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PathLP – Path-based Logic Programming

PathLP – Path-based Logic Programming. Mira Balaban, Igal Khitron Computer Science Department Ben-Gurion University. PathLP. A compact logic programming language Inspired from Object-Oriented Logic Programming languages: F-Logic ( Kifer , Lausen , Wu 1995 )

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PathLP – Path-based Logic Programming

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  1. PathLP – Path-based Logic Programming Mira Balaban, IgalKhitron Computer Science Department Ben-Gurion University Mini-project-course Fall 2013

  2. PathLP • A compact logic programminglanguage • Inspired from • Object-Oriented Logic Programming languages: • F-Logic (Kifer, Lausen, Wu 1995) • FLORA-2 (http://flora.sourceforge.net/, 2009) • Object-Oriented databaseandwebquery languages : • XSQL(Kifer, Kim, Sagiv 1992) • XPATH – a query language over XML documents (http://www.w3schools.com/xpath/). • Supports reasoning over guarded path expressions • Supports typing notions: • Hierarchy • Membership Mini-project-course Fall 2013

  3. PathLP status • PathLP is still under development by Mira Balaban, Igal Khitron, Michael Kifer (alphabetical order). • Intended for: • Formal support for Model-Level Integrated Development Environments: • Simultaneous reasoning over multiple models • Reasoning over applications that support hierarchical structures, like • Access policy in Network Management • Publications: • Mira Balaban and Michael Kifer: "An Overview of F-OML: An F-Logic Based Object Modeling Language", ECEASST'11 36. • Mira Balaban and Michael Kifer: "Logic Based Model-Level Software Development with F-OML", MoDELS'2011. • IgalKhitron, Michael Kifer, Mira Balaban: “PathLP: A Logic Programming Language of Path Expressions”, PLDE 2012. • Application: Version 1.4 PathLP1.4 Mini-project-course Fall 2013

  4. Model-level IDE – Needed modeling services • Provide a modeling constraint language for extending UML diagrams: • Object Constraint Language (OCL) • PathLP • Verification of UML diagrams • Specification of design patterns. • Reasoning about UML diagrams • TestingUML diagrams • Model refactoring • Meta-modeling: • DSML specification • Formalize UML specification Mini-project-course Fall 2013

  5. Model-level IDE – Integration with a modeling platform • Diagrammatic models • concrete external syntax. UML development platform model1 … modeln transformations model1-module … modeln-module Underlying formal modeling language Modeling services Mini-project-course Fall 2013

  6. Model-level IDE – Integration with a modeling platform • Diagrammatic models • concrete external syntax. UML development platform model1 … modeln transformations model1-module … modeln-module F-OML PathLP Modeling services Mini-project-course Fall 2013

  7. PathLP constructs • Path expressions • Facts • Rules • Constraints • Queries Mini-project-course Fall 2013

  8. PathLP: Object path expressions • Consist of constants, variables, ., guards • Denote objects ?C.friend.student[?S].name • The names of a student s of a friend of c, for some bindings s and c to variables ?S and ?C constant guard variable name student s friend … name student … friend c … student denotation Mini-project-course Fall 2013

  9. PathLP: Object path expressions & Query formulas elementary formula • Query formula: John.childWith(Mary)[?C].name[?N], ?C:Student,?C.ageAt(2010)<20 • The name ?N of ?C, who is a child with Mary of John, is a student and whose age at 2010 is less than 20 elementary formula elementary formula name … ?N childWith(Mary) ?C denotation name … John ageAt(2010) Student n<20 Mini-project-course Fall 2013

  10. PathLP: Type path expressions Cardinality constraint Person!spouse[Person]{0..1} • The type of spouses of nodes of type Person (nodes pointed by spouse edges) is Person (or a subtype of Person), and there is at most 1 such edge • Assume • ?n1.spouse[?n2] ?n2 spouse ?n1 Mini-project-course Fall 2013

  11. PathLP: Type path expressions Person!spouse[Person]{0..1} • The type of spouses of nodes of type Person is Person (or a subtype of Person), and there is at most 1 such edge • Assume • ?n1.spouse[?n2] • ?n1:Person Person ?n2 spouse ?n1 Mini-project-course Fall 2013

  12. PathLP: Type path expressions Person!spouse[Person]{0..1} • The type of spouses of nodes of type Person is Person (or a subtype of Person), and there is at most 1 such edge • Assume • ?n1.spouse[?n2] • ?n1:Person  ?n2:Person Person ?n2 spouse ?n1 and IF THEN at most 1 spouse edge Mini-project-course Fall 2013

  13. PathLP: Type path expressions Person!spouse[Person]{0..1} • The type of spouses of nodes of type Person is Person (or a subtype of Person), and there is at most 1 such edge • Assume • ?n1.spouse[?n2] • ?n1:Person  ?n2:Person spouse spouse Type edge Person … ?n2 spouse ?n1 and IF THEN at most 1 spouse edge Mini-project-course Fall 2013

  14. PathLP: Facts – specify assertions • John.spouse[Mary]; John.child[Bob]; John.child[Bill]; • John has a spouseMary and children Bob and Bill (and possibly others) • Type hierarchyand membership assertions: Bob:CS_teaching_committee; CS_teaching_committee::Teaching_committee; Teaching_committee:Committee; Committee::Group; • Bob CS_teaching_committeeTeaching_committee Committee Group • A type assertion:Person!spouse[Person]{0..1}; • The type of spouses of Person is Person, or one of its subtypes, and the cardinality constraint is {0..1} Mini-project-course Fall 2013

  15. PathLP: Rules, Constraints, Queries • Rules – specify implications: • ?A:advisor :- ?T:Thesis, ?T.author.advisor[?A].read[?T],?A:Professor; • ?A is an advisor if ?A has read a thesis ?T of an author that ?A advises • Constraints – restrict legal states: • !- ?P:Professor, not ?P.degree[PhD]; • forbid states with a professor ?P that does not have a PhD degree • Queries – trigger computation • ?- ?A:Professor, ?A.review[?Thesis], ?A.supervise.thesis-of[?Thesis]; • Find aprofessor that reviews a thesis of somebody s/he supervises. A more compact expression: ?- ?A:Professor,?A.review.author.advisor[?A]; Mini-project-course Fall 2013

  16. PathLP – as a basis for Object-Oriented modeling • Defines entities: • Inter-related by paths • Possiblytyped • inclusion “::” • membership“:” • Multi-levelmodeling: • Unrestricted “::“ and “:“ • Polymorphism: • Parameterized path expressions • Type hierarchy Object navigation Class Class hierarchy Object creation; Testing Reflection • Patterns • Model query • Static analysis Mini-project-course Fall 2013

  17. PathLP – implementation • Beta version 1.4: • pathlp.sf.net (IgalKhitron) • Compiler and interpreter • In XSB prolog • open source tabling prolog • supports well-founded negation • Windows, Linux, Unix • Large test cases: 200,000 facts Mini-project-course Fall 2013

  18. Mini-Project subject – Develop a Graph Services library in PathLP • An example library: JGraphT From the JGraphT home page: • JGraphT is a free Java graph library that provides mathematical graph-theory objects and algorithms. JGraphT supports various types of graphs including: • directed and undirected graphs. • graphs with weighted / unweighted / labeled or any user-defined edges. • various edge multiplicity options, including: simple-graphs, multigraphs, pseudographs. • unmodifiable graphs - allow modules to provide "read-only" access to internal graphs. • listenable graphs - allow external listeners to track modification events. • subgraphs graphs that are auto-updating subgraph views on other graphs. • all compositions of above graphs. • Although powerful, JGraphT is designed to be simple and type-safe (via Java generics). For example, graph vertices can be of any objects. You can create graphs based on: Strings, URLs, XML documents, etc; you can even create graphs of graphs! This code example shows how. Mini-project-course Fall 2013

  19. Mini-Project subject – Develop a Graph Services library in PathLP • Why having “yet another JGraphT” in PathLP? Mini-project-course Fall 2013

  20. Mini-Project subject – Develop a Graph Service library in PathLP • Why having “yet another JGraphT” in PathLP? • What are the special features of Logic Programming languages? • Reasoning! • Answer queries! • Analysis! Mini-project-course Fall 2013

  21. Graph representation in PathLP • Directed graph: • Facts: n1.edge[n2]; n1.edge[n3]; n1.edge[n4]; n2.edge[n3]; n2.edge[n5]; n4.edge[n2]; n4.edge[n4]; n5.edge[n2]; n5.edge[n4]; n2 n1 n4 n3 ?n5 n5 Mini-project-course Fall 2013

  22. Querying the directed graph • Directed graph: • Facts: n1.edge[n2]; n1.edge[n3]; n1.edge[n4]; n2.edge[n3]; n2.edge[n5]; n4.edge[n2]; n4.edge[n4]; n5.edge[n2]; n5.edge[n4]; • Queries: ?- n1.edge[?N]; ?- ?N1.edge[?N2]; ?- ?N1.edge[?_N2],?_N2.edge[?N1]; ?- ?n.edge[?n]; ?- not n1.edge[n2]; ?- ?N._size(edge)[?edge_number],?edge_number<2; n2 n1 n4 n3 ?n5 n5 Mini-project-course Fall 2013

  23. Reasoning about the directed graph • Paths in the directed graph: • Rules: ?n1.path[?n2]:- ?n1.edge[?n2]; ?n1.path[?n2]:- ?n1.path[?n3],?n3.edge[?n2]; • Facts: n1.edge[n3]; n4.edge[n2]; n1.edge[n4]; n4.edge[n4]; n2.edge[n3]; n5.edge[n2]; n2.edge[n5]; n5.edge[n4]; • Queries: ?- n5.path[n5]; ?- ?N.path[n5]; ?- ?N.path[n5],?N != n5; ?- ?n.path[?n]; ?- not(n1.path[n1]); ?- n1.path[?N],not(?N.path[?N]); • Rule:?n.selfPath[true]:- ?n.path[?n]; • Query:?- ?N._size(selfpath)[?path_num],?path_num>1; n2 n1 n4 n3 ?n5 n5 Mini-project-course Fall 2013

  24. Reasoning about the directed graph • Adding path details and node typing: • Rules: ?N1.path([?N1,?N2])[?N2]:- ?N1.edge[?N2]; ?N1.path([?N1|?P])[?N3]:- ?N1.edge[?N2],?N2.path(?P)[?N3]; ?N1.loop[?N2]:- ?N1.edge[?N2],?N2.edge[?N1]; ?N.origin[true]:- ?N:Node,not ?N.enter_edge[true]; ?N.enter_edge[true]:- ?N1.edge[?N]; ?N.sink[true]:- ?N:Node,not ?N.leaving_edge[true]; ?N.leaving_edge[true]:- ?N.edge[?N1]; isolated(?N)[true] :- origin(?N)[true],sink(?N)[true]; • Facts: n1:Node; n2:Node; n3:Node; n4:Node; n5:Node; n6:Node; n1.edge[n3]; n4.edge[n2]; n1.edge[n4]; n4.edge[n4]; n2.edge[n3]; n5.edge[n2]; n2.edge[n5]; n5.edge[n4]; • Queries: ?- n5.path(?P)[n5]; ?- ?N.path(?P)[n5]; ?- ?N.path(?_P)[n5]; is the same as ?- ?N.path[n5]; ?- ?N.path(?_P)[n5],not ?_P.member[n4]; ?- ?N.loop[n5]; ?- ?N1.origin[true],?N2.origin[true],?N1!=?N2; ?- ?_N.isolated[true]); n2 n1 n4 n3 ?n5 n5 n6 Mini-project-course Fall 2013

  25. Reasoning about the directed graph • Adding labeled edges, edge typing, path typing: • Rules: ?P:Path :-?N1.path(?P)[?N2]; % Bad modeling! Why? ?P.nodes[?P] :- ?P:Path,?N1.path(?P)[?N2]; ?P.node[?N] :- ?P.nodes[?Node_list],?Node_list.member[?N]; ?E:Edge :- ?N1.edge(?E)[?N2]; ?E.source[?N] :- ?E:Edge,?N.edge(?E)[?N1]; • Facts: n1:Node; n2:Node; n3:Node; n4:Node; n5:Node; n6:Node; n1.edge[n3]; n4.edge[n2]; n1.edge[n4]; n4.edge[n4]; n2.edge[n3]; n5.edge[n2]; n2.edge[n5]; n5.edge(e54)[n4]; • Note the different design decision about the status of nodes and edges: • Node typing is mandatory • Edge typing is inferred n2 n1 n4 n3 ?n5 n5 e54 n6 Mini-project-course Fall 2013

  26. Reasoning about the directed graph • Improved path modeling: • Rules: path(?node_list):Path :-?N1.path(?node_list)[?N2]; path(?node_list).nodes[?node_list] :-?N1.path(?node_list)[?N2]; ?P.node[?N] :- ?P.nodes[?Node_list], ?Node_list.member[?N]; ?P.first[?N] :- ?P:Path, ?P.nodes[ [?N|?rest_nodes] ]; ?P.last[?N] :- ?P:Path, ?P.nodes[?node_list], ?node_list.reverse[[?N|?rest_nodes]]; • Constraints: !- ?P:Path, ?P.first[?N1], ?P.last[?N2], ?P.nodes[?node_list], not ?N1.path(?node_list)[?N2]; • Facts: n1:Node; n2:Node; n3:Node; n4:Node; n5:Node; n6:Node; n1.edge[n3]; n4.edge[n2]; n1.edge[n4]; n4.edge[n4]; n2.edge[n3]; n5.edge[n2]; n2.edge[n5]; n5.edge(e54)[n4]; n2 n1 n4 n3 ?n5 n5 e54 n6 Mini-project-course Fall 2013

  27. Reasoning about the directed graph • Adding more constraints: • Rules: path(?node_list):Path :-?N1.path(?node_list)[?N2]; path(?node_list).nodes[?node_list] :-?N1.path(?node_list)[?N2]; ?E:Edge :- ?N1.edge(?E)[?N2]; ?E.source[?N] :- ?E:Edge,?N.edge(?E)[?N1]; • Constraint: !- ?E.source[?N1],?E.source[?N2], ?N1!=?N2; !- ?N1.path(?P)[?N2], ?P.member[?N],not ?N:Node; A single labeled edge between nodes: !- ?N1.edge(?L1)[?N2], ?N1.edge(?L2)[?N2], ?L1 != ?L2; A single labeled edge leaving a node: !- Node!edge(?L)[Node]{0..1}; n2 n1 n4 n3 ?n5 n5 e54 n6 Mini-project-course Fall 2013

  28. Reasoning about the directed graph • Adding path properties and sub-typing: • Rules: path(?node_list):Compact_Path :- path(?node_list):Path, ?node_list.compactList[true]; ?List.compactList[true] :- not ?L1.append([?N],?L2,[?N],?L3)[?List]; ?P:Cycle :- ?P:Path,?P.first[?N],?P.last[?N]; path(?node_list).length[?number] :- ?node_list.length[?number]; Compact_Path :: Path; Cycle :: Path; • Constraints: !- path(?node_list):Compact_Path, not ?node_list.compactList[true]; !- ?P:Cycle, ?P.first[?N1], ?P.last[?N2], ?N1 != ?N2; n2 n1 n4 n3 ?n5 n5 e54 n6 Mini-project-course Fall 2013

  29. Reasoning about the directed graph • Adding multiple graphs: • Rules: ?G.node[?N] :-?G.nodes[?Node_list],?Node_list.member[?N]; ?N.graph[?G] :-?G.node[?N]; ?G1.intersection(?G2)[?G] :- ?G1.nodes[?Ns1],?G2.nodes[?Ns2], ?G1.edges[?Es1],?G2.edges[?Es2], ?Ns1.intersection(?Ns2)[?Ns], ?Es1.intersection(?Es2)[?Es], ?G:Directed_graph,?G.nodes[?Ns],?G.edges[?Es]; ?G.is_empty[true] :- ?G:Directed_graph,?G.nodes[ [] ]; ?G1.disjoint[?G2] :- ?G1.intersection(?G2)[?G], ?G.is_empty[true]; ?G.path[?P]:- ?P.nodes[?Nodes_P],?G.nodes[?Nodes_G], ?Nodes_G.contains[?Nodes_P]; ?G:Cyclic_directed_graph :- ?G.path[?P],?P:Cycle; ?G:DAG :- not ?G:Cyclic_directed_graph; • A different modeling approach – using functional constructors: intersection(?G1,?G2):Directed_graph :- ?G1:Directed_graph,?G2:Directed_graph; intersection(?G1,?G2).nodes[intersection(?Ns1,?Ns2)] :- ?G1.nodes[?Ns1],?G2.nodes[?Ns2]; • A type Constraint: Directed_graph!nodes[List]{1..1}; • Facts: g1:Directed_graph; g1.nodes[[n1,n2,n3,n4,n5,n6]]; g1.edges[[e12,e13,e14,e25,e52,e23,e42,e44]]; ?n5 Mini-project-course Fall 2013

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