理与管理(Reasoning with Multi-version Ontologies) • 本体修改与本体演化(Ontology Revision and Ontology Evolution) • 结论和讨论 (Conclusion and Discussion) 4 China 2009

Ontology Reasoning and Inconsistency Management China 2009 5

语义网核心研究课题： SEKT Project • Semantically Enabled Knowledge Technologies (SEKT) • A European research and development project launched under the EU Sixth Framework Programme. . China 2009 6

Duration and Partners • Three year project: January 2004 – December 2006. • 13 partners: 公司： BT(英国电信), Empolis Gmb. H, i. SOCO(Spain), Kea-pro Gmb. H, Ontoprise, Sirma AI EOOD(Bulgaria), (+SIEMENS西门子公司) 大学： Jozef Stefan Institute(Slovenia), Univ. Karlsruhe(Germany), Univ. Sheffield(U. K. ), Univ. Innsbruck(O), Univ. Autonoma Barcelona(Spain), Vrije Universteit Amsterdam(The Netherlands) China 2009 7

Case Studies • Legal Domain (i. SOCO) • Telecom Domain (BT) • Siemens China 2009 8

SEKT Activities and Relationships China 2009 9

Core Tasks: WP 3 China 2009 10

SEKT WP 3 Architecture China 2009 11

Inconsistency and the Semantic Web • The Semantic Web is characterized by • scalability, • distribution, and • multi-authorship • All these may introduce inconsistencies. China 2009 12

Ontologies will be inconsistent Because of: • mistreatment of defaults • polysemy • migration from another formalism • integration of multiple sources • … (“Semantic Web as a wake-up call for KR”) China 2009 13

Example: Inconsistency by mistreatment of default rules • • • China 2009 Mad. Cow Ontology Cow Vegetarian Mad. Cow Eat. Brainof. Sheep Animal Vegetarian Eat. (Animal Partof. Animal) Brain Partof. Animal. . . the. Mad. Cow. . . 14

Example: Inconsistency through imigration from other formalism DICE Ontology • • Brain Central. Nervous. System Brain Body. Part Central. Nervous. System Body. Part Nervous. System China 2009 15

Inconsistency and Explosion • The classical entailment is explosive: P, ¬ P |= Q Any formula is a logical consequence of a contradiction. • The conclusions derived from an inconsistent ontology using the standard reasoning may be completely meaningless China 2009 16

Why DL reasoning cannot escape the explosion • The derivation checking is usually achieved by the satisfiability checking. • |= {¬ } is not satisfiable. • Tableau algorithms are approaches based on the satisfiability checking • is inconsistent => is not satisfiable => {¬ } is not satisfiable. China 2009 17

Two main approaches to deal with inconsistency • Inconsistency Diagnosis and Repair • Ontology Diagnosis(Schlobach and Cornet 2003) • Reasoning with Inconsistency • • • China 2009 Paraconsistent logics Limited inference (Levesque 1989) Approximate reasoning(Schaerf and Cadoli 1995) Resource-bounded inferences(Marquis et al. 2003) Belief revision on relevance (Chopra et al. 2000) 18

What an inconsistency reasoner is expected • Given an inconsistent ontology, return meaningful answers to queries. • General solution: Use non-standard reasoning to deal with inconsistency • |= : the standard inference relations | : nonstandard inference relations China 2009 19

Reasoning with inconsistent ontologies: Main Idea Starting from the query, 1. select consistent sub-theory by using a relevance-based selection function. 2. apply standard reasoning on the selected sub -theory to find meaningful answers. 3. If it cannot give a satisfying answer, the selection function would relax the relevance degree to extend consistent sub-theory for further reasoning. China 2009 20

New formal notions are needed • New notions: • Accepted: • Rejected: • Overdetermined: • Undetermined: • Soundness: (only classically justified results) • Meaningfulness: (sound & never overdetermined) soundness + China 2009 21

Some Formal Definitions • Soundness: | => ` ( ` consistent and `|= ). • Meaningfulness: sound and consistent ( | => ¬ ). • Local Completeness w. r. t a consistent ` : ( `|= => | ). • Maximality: locally complete w. r. t a maximal consistent set `. • Local Soundness w. r. t. a consistent set `: | => `|= ). China 2009 22

Selection Functions Given an ontology T and a query , a selection function s(T, , k) returns a subset of the ontology at each step k>0. China 2009 23

General framework Use selection function s(T, , k), with s(T, , k) s(T, , k+1) 1. Start with k=0: s(T, , 0) |= or s(T, , 0) |= ? 2. Increase k, until s(T, , k) |= or s(T, , k) |= 3. Abort when • • China 2009 undetermined at maximal k overdetermined at some k 24

Inconsistency Reasoning Processing: Linear Extension China 2009 25

Proposition: Linear Extension • • Never over-determined May undetermined Always sound Always meaningful Always locally complete May not maximal Always locally sound China 2009 26

Direct Relevance and K Relevance • Direct relevance (0 -relevance). • there is a common name in two formulas: C( ) R( ) I( ) . • K-relevance: there exist formulas 0, 1, …, k such that and 0, 0 and 1 , …, k and are directly relevant. China 2009 27

Relevance-based Selection Functions • s(T, , 0)= • s(T, , 1)= { T: is directly relevant to }. • s(T, , k)= { T: is directly relevant to s(T, , k-1)}. China 2009 28

PION Prototype PION: Processing Inconsistent ONtologies http: //wasp. cs. vu. nl/sekt/pion China 2009 29

An Extended DIG Description Logic Interface for Prolog (XDIG) • A logic programming infrastructure for the Semantic Web • Similar to SOAP • Application independent, platform independent • Support for DIG clients and DIG servers. China 2009 30

XDIG • As a DIG client, the Prolog programs can call any external DL reasoner which supports the DIG DL interface. • As a DIG server, the Prolog programs can serve as a DL reasoner, which can be used to support additional reasoning processing, like inconsistency reasoning multi-version reasoning, and inconsistency diagnosis and repair. China 2009 31

XDIG package • The XDIG package and the source code are now available for public download at the website: http: //wasp. cs. vu. nl/sekt/dig/ • In the package, we offer five examples how XDIG can be used to develop extended DL reasoners. China 2009 32

Answer Evaluation • • Intended Answer (IA): PION answer = Intuitive Answer Cautious Answer (CA): PION answer is ‘undetermined’, but intuitive answer is ‘accepted’ or ‘rejected’. Reckless Answer (RA): PION answer is ‘accepted’ or ‘rejected’, but intuitive answer is ‘undetermined’. Counter Intuitive Answer (CIA): PION answer is ‘accepted’ but intuitive answer is ‘rejected’, or vice verse. China 2009 33

Preliminary Tests with Syntactic-relevance Selection Function Ontology Queries IA Bird 50 50 CA RA CIA IA (%) 0 0 0 100 Brain (DICE) Married Woman Mad. Cow 42 36 4 2 0 85. 7 100 50 48 0 2 0 96 254 236 16 0 2 92. 9 99 China 2009 ICR (%) 100 34

Observation • Intended answers include many undetermined answers. • Some counter-intuitive answers • Reasonably good performance China 2009 35

Intensive Tests on PION • Evaluation and test on PION with several realistic ontologies: • Communication Ontology • Transportation Ontology • Mad. Cow Ontology Each ontology has been tested by thousands of queries with different selection functions. China 2009 36

Summary • we proposed a general framework for reasoning with inconsistent ontologies • based on selecting ever increasing consistent subsets • choice of selection function is crucial • query-based selection functions are flexible to find intended answers • simple syntactic selection works surprisingly well China 2009 37

Extension • Semantic Relevance Based Selection Functions • K-extension • Variants of over-determined processing strategies • Integrating with the diagnosis approach China 2009 38

Using Semantic Distances for Reasoning with Inconsistent Ontologies • Google distances are used to develop semantic relevance functions to reason with inconsistent ontologies. • Assumption: two concepts appear more frequently in the same web page, they are semantically more similar (relevant). 39

Google Distances (Cilibrasi and Vitanyi 2004) • Google distance is measured in terms of the cooccurrence of two search items in the Web by Google search engine. • Normalized Google Distance (NGD) is introduced to measure the similarity/light-weight semantic relevance • NGD(x, y)= (max{log f(x), log f(y)}-log f(x, y))/(log Mmin{log f(x), log f(y)} where f(x) is the number of Google hits for x f(x, y) is the number of Google hits for the tuple of search items x and y M is the number of web pages indexed by Google. 40

Semantic Distances • Define semantic distances (SD) between two formulas in terms of semantic distances between two concepts/roles/individuals (NGD) China 2009 41

Postulates for Semantic Distances China 2009 42

Semantic Distances Semantic distance are measured by the ratio of the summed distance of the difference between two formulae to the maximal distance between two formulae. 43

Proposition • The semantic distance SD satisfies the properties Range, Reflexivity, Symmetry, Maximum Distance, and Intermediate Values. China 2009 44

Example: Mad. Cow NGD(Mad. Cow, Grass)=0. 7229 NGD(Mad. Cow, Sheep)=0. 6120 China 2009 45

Implementation: PION: Processing Inconsistent ONtologies http: //wasp. cs. vu. nl/sekt/pion China 2009 46

Answer Evaluation • • Intended Answer (IA): Query answer = Intuitive Answer Cautious Answer (CA): Query answer is ‘undetermined’, but Intutitve answer is ‘accepted’ or ‘rejected’. Reckless Answer (RA): Query answer is ‘accepted’ or ‘rejected’, but Intutive answer is ‘undetermined’. Counter Intuitive Answer (CIA): Query answer is ‘accepted’ but Intuitive answer is ‘rejected’, or vice versa. 47

Syntactic approach vs. Semantic approach: quality of query answers 48

Syntactic approach vs. Semantic approach: Time Performance 49

Summary • The run-time of the semantic approach is much better than the syntactic approach, while the quality remains comparable. • The semantic approach can be parameterised so as to stepwise further improve the run-time with only a very small drop in quality. 50

Summary (cont. ) • The semantic approach for reasoning with inconsistent ontologies trade-off computational cost for inferential completeness, and provide attractive scalability. 51

Multi-versioning: Why • Change Recovery: allow the possibilities for the developers to withdraw or adjust the changes to avoid unintended impacts. • Compatibility: Ontology users may prefer an earlier version with less resource requirement to a newer version with higher resource requirement. • …… China 2009 52

The Idea of Versioning • Version Spaces: • Models resulting from changes are stored separately • Models and change operations form a graphcalled Version Space • Data is accessed through the “right” version v 2 v 1 China 2009 v 3 v 4 v 5 v 6 53

Managing Version Spaces • Idea: Enable Administrator to ask questions about the version space • Combine Reasoning: • Ontologies: DL reasoner (RACER) • Version Space: Modal Logic • Principle: • Each Ontology is a possible world • Truth of statements in a state is determine by the DL reasoner China 2009 54

Simplifying Assumptions • Linear Time Temporal Logic • Linear Version Space • Operators • Conjunction, Negation, Previous. Version, All. Prior. Versions • Pre-defined Statement predicates • Child-of, parent-of, • Any other RACER function. . China 2009 55

Version Space • Version space: A version space S over an ontology set Os is a set of ontology pairs, namely, S Os × Os. • Linear version space: S = {<o 1, o 2>, <o 2, o 3>, · · · , <on− 1, on>} such that oi oj for i j. alternatively, we write S=(o 1, o 2, …, on) • Linear ordering: o’ < o iff o’ occurs prior to o in the sequence S. China 2009 56

Linear Time Logic LTLm • Operators: • Boolean operators: negation, conjunction, etc. • Temporal operators (Backlooking operators) • Prev : holds in the previous version • P : holds in a prior version(Sometimes in the past) • H : holds in all prior versions (Always in the past) • S : always holds in the prior versions since holds in a prior version China 2009 57

Linear Time Logic LTLm(F) • Operators: • Temporal operators (forward-looking operators) • Next : holds in the next version • F : holds in a sequel version(Sometimes in the future) • G : holds in all sequel versions (Always in the future) • U : always holds in all of the sequel versions until holds. China 2009 58

Semantics China 2009 59

Semantics • S, o |= Prev iff <o’, o> S and S, o’ |= . • S, o |= H iff o’< o and S, o’ |= . • S, o |= S iff o 1, …, on (<o 1, o 2>, …, <on -1, on> S and on=o and S, oi |= and S, o 1|= China 2009 60

Formal Properties • H -> P . • H -> Prev . • Prev -> P . • Prev P -> P . • P P -> P . • H H -> H . • Prev -> P . China 2009 61

Reasoning Queries • : holds in the current version • Prev : holds in the current version but no in the previous version. • P : incompactible (with respect to ). • H : holds only in the current version, it never holds before. China 2009 62

Reasoning Query: stable change • Once is changed, it is never changed again. S (H ). China 2009 63

Change Accounting: Only Twice • is changed only twice. S Prev( S H ). China 2009 64

Change Accounting: Only N times • Change(1, ) =df S H. • Change(n, ) =df S Prev(Change(n-1, )), for n = 2, 4, 6, …, • Change(n, ) =df S Prev(Change(n-1, )), for n = 3, 5, 7, …, China 2009 65

Reasoning Query: last version I • holds at the last version in which holds. S (Prev( )) China 2009 66

Reasoning Query: last version II holds at the last version in which does not hold before a version holds. S (Prev( S Prev( ))). China 2009 67

Retrieval Queries • child, parent concept relation China 2009 68

Relative Versioning • Version 0 . (the current version) • Version-i Prev(Version -(i-1) ) China 2009 69

Absolute Versioning • Version(i, S) Version i-n where |S|=n China 2009 70

Retrieval Query China 2009 71

The MORE System • Milestone 3. 5 – Software Prototype • . • Prototype: MORE (Multi-version Ontology REasoner) • MORE website: http: //wasp. cs. vu. nl/sekt/more China 2009 72

The MORE System • Functionality • • Temporal Reasoning Queries Ontology Comparison Queries: Versioning Retrieval Queries Ontology Data format: OWL and DIG • Test Data • Bio. SAIL ontologies (3 versions) • SEKT legal case study ontologies (5 versions) China 2009 73

Test Result: Change Log China 2009 74

Summary • A framework of multi-version ontology reasoning • Temporal logic approach • Expressive power of LTLm • Semantic differences on multi-version ontologies. China 2009 75

Future Work • Integrating MORE with ontology evolution (Dynamic logic approach). • Hybrid logic approach for nominals • Branching time version space. • Merging time model (merging multiple ontologies). China 2009 76

WP 3. 6 Inconsistency Diagnosis and Repair • Software Prototypes • DION: Inconsistency Diagnosis and Repair • Task: Given an inconsistent ontology, locate possible sources of inconsistencies and offer the user (a knowledge engineer) to repair them. • Prototypes: DION/Mupster • Using the pinpointing technology China 2009 77

Pinpointing Technique • MUPS: Minimal unsatisfiability-preserving sub-TBox w. r. t. a concept • MIPS: Minimal incoherence-preserving sub-TBox • MIPS-Core: A non-empty intersection of n different MIPS • Pinpoints are calculated from MIPS-Core. A pinpoint is a diagnosis in the sense of (Reiter 1987)"A Theory of Diagnosis from First Principles“. China 2009 78

Applying Debugging within Se. KT Debugging for Learning complex ontologies (UKA) • Given natural language text • Calculate complex (OWL) ontology • this ontology might be inconsistent • Strategy: • learn as many axioms as possible, and • debug those that lead to logical contradictions China 2009 79

Debugging for Learning (more) • UKA developed methods for learning disjointness axioms from free-text. • Ontology can become inconsistent: • Conceptually correct inconsistency • Incorrectly learned axiom • Debugging can help solve the latter: • MIPS (from learned axioms only) contains at least one axioms with a mistake. • Pinpoint suggests a way of correcting China 2009 80

Debugging for learning (example) • The problems are already on a simpler level: what is a correct disjointness statement. • UKA tested agreement on added disjointness statements for PROTON. • Even on expert level -> inconsistencies! • Debugging can explain! • Let us see an example: • • China 2009 Even in the most expert level, there are three unsatisfiable concepts: <unsatisfiable. Concept ontology="proton_100_all. owl" number="3"> <catom name="http: //proton. semanticweb. org/2004/12/protonu#Reservoir"/> <catom name="http: //proton. semanticweb. org/2004/12/protonu#Harbor"/> <catom name="http: //proton. semanticweb. org/2004/12/protonu#Canal"/> </unsatisfiable. Concept> 81

Debugging for Learning (ex: cont) • A minimal incoherent subterminology(MIPS) Facility !== Water. Region Reservoir isa Hydrographic. Structure Reservoir isa Lake Hydrographic. Structure isa Facility Lake isa Water. Region • There are two pinpoints (i. e. possible errors) Facility !== Water. Region and Hydrographic. Structure isa Facility • Experts have to decide which one is faulty!82 China 2009

Debugging for Learning (ex: cont) China 2009 83

Debugging: Evaluation of Prototypes • Evaluation of MUPSter and DION showed: • Comparable runtimes • DION more flexible, expressive and easy to adapt . China 2009 84

DION • • • China 2009 Queries on MUPS/MIPS/Core/Pinpoints Data Format Support: DIG/OWL Integration with RACER/KAON 2 Platform Support: Windows/Linux Graphical User Interface: DION Testbed Ontology Data Pre-processing: more fine-grained debugging Example: A D 1 D 2 => A D 1, A D 2 85

DION Testbed China 2009 86

Ontology Evolution China 2009 87

AGM Postulates for Belief Revision China 2009 88

Postulates for Contraction China 2009 89

Levi and Harper Identities China 2009 90

Problems for Ontology Revisions • Many description logics (including OWL DL) are not AGM-compliant • Problem: (implicit) negation and base recovery postulate China 2009 91

Variants of Inconsistencies in SW • Schlobach at el. (IJCAI 03): Incoherence: unsatisfiable concept in Tbox • Huang at el. (IJCAI 05): Classical sense of logical inconsistency • Haase at el. (ISWC 05): Example in a footnote. • …… China 2009 92

Incoherence and Inconsistency • Unsatisfiable concept in a Tbox: its interpretation is empty in any interpretation of Tbox • Incoherent Tbox: there exists unsatisfiable concept • Incoherent Ontology: its Tbox is incoherent • Inconsistent Ontology: there exists no models China 2009 93

Example I: Coherent and Inconsistent Ontology C 1 disjoint C 2 a China 2009 94

Example II: Incoherent and Inconsistent Ontology C 1 disjoint C 3 China 2009 C 2 a 95

Example III: Incoherent and consistent Ontology China 2009 C 1 disjoint a C 3 C 2 b 96

Example IV: Inconsistent (and coherent? ) Ontology C 1 disjoint C 2 {a} China 2009 97

Consistency Negation China 2009 98

Coherence Negation China 2009 99

Example China 2009 100

New Postulates for Ontology Revision China 2009 101

New Postulates for Ontology Changes China 2009 102

Levi and Harper Identities China 2009 103

Summary • Framework accounts for negation, inconsistency and change for DL-based ontologies for management of dynamic ontologies. • Proposed negations achieve the Harper identity and Levi identity for ontology change • Distinction between incoherence and inconsistency provides us two different approaches covering different needs in different application scenarios China 2009 104

练习题：PION • 提出其他方式的扩展策略 Variants of extension strategies • 提出其他方式的ODP策略 Variants of overdetermined processing strategies • 提出PION与本体诊断的整 合方法 Integrating with the diagnosis approach China 2009 105

Questions and Discussions China 2009 107