130 research outputs found
An Institutional Framework for Heterogeneous Formal Development in UML
We present a framework for formal software development with UML. In contrast
to previous approaches that equip UML with a formal semantics, we follow an
institution based heterogeneous approach. This can express suitable formal
semantics of the different UML diagram types directly, without the need to map
everything to one specific formalism (let it be first-order logic or graph
grammars). We show how different aspects of the formal development process can
be coherently formalised, ranging from requirements over design and Hoare-style
conditions on code to the implementation itself. The framework can be used to
verify consistency of different UML diagrams both horizontally (e.g.,
consistency among various requirements) as well as vertically (e.g.,
correctness of design or implementation w.r.t. the requirements)
Hybridisation at work
This paper presents the encoding of the hybridisation method into the HETS platform.FC
Hilbert-Post completeness for the state and the exception effects
In this paper, we present a novel framework for studying the syntactic
completeness of computational effects and we apply it to the exception effect.
When applied to the states effect, our framework can be seen as a
generalization of Pretnar's work on this subject. We first introduce a relative
notion of Hilbert-Post completeness, well-suited to the composition of effects.
Then we prove that the exception effect is relatively Hilbert-Post complete, as
well as the "core" language which may be used for implementing it; these proofs
have been formalized and checked with the proof assistant Coq.Comment: Siegfried Rump (Hamburg University of Technology), Chee Yap (Courant
Institute, NYU). Sixth International Conference on Mathematical Aspects of
Computer and Information Sciences , Nov 2015, Berlin, Germany. 2015, LNC
Algebraic Properties of Qualitative Spatio-Temporal Calculi
Qualitative spatial and temporal reasoning is based on so-called qualitative
calculi. Algebraic properties of these calculi have several implications on
reasoning algorithms. But what exactly is a qualitative calculus? And to which
extent do the qualitative calculi proposed meet these demands? The literature
provides various answers to the first question but only few facts about the
second. 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. We also analyze existing qualitative calculi
and provide a classification involving different notions of a relation algebra.Comment: COSIT 2013 paper including supplementary materia
An Institution for Simple UML State Machines
We present an institution for UML state machines without hierarchical states.
The interaction with UML class diagrams is handled via institutions for guards
and actions, which provide dynamic components of states (such as valuations of
attributes) but abstract away from details of class diagrams. We also study a
notion of interleaving product, which captures the interaction of several state
machines. The interleaving product construction is the basis for a semantics of
composite structure diagrams, which can be used to specify the interaction of
state machines. This work is part of a larger effort to build a framework for
formal software development with UML, based on a heterogeneous approach using
institutions.Comment: 24 pages. arXiv admin note: substantial text overlap with
arXiv:1403.774
Notions of Bidirectional Computation and Entangled State Monads
Bidirectional transformations (bx) support principled consistency maintenance between data sources. Each data source corresponds to one perspective on a composite system, manifested by operations to ‘get’ and ‘set’ a view of the whole from that particular perspective. Bx are important in a wide range of settings, including databases, interactive applications, and model-driven development. We show that bx are naturally modelled in terms of mutable state; in particular, the ‘set’ operations are stateful functions. This leads naturally to considering bx that exploit other computational effects too, such as I/O, nondeterminism, and failure, all largely ignored in the bx literature to date. We present a semantic foundation for symmetric bidirectional transformations with effects. We build on the mature theory of monadic encapsulation of effects in functional programming, develop the equational theory and important combinators for effectful bx, and provide a prototype implementation in Haskell along with several illustrative examples
Bisimilarity and refinement for hybrid(ised) logics
The complexity of modern software systems entails the need for reconfiguration mechanisms governing the dynamic evolution of their execution configurations in response to both external stimulus or internal performance measures. Formally, such systems may be represented by transition systems whose nodes correspond to the different configurations they may assume. Therefore, each node is endowed with, for example, an algebra, or a first-order structure, to precisely characterise the semantics of the services provided in the corresponding configuration.
Hybrid logics, which add to the modal description of transition structures the ability to refer to specific states, offer a generic framework to approach the specification and design of this sort of systems. Therefore, the quest for suitable notions of equivalence and refinement between models of hybrid logic specifications becomes fundamental to any design discipline adopting this perspective. This paper contributes to this effort from a distinctive point of view: instead of focussing on a specific hybrid logic, the paper introduces notions of bisimilarity and refinement for hybridised logics, i.e. standard specification logics (e.g. propositional, equational, fuzzy, etc) to which modal and hybrid features were added in a systematic way.FC
Untyping Typed Algebras and Colouring Cyclic Linear Logic
We prove "untyping" theorems: in some typed theories (semirings, Kleene
algebras, residuated lattices, involutive residuated lattices), typed equations
can be derived from the underlying untyped equations. As a consequence, the
corresponding untyped decision procedures can be extended for free to the typed
settings. Some of these theorems are obtained via a detour through fragments of
cyclic linear logic, and give rise to a substantial optimisation of standard
proof search algorithms.Comment: 21
ASP, Amalgamation and the Conceptual Blending Workflow
We present a framework for conceptual blending – a concept invention method that is advocated in cognitive science as a fundamental, and uniquely human engine for creative thinking. Herein, we employ the search capabilities of ASP to find commonalities among input concepts as part of the blending process, and we show how our approach fits within a generalised conceptual blending workflow. Specifically, we orchestrate ASP with imperative Python programming, to query external tools for theorem proving and colimit computation. We exemplify our approach with an example of creativity in mathematics. © Springer International Publishing Switzerland 2015.This work is supported by the 7th Framework Programme for Research of the European Commission funded COINVENT project (FET-Open grant number: 611553). M. Eppe is supported by the German Academic Exchange ServicePeer Reviewe
- …