This collection of surveys is aimed at both researchers and Master's students in computer science and mathematics and deals with various aspects of bisimulation and coinduction, with an emphasis on process theory. Concepts such as continuity, differentiation and integration are shown to be definable and tractable in this setting; Newton's Method is presented as an example of a numerical application. Phillip James, Alexander Knapp, Till Mossakowski and Markus Roggenbach. As an example, we show how to generate survey knowledge from local observations in a street network. Our library covers a subset of the Haskell Prelude library, including data types and classes representing Booleans, lists, characters, strings, equality, and ordering functions.
Coinduction is the dual of induction and as such it brings in quite different tools. The benefit of this method is that the number of proof obligations that is to be proven by hand with a semi-automatic reasoner can be minimized to an acceptable level. Mihai Codescu, Fabian Neuhaus, Till Mossakowski, Oliver Kutz and Danny de Jesús Gómez-Ramírez. Further, we provide the first semantics for bipolar weighted graphs that converges for all graphs. In Martin Wirsing, Dirk Pattinson, Rolf Hennicker Eds. Norms and Space: Integrating Qualitative Rules in the Situation Calculus. E pluribus unum - Formalisation, Use-Cases, and Computational Support for Conceptual Blending.
The languages, methodologies and tools which support these - tivities are all well within its scope. For a number of programming languages, among them Eiffel, C, Java, and Ruby, Hoare-style logics and dynamic logics have been developed. We thus provide the first theorem proving support for Common Logic covering the full language, including the possibility of verifying meta-theoretical relationships between Common Logic theories. We here present a brief outline of this framework, discuss its features and merits, and illustrate its usefulness for the domain of biomedical ontology design by providing and discussing a number of examples. Maude modules can be understood as models that can be formally analyzed and verifi ed with respect to di fferent properties expressing various formal requirements. Dirk Pattinson, Lutz Schröder 2008. They faithfully represent theories, model categories, theory morphisms, colimit of theories, reducts etc.
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. Hedblom, Tarek Richard Besold, Tony Veale, Frederik Gailly, Giancarlo Guizzardi, Mark Lycett, Chris Partridge, Oscar Pastor, Michael Grüninger, Fabian Neuhaus, Till Mossakowski, Stefano Borgo, Loris Bozzato, Chiara Del Vescovo, Martin Homola, Frank Loebe, Adrien Barton and Jean-Rémi Bourguet. This framework can also be used for obtaining proof systems for heterogeneous theories involving institution semi-morphisms. Algebraic Properties of Qualitative Spatio-Temporal Calculi. Talcott, editors, Logic, Rewriting, and Concurrency - Essays dedicated to José Meseguer on the Occasion of His 65th Birthday, volume 9200, series Lecture Notes in Computer Science, pages 361-379. Many of the issues involved in software design apply to systems in general, including hardware s- tems,andtheemphasisonsoftwareisnotintendedtobeexclusive. Compared with other institution-independent kernel languages, the advantage is that translations, hidings etc.
In this work, we will try to give an overview over this variety. Oliver Kutz, Sergio de Cesare, Maria M. In this paper we identify the minimal requirements to binary spatio-temporal calculi and we discuss the relevance of the according axioms for representation and reasoning. In contrast to the points that are normally used, dipoles are extended and have an intrinsic direction. To support this, we show that natural spatial descriptions commonly appeal to diverse theories of space and these need to be formally combined to be fully interpreted. In the literature, there are described not only one, but many categories of logical frameworks: institutions with maps of institutions, specification frames, institutions with simulations, pre-institutions with transformations, institutional frames, pi- and tau-institutions, institutions with contexts, etc. Several invariants are defined for this equivalence, including a Lindenbaum algebra construction, its generalization to a Lindenbaum category construction that includes proofs, and model cardinality spectra; these are used in some examples to show logics inequivalent.
The logic is presented in a modular step-by-step reduction: the logic is defined in terms of a generalized subsorted partial logic which in turn is defined in terms of many-sorted partial first-order logic. But an open issue is whether they can be employed in applications. In other words, unless further measures are taken, type class polymorphism fails to constitute a proper institution, being only a so-called rps preinstitution; this is unfortunate, as it means that one cannot use institution-independent or heterogeneous structuring languages, proof calculi, and tools with it. Lange, editors, Intelligent Computer Mathematics, Conferences on Intelligent Computer Mathematics, volume 7961, series Lecture Notes in Computer Science, pages 200-215. We develop a relatively complete calculus for structured heterogeneous specifications that does not need interpolation.
We introduce a dynamic logic from which, as usual, a Hoare logic can be derived whose logical formulae are pure programs in a strong sense. In Theoretical Computer Science, 366 1-2 , pp. 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. This leads to a category of logical frameworks. We illustrate the approach with a sample heterogeneous proof proving the correctness of the composition table of a qualitative spatial calculus. In this paper, we investigate several logical frameworks whose expressiveness lies between Conditional Equational Logic and Horn Clause Logic.
Examples of spatial calculi include mereotopological calculi, Frank's cardinal direction calculus, Freksa's double cross calculus, Egenhofer and Franzosa's intersection calculi, and Randell, Cui, and Cohn's region connection calculi. The proposed categorial approach was essential in finding a suitably abstract treatment of binding. We verify that the revised version satisfies the previously mentioned proof-theoretic semantic principles, and show that it enjoys cut-elimination as a consequence of the generalized metatheorem. However, current research in integrated formal methods only deals with ad-hoc integrations of different formalisms. Typically, completeness of these calculi requires interpolation properties of the underlying logic. In particular, usually for each effect or each combination of these , an own logic needs to be designed.