Consistency Checking of RM-ODP Specifications

Kenneth Baclawski

Mieczyslaw Kokar

Jeffrey Smith

Jerzy Letkowski

Themes

Consistency Checking Fundamental requirement Techniques for checking consistency Demonstration of ConsVISor

Category Theory Component framework for logical theories Component composition 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

DepartmentStudent

Cardinality constraint violation: George can’t have two majors

OR There is no inconsistency: Computer Science = Chemistry

type

ChemistryGeorge

type

equivalentTo

Computer Science

typemajor

major

major(0,1)

Checking Consistency

Consistency checking is very hard. Church showed that first-order logic is only

semi-decidable.

ConsVISor uses two concurrent strategies: Warn about possible inconsistencies. This part

is in Prolog and Java. If none, then consistent. Use the SNARK theorem prover to find true

inconsistencies. This need not terminate.

InconsistenciesManual consistency checking is difficult.

It is very hard to determine the consequences of a set of axioms just by looking at them.

Multiple viewpoints increase the difficulty. Translation may introduce inconsistency.

Inconsistent languages: Resource Description Framework (RDF) DARPA Agent Markup Language (DAML) 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: Sorts are mapped to sorts Operations are mapped to operations. 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 VehicleOne-Sort Spec

Land VehicleLand 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 <Baclawski.com/woodpecker.ppt>

Versatile Information Systems (VIS) Web site <vis.home.mindspring.com>

Inconsistent languages (on VIS Web site): RDF <www.w3.org/rdf> DAML <www.daml.org> KIF <logic.stanford.edu/kif>

More Web links

Ontology-based computing talk <Baclawski.com/gbctalk.ppt>

Specware and Slang <www.kestrel.edu>SNARK automated theorem prover <www.ai.sri.com/~stickel/snark.html>