A Six-valued Logic to Reason about Uncertainty and Inconsistency in Requirements Specifications

The development of requirements specifications is characterized by the uncertain and changeable knowledge available about the systems to be built. This paper presents a many-valued logic that enables effective reasoning about uncertainty and inconsistency in requirements specifications, motivating the election of six truth values and the definition of a new implication connective. The adequacy of this logic to support a formal development methodology is assessed through a comparison with Belnap's four-valued logic in combination with the classical implications.

[1]  Sébastien Konieczny,et al.  Three-Valued Logics for Inconsistency Handling , 2002, JELIA.

[2]  Jorge García Duque,et al.  Locating crosscutting concerns in the formal specification of distributed reactive systems , 2005, ACM SIGSOFT Softw. Eng. Notes.

[3]  Richard Banach,et al.  Retrenchment: extending the reach of refinement , 1999, 14th IEEE International Conference on Automated Software Engineering.

[4]  Bashar Nuseibeh,et al.  Managing inconsistent specifications: reasoning, analysis, and action , 1998, TSEM.

[5]  Axel van Lamsweerde,et al.  Formal specification: a roadmap , 2000, ICSE '00.

[6]  Bashar Nuseibeh,et al.  Viewpoints: A Framework for Integrating Multiple Perspectives in System Development , 1992, Int. J. Softw. Eng. Knowl. Eng..

[7]  Jorge García Duque,et al.  Arifs Methodology Reusing Incomplete Models at the Requirements Specification Stage , 2005, Int. J. Softw. Eng. Knowl. Eng..

[8]  Gerhard Gentzen,et al.  Investigations into Logical Deduction , 1970 .

[9]  Ian Sommerville,et al.  Viewpoints: principles, problems and a practical approach to requirements engineering , 1997, Ann. Softw. Eng..

[10]  Maritta Heisel,et al.  Specifying embedded systems with statecharts and Z: an agenda for cyclic software components , 2001, Sci. Comput. Program..

[11]  Matthew L. Ginsberg,et al.  Multivalued logics: a uniform approach to reasoning in artificial intelligence , 1988, Comput. Intell..

[12]  Arnon Avron,et al.  Reasoning with logical bilattices , 1996, J. Log. Lang. Inf..

[13]  Newton C. A. da Costa α-models and the systems T and T* , 1974, Notre Dame J. Formal Log..

[14]  Victor R. Basili,et al.  Iterative and incremental developments. a brief history , 2003, Computer.

[15]  Arnon Avron On the Expressive Power of Three-Valued and Four-Valued Languages , 1999, J. Log. Comput..

[16]  Melvin Fitting,et al.  Bilattices in logic programming , 1990, Proceedings of the Twentieth International Symposium on Multiple-Valued Logic.

[17]  Barry W. Boehm,et al.  A spiral model of software development and enhancement , 1986, Computer.

[18]  Natarajan Shankar,et al.  Formal Verification for Fault-Tolerant Architectures: Prolegomena to the Design of PVS , 1995, IEEE Trans. Software Eng..

[19]  Josep Maria Font,et al.  Note on a six-valued extension of three-valued logic , 1993, J. Appl. Non Class. Logics.

[20]  Nuel D. Belnap,et al.  A Useful Four-Valued Logic , 1977 .

[21]  S. C. Kleene,et al.  Introduction to Metamathematics , 1952 .

[22]  Andrea Zisman,et al.  Inconsistency Management in Software Engineering: Survey and Open Research Issues , 2000 .

[23]  Steve M. Easterbrook,et al.  Using ViewPoints for inconsistency management , 1996, Softw. Eng. J..

[24]  Thomas G. Dietterich What is machine learning? , 2020, Archives of Disease in Childhood.

[25]  D. Gabbay,et al.  Inconsistency Handling in Multiperspective Specifications , 1994 .

[26]  Arnon Avron Classical Gentzen-type methods in propositional many-valued logics , 2001 .

[27]  Bashar Nuseibeh,et al.  Combining abductive reasoning and inductive learning to evolve requirements specifications , 2003, IEE Proc. Softw..

[28]  Bashar Nuseibeh,et al.  Making inconsistency respectable in software development , 2001, J. Syst. Softw..

[29]  Graham Priest,et al.  Reasoning About Truth , 1989, Artif. Intell..

[30]  José Juan Pazos-Arias,et al.  Merging requirements views with incompleteness and inconsistency , 2005, 2005 Australian Software Engineering Conference.

[31]  Edmund M. Clarke,et al.  Formal Methods: State of the Art and Future Directions Working Group Members , 1996 .

[32]  Arnon Avron,et al.  The Value of the Four Values , 1998, Artif. Intell..

[33]  Donald Sannella Algebraic Specification and Program Development by Stepwise Refinement , 1999, LOPSTR.

[34]  J. Pazos,et al.  Eliciting Requirements and Scenarios using the SCTL›MUS Methodology. The Shuttle System Case Study , 2005 .

[35]  Ralph-Johan Back,et al.  Refinement Calculus: A Systematic Introduction , 1998 .

[36]  Jorge García Duque,et al.  SCTL-MUS: A Formal Methodology for Software Development of Distributed Systems. A Case Study , 2001, Formal Aspects of Computing.

[37]  Leslie Lamport,et al.  Specifying Systems: The TLA+ Language and Tools for Hardware and Software Engineers [Book Review] , 2002, Computer.

[38]  Stephan Merz,et al.  Model Checking , 2000 .

[39]  Ray Offen,et al.  A logical framework for modeling and reasoning about the evolution of requirements , 1997, Proceedings of ISRE '97: 3rd IEEE International Symposium on Requirements Engineering.

[40]  B. H. Slater,et al.  Paraconsistent logics? , 1995, J. Philos. Log..

[41]  Melvin Fitting,et al.  Kleene's Logic, Generalized , 1991, J. Log. Comput..

[42]  Jorge García Duque,et al.  An analysis-revision cycle to evolve requirements specifications by using the SCTL-MUS methodology , 2002, Proceedings IEEE Joint International Conference on Requirements Engineering.

[43]  Philippe Massonet,et al.  Goal-oriented requirements animation , 2004, Proceedings. 12th IEEE International Requirements Engineering Conference, 2004..

[44]  Mary Shaw,et al.  Comparing Architectural Design Styles , 1995, IEEE Softw..

[45]  Jorge García Duque,et al.  Incremental specification with SCTL/MUS-T: a case study , 2004, J. Syst. Softw..