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23
Moving Between Logical Systems
 Recent Trends in Data Type Specification
, 1998
"... : This paper presents a number of concepts of a mapping between logical systems modelled as institutions, discusses their mutual merits and demerits, and sketches their role in the process of system specification and development. Some simple properties of the resulting categories of institutions are ..."
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Cited by 50 (3 self)
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: This paper presents a number of concepts of a mapping between logical systems modelled as institutions, discusses their mutual merits and demerits, and sketches their role in the process of system specification and development. Some simple properties of the resulting categories of institutions are given. 1 Introduction We have to live with a multitude of logical systems used in various approaches to software specification and development. The proliferation of logical systems in the area is not just researchers' fancy, but results from the very practical needs to capture various aspects of software systems and to cater for various programming paradigms. Each of them leads to a different notion of a semantic model capturing the semantic essence of the adopted view of software systems. For instance, standard (manysorted) algebras [BL70], [GTW78] provide a satisfactory framework for modelling data types where all operations always yield welldefined results. However, if general recursi...
Relating CASL with Other Specification Languages: the Institution Level
, 2000
"... In this work, we investigate various specification languages and their relation to Casl, the recently developed Common Algebraic Specification Language. In particular, we consider the languages Larch, OBJ3, CafeOBJ, ACT ONE, ASF, and HEPtheories, as well as various sublanguages of Casl that more or ..."
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Cited by 34 (16 self)
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In this work, we investigate various specification languages and their relation to Casl, the recently developed Common Algebraic Specification Language. In particular, we consider the languages Larch, OBJ3, CafeOBJ, ACT ONE, ASF, and HEPtheories, as well as various sublanguages of Casl that more or less directly correspond to these. All these languages are translated to an appropriate sublanguage of Casl. The translation mainly concerns the level of specification inthesmall: the logics underlying the languages are formalized as institutions, and representations among the institutions are developed. However, it is also considered how these translations interact with specification inthelarge. Thus, we obtain one hand translations of any of the abovementioned specification languages to an appropriate sublanguage of Casl. This allows us to take libraries and case studies that have been developed for other languages and reuse them in Casl. On the other hand, we set up institution repre...
From Total Equational to Partial First Order Logic
, 1998
"... The focus of this chapter is the incremental presentation of partial firstorder logic, seen as a powerful framework where the specification of most data types can be directly represented in the most natural way. Both model theory and logical deduction are described in full detail. Alternatives to pa ..."
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Cited by 19 (8 self)
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The focus of this chapter is the incremental presentation of partial firstorder logic, seen as a powerful framework where the specification of most data types can be directly represented in the most natural way. Both model theory and logical deduction are described in full detail. Alternatives to partiality, like (variants of) error algebras and ordersortedness are also discussed, showing their uses and limitations. Moreover, both the total and the partial (positive) conditional fragment are investigated in detail, and in particular the existence of initial (free) models for such restricted logical paradigms is proved. Some more powerful algebraic frameworks are sketched at the end. Equational specifications introduced in last chapter, are a powerful tool to represent the most common data types used in programming languages and their semantics. Indeed, Bergstra and Tucker have shown in a series of papers (see [BT87] for a complete exposition of results) that a data type is semicompu...
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...
Using Limits of Parchments to Systematically Construct Institutions of Partial Algebras
 Recent Trends in Data Type Specifications. 11th Workshop on Specification of Abstract Data Types, volume 1130 of Lecture Notes in Computer Science
, 1996
"... this paper, so we leave them out here. Thus we can apply the idea of combining things via colimits to institutions themselves, with the special point that we have to take limits here instead of colimits. Taking limits in CAT results in categories of "amalgamated objects", i. e. we put sig ..."
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Cited by 15 (5 self)
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this paper, so we leave them out here. Thus we can apply the idea of combining things via colimits to institutions themselves, with the special point that we have to take limits here instead of colimits. Taking limits in CAT results in categories of "amalgamated objects", i. e. we put signatures and models together at the level of single objects. In contrast to this, sentences are combined with colimits in Set (due to the contravariant direction of the sentence component). That is, sets of sentences are combined. To show how this works, we introduce some wellknown institutions and morphisms between them.
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...
Foundations of Heterogeneous Specification
"... We provide a semantic basis for heterogeneous specifications that not only involve different logics, but also different kinds of translations between these. We show that Grothendieck institutions based on spans of (co)morphisms can serve as a unifying framework providing a simple but powerful semant ..."
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Cited by 10 (3 self)
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We provide a semantic basis for heterogeneous specifications that not only involve different logics, but also different kinds of translations between these. We show that Grothendieck institutions based on spans of (co)morphisms can serve as a unifying framework providing a simple but powerful semantics for heterogeneous specification.
A Systematic Study of Mappings between Institutions
 Recent Trends in Algebraic Development Techniques, volume 1376 of Lecture Notes in Computer Science
, 1998
"... . Concerning different notions of mappings between institutions, we believe that the current state of the art is somehow unsatisfactory. On the one hand because of the variety of different concepts proposed in the literature. On the other hand because of the apparent lack of a suitable basis to form ..."
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Cited by 6 (1 self)
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. Concerning different notions of mappings between institutions, we believe that the current state of the art is somehow unsatisfactory. On the one hand because of the variety of different concepts proposed in the literature. On the other hand because of the apparent lack of a suitable basis to formally discuss about what they mean and how they relate to each other. In this paper we aim at a systematic study of some of the most important notions of these mappings by proposing a methodology based on the concept of power institutions. Firstly, power institutions allow the investigation of the entire logical structure of an institution along these mappings, i.e., the satisfaction relation together with the satisfaction condition. Secondly, they allow this investigation in a systematic way, i.e., the transformation of the institutional logical structure can be described by means of simpler, more elementary transformations or units which are themselves also power institutions. These units ...
Institutional frames
 In Recent Trends in Data Type Specification. Proceedings, LNCS 906, 469482
, 1995
"... ..."
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