Bialgebraic methods and modal logic in structural operational semantics

Klin, Bartek

doi:10.1016/j.ic.2007.10.006

Cited by 17 publications

(10 citation statements)

References 44 publications

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“…In [12] (see [20] for a more elementary introduction), Turi and Plotkin proposed an abstract way of understanding well-behaved structural operational semantics for systems of various kinds. There, behaviour of transition systems is modeled by coalgebras, and their syntax by algebras.…”

Section: Abstract Gsosmentioning

confidence: 99%

Structural Operational Semantics for Weighted Transition Systems

Klin

2009

Semantics and Algebraic Specification

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Abstract. Weighted transition systems are defined, parametrized by a commutative monoid of weights. These systems are further understood as coalgebras for functors of a specific form. A general rule format for the SOS specification of weighted systems is obtained via the coalgebraic approach of Turi and Plotkin. Previously known formats for labelled transition systems (GSOS) and stochastic systems (SGSOS) appear as special cases.

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Section: Abstract Gsosmentioning

confidence: 99%

Structural Operational Semantics for Weighted Transition Systems

Klin

2009

Semantics and Algebraic Specification

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“…The relationship to modal logics as specification languages is well studied, too. Some of these results there have seen their categorical generalization [42,58,81], where system dynamics and their algebraic composition together form a categorical notion of bialgebra, and modal logics are nicely accommodated in the categorical picture via Stone-like dualities. We shall start with adapting these existing results to CPS examples, also using our results in the topics we discussed in Sects.…”

Section: Compositionalitymentioning

confidence: 99%

Metamathematics for Systems Design

Hasuo

2017

New Gener. Comput.

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This position paper describes the context, the goal, the strategy and the tactics of the ERATO MMSD project (2016-2022. The project aims at enhanced quality assurance measures for industry products like cars. In doing so, we follow a recent trend and exploit formal methods, a body of mathematical techniques originally developed for computer systems. However, there are fundamental gaps in application of formal methods to industry products: additional concerns in industry products such as continuous dynamics of physical components and quantitative measures such as probability, time, and cost make problems fundamentally different from those about software. Formal methods that accommodate these concerns is an active research area, which shows that it is a hard problem. There are several successful theoretical developments in this direction. They typically combine one individual technique with one specific concern, such as hybrid automata that extend automata with continuous dynamics. Our project aims to contribute to this hard problem in a unique way. In our project we will take a unique metamathematical strategy to bridging the gaps: instead of creating one technique for each concern, we want to find a meta-level theory that describes how to develop such techniques for many potential concerns in general. Through this strategy, together with our emphasis on real-world applications in industry, we expect a new prototype of applied mathematics will emerge. In this prototype, abstraction and genericitycharacteristics of modern mathematics that are not often associated with application-are turned into crucial advantages in applications.

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“…A major concern there is compositionality, much like in the study of process calculi (see e.g. [3]); and successful (co)algebraic techniques have been developed for the latter [21,32] as well as for the former [5]. We rely on the categorical formalization of component calculi in [5,15] where components are coalgebras; categorical genericity is needed since our transducers are parametrized by a monad T .…”

Section: Contributions-from Coalgebraic Components To Algebraic Effectsmentioning

confidence: 99%

Memoryful geometry of interaction

Hoshino

Muroya

Hasuo

2014

Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Nin

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Girard's Geometry of Interaction (GoI) is interaction based semantics of linear logic proofs and, via suitable translations, of functional programs in general. Its mathematical cleanness identifies essential structures in computation; moreover its use as a compilation technique from programs to state machines-"GoI implementation," so to speak-has been worked out by Mackie, Ghica and others. In this paper, we develop Abramsky's idea of resumption based GoI systematically into a generic framework that accounts for computational effects (nondeterminism, probability, exception, global states, interactive I/O, etc.). The framework is categorical: Plotkin & Power's algebraic operations provide an interface to computational effects; the framework is built on the categorical axiomatization of GoI by Abramsky, Haghverdi and Scott; and, by use of the coalgebraic formalization of component calculus, we describe explicit construction of state machines as interpretations of functional programs. The resulting interpretation is shown to be sound with respect to equations between algebraic operations, as well as to Moggi's equations for the computational lambda calculus. We illustrate the construction by concrete examples.

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Bialgebraic methods and modal logic in structural operational semantics

Cited by 17 publications

References 44 publications

Structural Operational Semantics for Weighted Transition Systems

Structural Operational Semantics for Weighted Transition Systems

Metamathematics for Systems Design

Memoryful geometry of interaction

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