A Logical Framework for XML Reference Specification

Transcription

1 A Logical Framework for XML Reference Specification C. Combi, A. Masini, B. Oliboni, M. Zorzi Department of Computer Science, University of Verona, Italy DEXA 2015, Valencia, 3th September

2 XML Constraints DTD: simple, limited expressive power? XMLSchema (XPath expressions)...: powerful, complex

3 XML Constraints DTD: simple, compact; limited expressive power A simple framework expressive enough to allow the specification of the most common integrity constraints on ID and IDREF(S) attributes XMLSchema: powerful and complex

4 XML and Modal/Temporal Logics The shape of XML documents naturally fits the shape of modal logic semantical models (Kripke, tree/oriented graph-like structures) C={prof_ref, stud_ref,cour_ref, stud_refs} university student stud_id stud_id student student student stud_id stud_id professor prof_id professor prof_id professor prof_id course cour_id course cour_id course cour_id course cour_id examination examination examination name name name name name name name surname surname surname surname surname surname surname title title title title mark mark mark supervisor supervisor supervisor supervisor thesis_stud thesis_ reviewer thesis_ reviewer

5 XML and Hybrid Logic Hybrid Logics are extensions of modal logic. Nominals: names for a is the hybrid at operator and it provides a direct access to the state (uniquely) named by a F means that the formula F holds in the state a

6 Related Literature in a Nutshell P. Blackburn et all: literature about hybrid logic proof-theory Marteen Marx: XML Documents as DAGs de Rijke and Franceschet: Model Checking for Hybrid Logic

7 Running Example: (a fragment of) the University Record university professor student prof_ref stud_refs supervisor thesis_stud

8 XHyb The peculiar feature of XHyb is the extension of quantified hybrid logic by means of a new modal operator c, which explicitly captures the presence of ID/IDREF(S) relation between elements of XML documents Examples: prof ref (professor), stud ref (student)

9 The alphabet of XHyb is built out of some sets of symbols for constants and variables. We define three distinct sets of constants: XHyb constants C (Colors) E (Element names) R (Identifier Names) XML interpretation IDREF(S) attribute declared in the DTD Tag names declared in the DTD ID attributes declared in the DTD

10 XHyb Formulae are built upon i, A, A, i A means that formula A holds at state i. A means that A holds at the current state and at all the descendant states; A means that A holds in each children of the current state; c is the reference operator: if c (i) holds in a given state, then there exists a reference, labelled by c, to state i.

11 XML Documents as Kripke Models XHyb model constructs Worlds Relations/constraints XML interpretation Values of ID attributes in the XML document, containment c references

12 XHyb Example: The presence of the IDREF relation between supervisor and professor can be encoded as prof ref (professor). The formula prof ref (professor) holds in a node (a world) supervisor: we can state (forgetting about interpretation) supervisor = prof ref (professor) supervisor professor prof_ref

13 XHyb, XML, Colored Xgraph Worlds university professor student thesis_stud supervisor

14 XHyb, XML, Colored Xgraph, : XTree university professor student thesis_stud supervisor

15 XHyb, XML, Colored Xgraph c : Colored XStructure university professor student thesis_stud supervisor

16 XHyb, XML, Colored Xgraph, + c : Colored XGraph university professor student thesis_stud supervisor

17 XHyb encoding of constraints (non-expressible by DTD) <! ATTLIST supervisor prof ref IDREF #REQUIRED > <! ATTLIST course cour id ID #REQUIRED prof ref IDREF #REQUIRED > The supervisor of a student must be a professor. i((supervisor prof ref i professor) A course must be taught by a professor. course k( proof ref k professor)

18 XHyb encoding of constraints (non-expressible by DTD) <! ATTLIST thesis stud stud refs IDREF #REQUIRED > A professor may be the supervisor of one or more students. thesis stud γ.( stud refs (γ) i.(i i student))

19 XHyb encoding of constraints (non-expressible by DTD) <! ATTLIST examination stud ref IDREF #REQUIRED cour ref IDREF #REQUIRED > A student can be evaluated only once for a given course. i. j.((@ i j course) m. n(@ m (examination stud ref (i) cour ref n (examination stud ref (i) cour ref m n)

20 XHyb encoding of constraints (non-expressible by DTD) <! ATTLIST supervisor prof ref IDREFS #REQUIRED > <! ATTLIST thesis reviewer prof ref IDREFS #REQUIRED > A professor cannot be both supervisor and reviewer of the same student. k.j.γ(@ k (professor (thesis reviewer stud refs (γ) j j (student (supervisor proof ref (k))))

21 Proof-Theoretical Study of XHyb: Soundness and Completeness Theorem, Expressive Power; We provided an Hilbert style axiomatization and we proved Soundness and Completeness Theorem; XHyb formulae can be translated into prenex normal forms. Expressive Power w.r.t. XML constraint taxonomies Model Checking: theoretical results and implementation

22 Essential bibliography P. Blackburn. Representation, reasoning, and relational structures: a hybrid logic manifesto. Logic Journal of the IGPL, 8(3): , W. Fan and J. Siméon. Integrity constraints for XML. Journal of Computer and System Sciences, 66(1): , Special Issue on PODS M. Franceschet and M. de Rijke. Model checking hybrid logics (with an application to semistructured data). Journal of Applied Logic, 4(3): , M. Marx. Xpath and modal logics of finite dag s. In Automated Reasoning with Analytic Tableaux and Related Methods, International Conference, TABLEAUX 2003, Rome, Italy, September 9-12, Proceedings, pages , 2003.

23 Gracias!