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Moving Specification Structures Between Logical Systems
 13th WADT’98
, 1998
"... The conditions under which a formal system for reasoning about structural specifications, built over one logical system could be reused for reasoning about structured specifications built over another logical system are formulated and studied. Following Goguen and Burstall, the notion of a logical s ..."
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Cited by 10 (1 self)
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The conditions under which a formal system for reasoning about structural specifications, built over one logical system could be reused for reasoning about structured specifications built over another logical system are formulated and studied. Following Goguen and Burstall, the notion of a logical system is formalized as an institution and extended to a Dinstitution. A new function between classes of specifications, inspired by a similar function from [HST 94], is defined as a natural extension of institution representations to structured specifications. 1
General logics
 In Logic Colloquium 87
, 1989
"... theory, categorical logic. model theory that emerged in computer science studies of software specification and semantics. To handle proof theory, our institutions use an extension of traditional categorical logic with sets of sentences as objects instead of single sentences, and with morphisms repre ..."
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Cited by 9 (3 self)
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theory, categorical logic. model theory that emerged in computer science studies of software specification and semantics. To handle proof theory, our institutions use an extension of traditional categorical logic with sets of sentences as objects instead of single sentences, and with morphisms representing proofs as usual. A natural equivalence relation on institutions is defined such that its equivalence classes are logics. Several invariants are defined for this equivalence, including a Lindenbaum
Context Institutions
, 1996
"... . The paper introduces a notion of a context institution. The notion is explicitly illustrated by two standard examples. Morphism between context institutions are introduced, thus yielding a category of context institutions. Some expected constructions on context institutions are presented as functo ..."
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Cited by 7 (2 self)
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. The paper introduces a notion of a context institution. The notion is explicitly illustrated by two standard examples. Morphism between context institutions are introduced, thus yielding a category of context institutions. Some expected constructions on context institutions are presented as functors from this category. The potential usefulness of these notions is illustrated by one such a construction, yielding a Hoare logic for an arbitrary small context institution satisfying mild extra assumptions. 1 Introduction The theory of institutions ([4], [6]) has proved its usefulness in the area of foundations of software specification and development. The modeltheoretic view of logical systems advocated in the theory of institutions captures very well the idea that in computer science applications of logic what we are really interested in are models. We always try to specify (logical) properties of concrete objects standard examples can be programs, database management systems or ...
Notes on Refinement, Interpolation and Uniformity.
"... The connection between some modularity properties and interpolation is revisited and restated in a general "logicindependent " framework. The presence of uniform interpolants is shown to assist in certain proof obligations, which suffice to establish the composition of refinements. The absence of th ..."
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Cited by 6 (5 self)
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The connection between some modularity properties and interpolation is revisited and restated in a general "logicindependent " framework. The presence of uniform interpolants is shown to assist in certain proof obligations, which suffice to establish the composition of refinements. The absence of the desirable interpolation properties from many logics that have been used in refinement, motivates a thorough investigation of methods to expand a specification formalism orthogonally, so that the critical uniform interpolants become available. A potential breakthrough is outlined in this paper. 1. A refinement paradigm Let us consider program development by means of stepwise refinements. One postulates some abstract data typelike specification 1 (ADT), suitable for the problem at hand, which has to be implemented on the available system. The end product consists of (the text of) an abstract program manipulating the postulated ADT, together with a suite of (texts of) modules implementin...
Representations, Hierarchies, and Graphs of Institutions
, 1996
"... For the specification of abstract data types, quite a number of logical systems have been developed. In this work, we will try to give an overview over this variety. As a prerequisite, we first study notions of {\em representation} and embedding between logical systems, which are formalized as {\em ..."
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Cited by 5 (4 self)
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For the specification of abstract data types, quite a number of logical systems have been developed. In this work, we will try to give an overview over this variety. As a prerequisite, we first study notions of {\em representation} and embedding between logical systems, which are formalized as {\em institutions} here. Different kinds of representations will lead to a looser or tighter connection of the institutions, with more or less good possibilities of faithfully embedding the semantics and of reusing proof support. In the second part, we then perform a detailed ``empirical'' study of the relations among various wellknown institutions of total, ordersorted and partial algebras and firstorder structures (all with Horn style, i.e.\ universally quantified conditional, axioms). We thus obtain a {\em graph} of institutions, with different kinds of edges according to the different kinds of representations between institutions studied in the first part. We also prove some separation results, leading to a {\em hierarchy} of institutions, which in turn naturally leads to five subgraphs of the above graph of institutions. They correspond to five different levels of expressiveness in the hierarchy, which can be characterized by different kinds of conditional generation principles. We introduce a systematic notation for institutions of total, ordersorted and partial algebras and firstorder structures. The notation closely follows the combination of features that are present in the respective institution. This raises the question whether these combinations of features can be made mathematically precise in some way. In the third part, we therefore study the combination of institutions with the help of socalled parchments (which are certain algebraic presentations of institutions) and parchment morphisms. The present book is a revised version of the author's thesis, where a number of mathematical problems (pointed out by Andrzej Tarlecki) and a number of misuses of the English language (pointed out by Bernd KriegBr\"uckner) have been corrected. Also, the syntax of specifications has been adopted to that of the recently developed Common Algebraic Specification Language {\sc Casl} \cite{CASL/Summary,Mosses97TAPSOFT}.
Categorybased Modularisation for Equational Logic Programming
 Acta Informatica
, 1996
"... : Although modularisation is basic to modern computing, it has been little studied for logicbased programming. We treat modularisation for equational logic programming using the institution of categorybased equational logic in three different ways: (1) to provide a generic satisfaction conditio ..."
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: Although modularisation is basic to modern computing, it has been little studied for logicbased programming. We treat modularisation for equational logic programming using the institution of categorybased equational logic in three different ways: (1) to provide a generic satisfaction condition for equational logics; (2) to give a categorybased semantics for queries and their solutions; and (3) as an abstract definition of compilation from one (equational) logic programming language to another. Regarding (2), we study soundness and completeness for equational logic programming queries and their solutions. This can be understood as ordinary soundness and completeness in a suitable "nonlogical" institution. Soundness holds for all module imports, but completeness only holds for conservative module imports. Categorybased equational signatures are seen as modules, and morphisms of such signatures as module imports. Regarding (3), completeness corresponds to compiler correc...
Generalized Interpolation in CASL
 Information Processing Letter, 76:19–24
, 2000
"... In this paper we consider the partial manysorted firstorder logic and its extension to the subsorted partial manysorted firstorder logic that underly the Casl specification formalism. First we present counterexamples showing that the generalization of the Craig Interpolation Property does not h ..."
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Cited by 4 (0 self)
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In this paper we consider the partial manysorted firstorder logic and its extension to the subsorted partial manysorted firstorder logic that underly the Casl specification formalism. First we present counterexamples showing that the generalization of the Craig Interpolation Property does not hold for these logics in general (i.e., with respect to arbitrary signature morphisms). Then we formulate conditions under which the generalization of the Craig Interpolation Property holds for the first logic.
Structural Properties of Some Categories of Institutions
, 1996
"... : This is a technical paper stating and proving completeness and cocompleteness results for various categories of institutions. 1 Introduction This is a technical companion report to [Tar96], where an overview of various notions of a mapping between institutions is given and some structural propert ..."
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Cited by 3 (1 self)
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: This is a technical paper stating and proving completeness and cocompleteness results for various categories of institutions. 1 Introduction This is a technical companion report to [Tar96], where an overview of various notions of a mapping between institutions is given and some structural properties of the resulting categories of institutions are indicated. The main goal of the current report is to provide technical statements of these results and to prove them in sufficient detail. Some of the results given here have been only hinted at in [Tar96], some of them are repeated from [Tar96], and some are known from the earlier literature. For the sake of completeness of this report we recall all the formal definitions which underly the results  we refrain however from giving any motivations and informal analysis of the role of the notions introduced and results proved. We will also sketch the proofs of known results, since they provide a necessary background for the proofs which hav...
Correctness of the Logical System for Structured Specifications
 in Algebraic Development Techniques, WADT'97 Seleted Papers. Lecture Notes in Computer Science 1376
, 1997
"... The main aim of this paper is to present the completeness proof of a formal system for reasoning about logical consequences of structured specifications. The system is based on the proof rules for structural specifications build in an arbitrary institution as presented in [ST 88]. The proof of its c ..."
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The main aim of this paper is to present the completeness proof of a formal system for reasoning about logical consequences of structured specifications. The system is based on the proof rules for structural specifications build in an arbitrary institution as presented in [ST 88]. The proof of its completeness is inspired by the proof due to M. V. Cengarle (see [Cen 94]) for specifications in firstorder logic and the logical system for reasoning about them presented also in [Wir 91]. 1 Introduction In a number of papers on algebraic specifications (see [Cen 94, Far 92, ST 88, SST 92, Tar 86, Wir 91]) the main goal was to build: ffl a flexible enough specification formalism which allows one to cope with various problems of software engineering; ffl a sound and complete logic for reasoning about such specifications. We follow these goals when the first and a part of the second aim (soundness) is achieved by using structured specifications and the logical system built over an arbitrary...
Behavioral extensions of institutions
 Proc. 1st Conf. on Algebra and Coalgebra in Computer Science CALCO’05, Swansea. Springer LNCS 3629
, 2005
"... Abstract. We show that any institution I satisfying some reasonable conditions can be transformed into another institution, Ibeh, which captures formally and abstractly the intuitions of adding support for behavioral equivalence and reasoning to an existing, particular algebraic framework. We call o ..."
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Abstract. We show that any institution I satisfying some reasonable conditions can be transformed into another institution, Ibeh, which captures formally and abstractly the intuitions of adding support for behavioral equivalence and reasoning to an existing, particular algebraic framework. We call our transformation an “extension ” because Ibeh has the same sentences as I and because its entailment relation includes that of I. Many properties of behavioral equivalence in concrete hidden logics follow as special cases of corresponding institutional results. As expected, the presented constructions and results can be instantiated to other logics satisfying our requirements as well, thus leading to novel behavioral logics, such as partial or infinitary ones, that have the desired properties. 1