On the Relationship between Logic Programs and Specifications

The fundamental relation between a program P and its speciication S is cor-rectness: P satisses S if and only if P is correct with respect to S. In logic programming, this relationship can be particularly close, since logic can be used to express both speciications and programs. Indeed logic programs are often regarded and used as (executable) speciications themselves. In this paper, we argue that the relation between S and P should be rmly set in the context of the underlying problem domain, which we call a framework F, and we give a model-theoretic view of the correctness relation between speciications and programs in F. We show that the correctness relation between S and P is always well-deened. It thus provides a basis for properly distinguishing between S and P. We use the subset example throughout, to illustrate our model-theoretic approach.

[1]  Kenneth Kunen,et al.  Negation in Logic Programming , 1987, J. Log. Program..

[2]  Kung-Kiu Lau,et al.  The Relationship Between Logic Programs and Specifications - The Subset Example Revisited , 1997, J. Log. Program..

[3]  Wilfrid Hodges,et al.  Logical features of Horn Clauses , 1993 .

[4]  R. Kowalski,et al.  The relation between logic programming and logic specification , 1984, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[5]  Alberto Bertoni,et al.  On the power of model theory in specifying abstract data types and in capturing their recursiveness , 1983 .

[6]  Kung-Kiu Lau,et al.  A Formal Approach to Deductive Synthesis of Constraint Logic Programs , 1995, ILPS.

[7]  Kung-Kiu Lau,et al.  Steadfast Logic Programs , 1999, J. Log. Program..

[8]  Evelina Lamma,et al.  Composing Open Logic Programs , 1993, J. Log. Comput..

[9]  Jean H. Gallier,et al.  Logic for Computer Science: Foundations of Automatic Theorem Proving , 1985 .

[10]  Maurizio Gabbrielli,et al.  A Compositional Semantics for Logic Programs , 1994, Theor. Comput. Sci..

[11]  Yves Deville,et al.  Logic Program Synthesis , 1994, J. Log. Program..

[12]  Kung-Kiu Lau,et al.  Towards an Object-Oriented Methodology for Deductive Synthesis of Logic Programs , 1995, LOPSTR.

[13]  Pierangelo Miglioli,et al.  Abstract Parametric Classes and Abstract Data Types defined by Classical and Constructive Logical Methods , 1994, J. Symb. Comput..

[14]  Kung-Kiu Lau,et al.  On Specification Frameworks and Deductive Synthesis of Logic Programs , 1994, International Workshop/Symposium on Logic-based Program Synthesis and Transformation.

[15]  Kung-Kiu Lau,et al.  The Halting Problem for Deductive Synthesis of Logic Programs , 1994, ICLP.