Consistency Checking of RM-ODP Specifications Kenneth Baclawski Mieczyslaw Kokar Jeffrey Smith Jerzy Letkowski

Themes §Consistency Checking l Fundamental requirement l Techniques for checking consistency l Demonstration of ConsVISor §Category Theory l Component framework for logical theories l Component composition l Refinement for code generation

Logical Consistency §A fundamental requirement of any rigorous formalization §Definition: there exists a non-trivial model of the theory. §If a theory is inconsistent then every logical statement is true. §Inconsistency is dangerous for autonomous agents!

Logical Reasoning Person Fish Wanda type Wendy type owns Type constraint violation: The range of owns is Fish. OR There is no inconsistency: Wanda is a fish! type Mermaid? owns

Department Student Cardinality constraint violation: George can’t have two majors OR There is no inconsistency: Computer Science = Chemistry type Chemistry George type equivalentTo Computer Science type major (0,1)

Checking Consistency §Consistency checking is very hard. l Church showed that first-order logic is only semi-decidable. §ConsVISor uses two concurrent strategies: l Warn about possible inconsistencies. This part is in Prolog and Java. If none, then consistent. l Use the SNARK theorem prover to find true inconsistencies. This need not terminate.

Inconsistencies §Manual consistency checking is difficult. l It is very hard to determine the consequences of a set of axioms just by looking at them. l Multiple viewpoints increase the difficulty. l Translation may introduce inconsistency. §Inconsistent languages: l Resource Description Framework (RDF) l DARPA Agent Markup Language (DAML) l Knowledge Interchange Format (KIF)

Category Theory: Specware §Category theory furnishes a formal component framework for logical theories. §Specification morphisms are more powerful than the include mechanism. §Specifications are intensional. §Specifications can be refined to be progressively more detailed.

Category of Specifications §A category consists of objects and morphisms. §An object is a formal specification (spec) consisting of sorts, operations, axioms and theorems. Each spec is a logical theory. §A morphism is a mapping of specs: l Sorts are mapped to sorts l Operations are mapped to operations. l Axioms and theorems map to theorems.

Component Composition §Components can be composed by using the colimit mechanism. Vehicle Spec Amphibian Spec One-Sort Spec Water Craft Water Vehicle One-Sort Spec Land Vehicle Composed Spec

Importing and Templates Linked List Spec Vehicle Spec Linked List and Vehicle Import specification One-Sort Spec Linked List Spec Vehicle Spec Linked List of Vehicles Template instantiation

Web Links  This presentation is available online at  Versatile Information Systems (VIS) Web site §Inconsistent languages (on VIS Web site): RDF DAML KIF

More Web links  Ontology-based computing talk  Specware and Slang  SNARK automated theorem prover