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Equivalences among Various Logical Frameworks of Partial Algebras
 Computer Science Logic. 9th Workshop, CSL'95. Paderborn
, 1996
"... We examine a variety of liberal logical frameworks of partial algebras. Therefore we use simple, conjunctive and weak embeddings of institutions which preserve model categories and may map sentences to sentences, finite sets of sentences, or theory extensions using unique existential quantifiers, re ..."
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Cited by 17 (7 self)
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We examine a variety of liberal logical frameworks of partial algebras. Therefore we use simple, conjunctive and weak embeddings of institutions which preserve model categories and may map sentences to sentences, finite sets of sentences, or theory extensions using unique existential quantifiers, respectively. They faithfully represent theories, model categories, theory morphisms, colimit of theories, reducts etc. Moreover, along simple and conjunctive embeddings, theorem provers can be reused in a way that soundness and completeness is preserved. Our main result states the equivalence of all the logical frameworks with respect to weak embeddability. This gives us compilers between all frameworks. Thus it is a chance to unify the different branches of specification using liberal partial logics. This is important for reaching the goal of formal interoperability of different specification languages for software development. With formal interoperability, a specification can contain part...
Diagrams for Software Synthesis
 Proceedings of the 8 th KnowledgeBased Software Engineering Conference
, 1993
"... We describe the formal environment at Kestrel for synthesizing programs. We show that straightforward formalization, persistently applied at all levels of system description and system derivation, produces a scalable architecture for a synthesis environment. The primitive building blocks of our fram ..."
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Cited by 16 (0 self)
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We describe the formal environment at Kestrel for synthesizing programs. We show that straightforward formalization, persistently applied at all levels of system description and system derivation, produces a scalable architecture for a synthesis environment. The primitive building blocks of our framework are specifications, which encapsulate types and operations, and specification arrows, which are relations between specifications. The design of a system is represented as a diagram of specifications and arrows. Synthesis steps manipulate such diagrams, for example, by adding design detail to some specification, or by building new diagrams. A design history is a diagram of diagrams. Thus, we have a formal, knowledgebased, and machinesupported counterpart to such software engineering methodologies as CASE and OOP. 1 Introduction At the heart of the software problem lies the lack of adequate means to express and manage (1) clear, wellstructured problem specifications, (2) efficient sof...
A General Framework for Modular Implementations of Modular System Specifications
, 1993
"... . We investigate the impact of modularity on the semantics and on the implementation of software specifications. Based on the stratified loose semantics approach we develop a suitable specification framework which meets our basic requirements: the independent construction of implementations for the ..."
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Cited by 13 (6 self)
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. We investigate the impact of modularity on the semantics and on the implementation of software specifications. Based on the stratified loose semantics approach we develop a suitable specification framework which meets our basic requirements: the independent construction of implementations for the single constituent parts (modules) of a system specification and the encapsulated development of each implementation part using the principle of stepwise refinement. Our paper is not aimed at providing an elaborated specification language but rather to concentrate on the modularity issues of system development. Hence, only few but powerful constructs are provided which can be seen as a kernel for further extensions. In particular, we will show that implementation and parameterization can be handled within a uniform concept and we will prove compatibility theorems like the horizontal composition property. All constructs are defined on top of a very general logical framework thus being applica...
Combining and Representing Logical Systems
, 1997
"... The paper addresses important problems of building complex logical systems and their representations in universal logics in a systematic way. Following Goguen and Burstall, we adopt the modeltheoretic view of logic as captured in the notion of institution and of parchment (a certain algebraic ..."
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Cited by 12 (3 self)
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The paper addresses important problems of building complex logical systems and their representations in universal logics in a systematic way. Following Goguen and Burstall, we adopt the modeltheoretic view of logic as captured in the notion of institution and of parchment (a certain algebraic way of presenting institutions). We propose a modified notion of parchment together with a notion of parchment morphism and representation, respectively. We lift formal properties of the categories of institutions and their representations to this level: the category of parchments is complete, and parchment representations may be put together using categorical limits as well. However, parchments provide a more adequate framework for systematic combination of logical systems than institutions. We indicate how the necessary invention for proper combination of various logical features may be introduced either on an ad hoc basis (when putting parchments together using limits in the cat...
Different Types of Arrow Between Logical Frameworks
 Proc. ICALP 96, LNCS 1099, 158169
, 1996
"... this paper we argue that these different types of arrow can be generated by one basic type of arrow and monadic constructions on categories of logical frameworks, with the effect of automatically having functors relating the new categories of logical frameworks with the old ones. The paper is organi ..."
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Cited by 5 (2 self)
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this paper we argue that these different types of arrow can be generated by one basic type of arrow and monadic constructions on categories of logical frameworks, with the effect of automatically having functors relating the new categories of logical frameworks with the old ones. The paper is organized as follows: in Sect. 2, some types of logical framework and some categorical notions are recalled. Section 3 then introduces, using monads and adjunctions, one wellknown and three new notions of maps between institutions, which vary in the strictness of keeping the signaturesentence distinction. In each case, we briefly show the application to different logical frameworks. Section 4 concludes the paper. Due to lack of space, we omit proofs, which will appear elsewhere. 2 Preliminaries
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...
A Survey of Concepts and New Compositionality Results
"... Abstract In this paper we try to shed some light on the similarities and differences in the different approaches defining the notions of implementation and implementation correctness. For obvious reasons, we do not discuss all existing approaches individually. Instead a formal framework is introduce ..."
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Abstract In this paper we try to shed some light on the similarities and differences in the different approaches defining the notions of implementation and implementation correctness. For obvious reasons, we do not discuss all existing approaches individually. Instead a formal framework is introduced in order to discuss the most important ones. Additionally, we discuss some issues which in our opinion are often misunderstood, concerning transitivity of implementation correctness and its rôle in the software development process. In particular, on the one hand, we show that for reasonable notions of implementation it is almost impossible to prove transitivity of implementation correctness at the specification level. On the other hand, we show that this is not really important if the programming language satisfies the properties of horizontal an vertical composition. 1. What is an Implementation? In the framework of software development, programs may be seen as the result of a process starting from a &quot;highlevel specification &quot; SP0 and ending at a &quot;low level program &quot; P. In between, different &quot;lowerlevel specifications &quot; SP1,..., SPn are produced. This process is called &quot;implementation &quot; and P is said to be an implementation of SP0 (and of SP1,...,
A Monotonic Declarative Semantics for Normal Logic Programs
"... In this paper, we propose a declarative semantics for normal logic programs in terms of model classes that is monotonic in the sense that Mod(PP') # Mod(P), for any programs P and P'. In addition, we show that in the model class associated to every program there is a least model that ca ..."
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In this paper, we propose a declarative semantics for normal logic programs in terms of model classes that is monotonic in the sense that Mod(PP') # Mod(P), for any programs P and P'. In addition, we show that in the model class associated to every program there is a least model that can be seen as the semantics of the program, which may be built upwards as the least fixpoint of a continuous immediate consequence operator, and such that this least model is "typical" for the class of models of the ClarkKunen's completion of the program. This means that our semantics is equivalent to ClarkKunen's completion. The final aim of our work is the definition of compositional semantics for modular units over the class of normal logic programs. In this sense, following the results of a previous paper, it has been shown that our semantics constitutes a "specification frame" equipped with the adequate categorical constructions to guarantee the existence of such semantics. 1 Introducti...