Exceptions for Algebraic Specifications: On the Meaning of "but"

Abstract When building large specifications from requirements, the structure of the specification becomes a central problem: the specification language should allow a decomposition that closely reflects the structure of requirements. In this paper, we propose a decomposition into defaults (general rules) and exceptions to these general rules that fits the requirements found in some application domains. It is complementary, and builds upon, the modular decomposition proposed by the algebraic specification school. Its definition is based on abstract model theory, leading to the definition of default institutions.

[1]  Ronald J. Brachman,et al.  "I Lied About the Trees", Or, Defaults and Definitions in Knowledge Representation , 1985, AI Mag..

[2]  Rachid Echahed,et al.  Design and Implementation of a Generic, Logic and Functional Programming Language , 1986, ESOP.

[3]  Benjamin N. Grosof,et al.  Generalizing Prioritization , 1991, KR.

[4]  Éric Grégoire Logiques non monotones et intelligence artificielle , 1990, Langue, raisonnement, calcul.

[5]  Horst Reichel,et al.  Initial Computability, Algebraic Specifications, and Partial Algebras , 1987 .

[6]  Teodor C. Przymusinski On the Declarative Semantics of Deductive Databases and Logic Programs , 1988, Foundations of Deductive Databases and Logic Programming..

[7]  Michael J. Maher,et al.  Foundations of Deductive Databases and Logic Programming , 1988 .

[8]  Mukesh Dalal,et al.  Investigations into a Theory of Knowledge Base Revision , 1988, AAAI.

[9]  Donald Sannella,et al.  Completeness of Proof Systems for Equational Specifications , 1985, IEEE Transactions on Software Engineering.

[10]  Joseph A. Goguen,et al.  Institutions: abstract model theory for specification and programming , 1992, JACM.

[11]  Joseph A. Goguen,et al.  Some Fundamental Algebraic Tools for the Semantics of Computation. Part 1: Comma Categories, Colimits, Signatures and Theories , 1984, Theor. Comput. Sci..

[12]  John McCarthy,et al.  Applications of Circumscription to Formalizing Common Sense Knowledge , 1987, NMR.

[13]  Joseph Y. Halpern,et al.  “Sometimes” and “not never” revisited: on branching versus linear time temporal logic , 1986, JACM.

[14]  Ronald J. Brachman,et al.  What IS-A Is and Isn't: An Analysis of Taxonomic Links in Semantic Networks , 1983, Computer.

[15]  Vladimir Lifschitz,et al.  Computing Circumscription , 1985, IJCAI.

[16]  Garrett Birkhoff,et al.  A survey of modern algebra , 1942 .

[17]  David Poole,et al.  What the Lottery Paradox Tells Us About Default Reasoning , 1989, KR.

[18]  Raymond Reiter,et al.  On Inheritance Hierarchies With Exceptions , 1983, AAAI.

[19]  J. Michael Spivey,et al.  The Z notation - a reference manual , 1992, Prentice Hall International Series in Computer Science.

[20]  Bernhard Möller Algebraic Specifications with Higher-Order Operations , 1986, ADT.

[21]  Friedrich L. Bauer,et al.  The Munich Project CIP , 1988, Lecture Notes in Computer Science.

[22]  John McCarthy,et al.  Circumscription - A Form of Non-Monotonic Reasoning , 1980, Artif. Intell..

[23]  Raymond Reiter,et al.  A Logic for Default Reasoning , 1987, Artif. Intell..

[24]  Christine Froidevaux,et al.  General Logical Databases and Programs: Default Logic Semantics and Stratification , 1991, Inf. Comput..

[25]  W. N. Robinson,et al.  Integrating multiple specifications using domain goals , 1989, IWSSD '89.

[26]  William Harper,et al.  Rational Conceptual Change , 1976, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association.

[27]  Kurt Konolige,et al.  Hierarchic Autoepistemic Theories for Nonmonotonic Reasoning , 1988, AAAI.

[28]  Christine Froidevaux,et al.  Minimalism subsumes Default Logic and Circumscription in Stratified Logic Programming , 1987, LICS.

[29]  Yoav Shoham,et al.  A semantical approach to nonmonotonic logics , 1987, LICS 1987.

[30]  Pierre-Yves Schobbens,et al.  Precise standards through formal specifications: a case study: the UNIX file system , 1988 .

[31]  Marianne Winslett,et al.  Reasoning about Action Using a Possible Models Approach , 1988, AAAI.

[32]  José Meseguer,et al.  Principles of OBJ2 , 1985, POPL.

[33]  Pierre-Yves Schobbens,et al.  LPG: A Generic, Logic and Functional Programming Language , 1988, ESOP.

[34]  David S. Touretzky,et al.  A Skeptical Theory of Inheritance in Nonmonotonic Semantic Networks , 1987, Artif. Intell..

[35]  Arthur M. Keller,et al.  On the Use of an Extended Relational Model to Handle Changing Incomplete Information , 1985, IEEE Transactions on Software Engineering.

[36]  P. Tichý A counterexample to the Stalnaker-Lewis analysis of counterfactuals , 1976 .

[37]  Pierre Siegel,et al.  Saturation, Nonmonotonic Reasoning and the Closed-World Assumption , 1985, Artif. Intell..

[38]  Hartmut Ehrig,et al.  Fundamentals of Algebraic Specification 1: Equations and Initial Semantics , 1985 .

[39]  Marianne Winslett,et al.  Circumscribing Equality , 1989, IJCAI.

[40]  Mark Ryan,et al.  Defaults and revision in structured theories , 1991, [1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science.

[41]  André Fuhrmann,et al.  The Logic of Theory Change , 1991, Lecture Notes in Computer Science.

[42]  Sarit Kraus,et al.  Nonmonotonic Reasoning, Preferential Models and Cumulative Logics , 1990, Artif. Intell..

[43]  David W. Etherington Reasoning With Incomplete Information , 1988 .

[44]  David S. Touretzky,et al.  The Mathematics of Inheritance Systems , 1984 .

[45]  P G rdenfors,et al.  Knowledge in flux: modeling the dynamics of epistemic states , 1988 .

[46]  Donald Perlis,et al.  Completeness Results for Circumscription , 1986, Artif. Intell..

[47]  D. Perlis,et al.  The SUPREM architecture: a new intelligent paradigm , 1986 .