Project SPACMODL Semantic Stream Processing in Business Auditing Stephan Scheele Informatics Theory Group University of Bamberg Joint work with Michael Mendler. SYNCHRON 2008 1st - 5th December, 2008
Introduction Introduction & context Research Project “SPACMoDL” Funded by the German Research Council (DFG) Started June 2008 Topic: Investigate logics and semantic programming models for auditing Collaboration with industrial partners Stephan Scheele (UNI-BA) SPACMODL SYNCHRON´08 2 / 19
Introduction Area of interest: Auditing Verification of business transactions & data Mass data processing needs efficient stream processing procedures Audit problems: Purchasing: Analysis of behaviour of purchasers, completed and future orders, . . . Accounts Payable: Open-item accounting, supplier ranking, . . . . . . Offline Auditing: Auditing on database extracts (file streams) Online Auditing: Auditing in-place on information streams act as intelligent audit procedures within an information stream process transactions in real-time (as they come in) Stephan Scheele (UNI-BA) SPACMODL SYNCHRON´08 3 / 19
Introduction Area of interest: Auditing Verification of business transactions & data Mass data processing needs efficient stream processing procedures Audit problems: Purchasing: Analysis of behaviour of purchasers, completed and future orders, . . . Accounts Payable: Open-item accounting, supplier ranking, . . . . . . Offline Auditing: Auditing on database extracts (file streams) Online Auditing: Auditing in-place on information streams act as intelligent audit procedures within an information stream process transactions in real-time (as they come in) Stephan Scheele (UNI-BA) SPACMODL SYNCHRON´08 3 / 19
Classical Approach Classical Approach Spreadsheet-based, does not scale to large volume of data Database-based, specific and isolated applications Domain specific languages, ACL and Idea Old-fashioned languages Process mass-data stream based Not strongly typed, not type-safe, only flat types Modern features missing: Modularity, components, static typing Do not utilize modern hardware and parallelism (Multicore CPUs) Stephan Scheele (UNI-BA) SPACMODL SYNCHRON´08 4 / 19
Classical Approach Project objectives DSL for Auditing: Functional, declarative stream-processing language like Lustre Utilize Description Logics: Semantic interpretation of information streams Integrate Description Logic-reasoning services for advanced typing and knowledge-based data analysis Bring techniques from synchronous languages into the auditing world: component orientation, correct by construction, static typing, clear semantics, formal verification, clocktypes for optimization . . . Auditing is not (in every case) real-time critical but business critical Stephan Scheele (UNI-BA) SPACMODL SYNCHRON´08 5 / 19
Classical Approach Description Logics Family of logic based formalisms for the purpose of knowledge representation Well-suited for the representation of and reasoning about terminological knowledge ontologies database schemata . . . related to modal logic guarded fragment of predicate logic model theoretic semantics decidable decision problem Stephan Scheele (UNI-BA) SPACMODL SYNCHRON´08 6 / 19
Classical Approach Example: Syntax & Semantics of ALC #006600 #00FF00 #663300 Frog Atomic concepts: Frog, GrassFrog, TreeFrog, Colour, Green, Brown Roles: hasColour Stephan Scheele (UNI-BA) SPACMODL SYNCHRON´08 7 / 19
Classical Approach Example: Syntax & Semantics of ALC #006600 #00FF00 #663300 Frog TBox statements: Frog ⊑ Animal GrassFrog ⊑ Frog ⊓ ∃ hasColor . Brown Atomic concepts: Frog, GrassFrog, TreeFrog, Colour, Green, Brown TreeFrog ⊑ Frog ⊓ ∃ hasColor . Green Roles: hasColour Stephan Scheele (UNI-BA) SPACMODL SYNCHRON´08 7 / 19
Classical Approach Example: Syntax & Semantics of ALC #006600 #00FF00 #663300 Frog DL uses a variable free syntax: GrassFrog ⊑ Frog ⊓ ∃ hasColor . Brown can be translated into: Atomic concepts: Frog, GrassFrog, TreeFrog, Colour, Green, Brown ∀ x . GrassFrog ( x ) ⇒ Frog ( x ) ∧ ∃ y . hasColor ( x , y ) ∧ Brown ( y ) Roles: hasColour Stephan Scheele (UNI-BA) SPACMODL SYNCHRON´08 7 / 19
Classical Approach Example: Syntax & Semantics of ALC #006600 #00FF00 #663300 Frog ABox statements: Kermit : TreeFrog , Joe : GrassFrog Kermit : ∀ hasColor . Green Atomic concepts: Frog, GrassFrog, TreeFrog, Colour, Green, Brown Joe , Kermit : ∃ hasColor . Green ⊔ ∃ hasColor . Brown Roles: hasColour Stephan Scheele (UNI-BA) SPACMODL SYNCHRON´08 7 / 19
Classical Approach Syntax and semantics of ALC Elementary descriptions: atomic concepts atomic roles Concepts and roles are given standard Tarski-style model-theoretic semantics, their meaning is given by an interpretation I = (∆ I , · I ) with ∆ I as the universe of individuals and an interpretation function · I mapping Stephan Scheele (UNI-BA) SPACMODL SYNCHRON´08 8 / 19
Classical Approach Syntax and semantics of ALC Elementary descriptions: atomic concepts atomic roles Concepts and roles are given standard Tarski-style model-theoretic semantics, their meaning is given by an interpretation I = (∆ I , · I ) with ∆ I as the universe of individuals and an interpretation function · I mapping Stephan Scheele (UNI-BA) SPACMODL SYNCHRON´08 8 / 19
Classical Approach Syntax and semantics of ALC Elementary descriptions: atomic concepts atomic roles Concepts and roles are given standard Tarski-style model-theoretic semantics, their meaning is given by an interpretation I = (∆ I , · I ) with ∆ I as the universe of individuals and an interpretation function · I mapping Stephan Scheele (UNI-BA) SPACMODL SYNCHRON´08 8 / 19
Classical Approach Syntax and semantics of ALC Elementary descriptions: atomic concepts atomic roles Concepts and roles are given standard Tarski-style model-theoretic semantics, their meaning is given by an interpretation I = (∆ I , · I ) with ∆ I as the universe of individuals and an interpretation function · I mapping · I A I ⊆ ∆ I , a set of entities atomic concept A Stephan Scheele (UNI-BA) SPACMODL SYNCHRON´08 8 / 19
Classical Approach Syntax and semantics of ALC Elementary descriptions: atomic concepts atomic roles Concepts and roles are given standard Tarski-style model-theoretic semantics, their meaning is given by an interpretation I = (∆ I , · I ) with ∆ I as the universe of individuals and an interpretation function · I mapping · I A I ⊆ ∆ I , a set of entities atomic concept A · I R I ⊆ ∆ I × ∆ I , a binary relation Role R Stephan Scheele (UNI-BA) SPACMODL SYNCHRON´08 8 / 19
Classical Approach Description Logic specifications as stream types Business data come typically as streams of information, e.g. linearised database tables (streaming records) Considering streams as abstract entities DL concepts can act as typing system and specify semantical properties of stream elements Stephan Scheele (UNI-BA) SPACMODL SYNCHRON´08 9 / 19
Classical Approach Typing streams (I) Consider ∆ I = D ∗ ∪ D ∞ with D = N ⊎ B ⊎ ( N × B ) the universe of booleans, naturals and their pairings. Stephan Scheele (UNI-BA) SPACMODL SYNCHRON´08 10 / 19
� � � � � � Classical Approach Typing streams (I) Consider ∆ I = D ∗ ∪ D ∞ with D = N ⊎ B ⊎ ( N × B ) the universe of booleans, naturals and their pairings. Refinement � I (time shift) is the (inverse) suffix ordering v ∈ D v · s � P s where v · s is the stream s ∈ D ω prefixed by value v ∈ D . For instance, 1 · ( 2 , T ) · T · F � I ( 2 , T ) · T · F � I T · F � I F � I ǫ, where ǫ is the empty stream. Stephan Scheele (UNI-BA) SPACMODL SYNCHRON´08 10 / 19
� � � � � � Classical Approach Typing streams (I) Consider ∆ I = D ∗ ∪ D ∞ with D = N ⊎ B ⊎ ( N × B ) the universe of booleans, naturals and their pairings. Refinement � I (time shift) is the (inverse) suffix ordering v ∈ D v · s � P s where v · s is the stream s ∈ D ω prefixed by value v ∈ D . For instance, 1 · ( 2 , T ) · T · F � I ( 2 , T ) · T · F � I T · F � I F � I ǫ, DL Types have to be closed under time shift � ! where ǫ is the empty stream. Stephan Scheele (UNI-BA) SPACMODL SYNCHRON´08 10 / 19
Classical Approach Typing streams (II) Let N AT I = df N ω and B OOL I = df B ω be ususal programming language types considered as atomic DL concepts. Similarly ( N AT × B OOL ) I = df ( N × B ) ω . ǫ has no future projected behaviour, i.e. ⊥ I = { ǫ } , val is a functional role, relating a stream with its first data element considered as an infinite constant stream, i.e. val ( ǫ, ǫ ) and val ( v · s , v ∞ ) , e.g. val (( 2 , T ) · T · F , ( 2 , T ) ∞ ) . Stephan Scheele (UNI-BA) SPACMODL SYNCHRON´08 11 / 19
Classical Approach Typing streams (II) Let N AT I = df N ω and B OOL I = df B ω be ususal programming language types considered as atomic DL concepts. Similarly ( N AT × B OOL ) I = df ( N × B ) ω . ǫ has no future projected behaviour, i.e. ⊥ I = { ǫ } , val is a functional role, relating a stream with its first data element considered as an infinite constant stream, i.e. val ( ǫ, ǫ ) and val ( v · s , v ∞ ) , e.g. val (( 2 , T ) · T · F , ( 2 , T ) ∞ ) . Stephan Scheele (UNI-BA) SPACMODL SYNCHRON´08 11 / 19
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