Fibring has been shown to be useful for combining logics endowed with truth-functional semantics. One wonders if bring can be extended in order to cope with logics endowed with non-truth-functional semantics as, for example, paraconsistent logics. The rst main contribution of the paper is a positive answer to this question. Furthermore, it is shown that this extended notion of bring preserves completeness under certain reasonable conditions. This completeness transfer result, the second main contribution of the paper, generalizes the one established by Zanardo et al. and is obtained using a new technique exploiting the properties of the metalogic where the (possibly non-truth-functional) valuations are de ned. The modal paraconsistent logic of da Costa and Carnielli is obtained by bring and its completeness is so established.

The UniForM Workbench supports combination of Formal Methods (on a solid logical foundation), provides tools for the development of hybrid, real-time or reactive systems, transformation, verification, validation and testing. Moreover, it...

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 re-used 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...

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 D-institution. 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

. Experience shows that it is not economically feasible to formally specify all parts of a system in an industrial application. Either one already has a number of existing components which are trusted and therefore desirable for reuse, or components are so simple that there is no gain in formally specifying their behaviour. In both cases it may be felt that it is not worth spending time on developing a detailed formal specification of the entire system. This raises the questions what tools should be provided for the analysis of the the entire system in which actual code is combined with specifications. In this paper we propose an approach which enables to integrate code in a formal specification for prototyping facilities. The integration of code is supported by an extension to the IFAD VDM-SL Toolbox such that heterogeneous models can be interpreted. 1 Introduction The successful introduction of formal methods in an industrial setting is very dependent upon the choice of the parts of...

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 re-using proof support. In the second part, we then perform a detailed ``empirical'' study of the relations among various well-known institutions of total, order-sorted and partial algebras and first-order 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, order-sorted and partial algebras and first-order 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 so-called 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 Krieg-Br\"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}.

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 well-known and three new notions of maps between institutions, which vary in the strictness of keeping the signature--sentence 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

We describe a course of research examining formal and semiformal heterogeneous specifications, i.e., compositions of partial specifications written in different textual and visual notations. We describe why we believe this to be an interesting topic for further inquiry, and suggest why such specifications might prove beneficial for use in software development.

We describe a higraph-based notation for visualizing and writing predicate specifications, and for depicting formal derivations of programs from specifications. We show how to present various system views using the notation, and consider how to deal with abstraction, which is vital in coping with large specifications. We then describe how the notation can be extended to heterogeneous specifications [Paig95]. 1 Introduction Visualizing information has long been a subject of considerable interest and work. This is no more evident than in the literature relevant to the specification of complex computer-related systems. Indeed, the development of visual notations for the specification of information, reactive, and object-oriented systems is an ongoing field of research. Many of the notations used in writing visual specifications suffer from a common problem: while they are visual, they are informal. Typical notations like data flow diagrams and structure charts are mostly devoid of seman...

It is often useful to apply several specification techniques within the same software development project. This raises the question how specification techniques can be integrated. In this presentation we give three different examples of how this can be done. In the first example, we summarise how the wide-spectrum approach has been used in the RAISE Specification Language (RSL) to integrate algebraic and model-oriented, applicative and imperative, and sequential and concurrent specification styles in a common syntactic and semantic unifying framework. The wide-spectrum approach has the advantage that one can stay within the same language throughout the development, but the price is a complicated semantics. Therefore, a related, but different approach, is to have a smaller, simple base language together with a number of extension languages in which additional sp...