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16
Logical Support for Modularisation
 LOGICAL ENVIRONMENTS
, 1993
"... Modularisation is important for managing the complex structures that arise in large theorem proving problems, and in large software and/or hardware development projects. This paper studies some properties of logical systems that support the definition, combination, parameterisation and reuse of ..."
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Cited by 97 (31 self)
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Modularisation is important for managing the complex structures that arise in large theorem proving problems, and in large software and/or hardware development projects. This paper studies some properties of logical systems that support the definition, combination, parameterisation and reuse of modules. Our results show some new connections among: (1) the preservation of various kinds of conservative extension under pushouts; (2) various distributive laws for information hiding over sums; and (3) (Craig style) interpolation properties. In addition, we study differences between syntactic and semantic formulations of conservative extension properties, and of distributive laws. A model theoretic property that we call exactness plays an important role in some results. This paper explores the interplay between syntax and semantics, and thus lies in the tradition of abstract model theory. We represent logical systems as institutions. An important technical foundation is a new ...
Abstract Petri Nets as a Uniform Approach to HighLevel Petri Nets
, 1998
"... In the area of Petri nets, many different developments have taken place within the last 30 years, in academia as well as in practice. For an adequate use in practice, a coherent and application oriented combination of various types and techniques for Petri nets is necessary. In order to attain ..."
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Cited by 39 (20 self)
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In the area of Petri nets, many different developments have taken place within the last 30 years, in academia as well as in practice. For an adequate use in practice, a coherent and application oriented combination of various types and techniques for Petri nets is necessary. In order to attain a formal basis for different classes of Petri nets we introduce the concept of abstract Petri nets. The essential point of abstract Petri nets is to allow different kinds of net structures as well as the combination of various kinds of data types. This means that in abstract Petri nets the data type and the net structure part can be considered as abstract parameters which can be instantiated to different concrete net classes. We show that several net classes, like place/transition nets, elementary nets, Sgraphs, algebraic highlevel net...
Observational Specifications and the Indistinguishability Assumption
 Theoretical Computer Science
, 1995
"... To establish the correctness of some software w.r.t. its formal specification is widely recognized as a difficult task. A first simplification is obtained when the semantics of an algebraic specification is defined as the class of all algebras which correspond to the correct realizations of the spec ..."
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Cited by 19 (0 self)
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To establish the correctness of some software w.r.t. its formal specification is widely recognized as a difficult task. A first simplification is obtained when the semantics of an algebraic specification is defined as the class of all algebras which correspond to the correct realizations of the specification. A software is then declared correct if it corresponds to some algebra of this class. We approach this goal by defining an observational satisfaction relation which is less restrictive than the usual satisfaction relation. Based on this notion we provide an institution for observational specifications. The idea is that the validity of an equational axiom should depend on an observational equality, instead of the usual equality. We show that it is not reasonable to expect an observational equality to be a congruence. We define an observational algebra as an algebra equipped with an observational equality which is an equivalence relation but not necessarily a congruence. We assume th...
An Algebraic Framework For The Definition Of Compositional Semantics Of Normal Logic Programs
, 1994
"... ion) Given two normal programs P1 and P2, the following three facts are equivalent: (i) Sem(P 1) = Sem(P 2) (ii) For every program P , Sem(P [ P 1) = Sem(P [ P 2) (iii) For every program P , MP[P1 = MP[P2 . Proof. It is enough to prove that (iii) implies (i), because the other implications are d ..."
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Cited by 8 (6 self)
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ion) Given two normal programs P1 and P2, the following three facts are equivalent: (i) Sem(P 1) = Sem(P 2) (ii) For every program P , Sem(P [ P 1) = Sem(P [ P 2) (iii) For every program P , MP[P1 = MP[P2 . Proof. It is enough to prove that (iii) implies (i), because the other implications are direct consequences of lemma 3.1 and theorem 5.1. Let us suppose that there exists a model A in Mod(; ;) such that F 1(A) 6= F 2(A), where F1 = Sem(P 1) and F2 = Sem(P 2). Then, we will show that there exists a program P such that MP[P1 6= MP[P2 . Let j 2 IN be the least layer such that F 1(A) + j 6= F 2(A) + j or F 1(A) j 6= F 2(A) j . Then we can consider two cases. First, if there exists the given level k 2 IN , and F 1(A) + j 6= F 2(A) + j , for some j < k, then F 1(B) 6= F 2(B) for all models B 2 Mod(; ;) such that A + j = B + i and A j 1 = B i 1 for some layer i. This is the case for the model B such that, for all i 2 IN : B + i = A + j B i = A j 1 In any other cas...
Label algebras: a systematic use of terms
 In Bidot and Choppy [7
, 1991
"... We give the main definitions and results of a new framework for algebraic specifications: the framework of label algebras. The main idea underlying our approach is that the semantics of algebraic specifications can be deeply improved when the satisfaction relation is defined via assignments with ra ..."
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Cited by 6 (1 self)
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We give the main definitions and results of a new framework for algebraic specifications: the framework of label algebras. The main idea underlying our approach is that the semantics of algebraic specifications can be deeply improved when the satisfaction relation is defined via assignments with range in terms instead of values. Surprisingly, there are several cases where even if two terms have the same value, it is possible that one of them is a suitable instance of a variable in an formula while the other one is not. It is for instance the case for algebraic specifications with exception handling or with observability features. We show that our approach is a useful tool for solving this problem.
Institutions for Logic Programming
 Theoretical Computer Science
, 1997
"... The compositionality of the semantics of logic programs with respect to (different varieties of) program union has been studied recently by a number of researchers. The approaches used can be considered quite adhoc in the sense that they provide, from scratch, the semantic constructions needed to e ..."
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Cited by 4 (1 self)
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The compositionality of the semantics of logic programs with respect to (different varieties of) program union has been studied recently by a number of researchers. The approaches used can be considered quite adhoc in the sense that they provide, from scratch, the semantic constructions needed to ensure compositionality and, in some cases, full abstraction in the given framework. In this paper, we study the application of general algebraic methods for obtaining, systematically, this kind of results. In particular, the method proposed consists in studying the adequate institution for describing the given class of logic programs and, then, in using general institutionindependent results to prove compositionality and full abstraction. This is done in detail for the class of definite logic programs with respect to three kinds of composition operations: Wunion, standard union and module composition. In addition two different institutions are considered: the standard institution...
Specifications with Observable Formulae and Observational Satisfaction Relation
 In [BC93
, 1991
"... We consider algebraic specifications with observational features. Axioms as well as observations are formulae of full (ManySorted) First Order Logic with Equality. The associated semantics is based on a non standard interpretation of equality called observational equality. We study the adequacy of t ..."
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Cited by 3 (0 self)
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We consider algebraic specifications with observational features. Axioms as well as observations are formulae of full (ManySorted) First Order Logic with Equality. The associated semantics is based on a non standard interpretation of equality called observational equality. We study the adequacy of this semantics for software specification and the relationship with behavioural equivalence of algebras. We show that this framework defines an institution. Keywords: algebraic specification, observability, semantics. 1 Introduction Within an observational approach the loose semantics of a specification may either be defined as a class of algebras observationally equivalent to models satisfying the specification in the usual sense or as a class of algebras observationally satisfying the specification. The former way has already been deeply explored in [13] while in the latter one, the following problems remains open: 1. How to define an observational satisfaction relation w.r.t. more sophi...
Algebraic Methods in the Compositional Analysis of Logic Programs
 IN MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE 94 (I. PRIVARA, B. ROVAN, P. RUZICKA, EDS.) SPRINGERVERLAG LECTURE NOTES IN COMPUTER SCIENCE 841
, 1994
"... The compositionality of the semantics of logic programs with respect to (different varieties of) program union has been studied recently by a number of researchers. The approaches used can be considered quite adhoc in the sense that they provide, from scratch, the semantic constructions needed ..."
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Cited by 2 (1 self)
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The compositionality of the semantics of logic programs with respect to (different varieties of) program union has been studied recently by a number of researchers. The approaches used can be considered quite adhoc in the sense that they provide, from scratch, the semantic constructions needed to ensure compositionality and, in some cases, full abstraction in the given framework. In this paper, we study the application of general algebraic methods for obtaining, systematically, this kind of results. In particular, the method proposed consists in defining the adequate institution for describing the given class of logic programs and, then, in using general institutionindependent results to prove compositionality and full abstraction. This is done in detail for the class of definite logic programs, where the associated institution is defined in such a way that initial algebra semantics is equivalent to computed answer substitution semantics. Then a similar solution is sketc...
On The Usefulness of Carriers, Semiinitiality and Semiadjuncts for “Institution Independent ” Issues
"... When defining new specification formalisms, some notions are systematically defined in order to prove some properties of the formalism. Then it seems useful to work at a more abstract level, for several formalisms in a unique proof or definition. That is the goal of specification formalisms. Terms a ..."
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When defining new specification formalisms, some notions are systematically defined in order to prove some properties of the formalism. Then it seems useful to work at a more abstract level, for several formalisms in a unique proof or definition. That is the goal of specification formalisms. Terms are among those notions used by many specification formalisms. Together with congruences, they can lead to initial models or leftadjunct to the forgetful functor provided they exist. The goal of this work is to give a semantical characterization of terms, and to give some example of their use in a metaformalism framework.