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A modular approach to defining and characterising notions of simulation

A modular approach to defining and characterising notions of simulation
A modular approach to defining and characterising notions of simulation
We propose a modular approach to defining notions of simulation, and modal logics which characterise them. We use coalgebras to model state-based systems, relators to define notions of simulation for such systems, and inductive techniques to define the syntax and semantics of modal logics for coalgebras. We show that the expressiveness of an inductively defined logic for coalgebras w.r.t. a notion of simulation follows from an expressivity condition involving one step in the definition of the logic, and the relator inducing that notion of simulation. Moreover, we show that notions of simulation and associated characterising logics for increasingly complex system types can be derived by lifting the operations used to combine system types, to a relational level as well as to a logical level. We use these results to obtain Baltag’s logic for coalgebraic simulation, as well as notions of simulation and associated logics for a large class of non-deterministic and probabilistic systems.
Coalgebra, Simulation, Modal logic, Probabilistic system
0890-5401
469-502
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea
Adámek, J
b1ce974e-4e6a-46b5-8885-be263383a975
Milius, S
7d8771d7-6a93-4966-9d6a-5a6ff9a6497d
Cirstea, Corina
ce5b1cf1-5329-444f-9a76-0abcc47a54ea
Adámek, J
b1ce974e-4e6a-46b5-8885-be263383a975
Milius, S
7d8771d7-6a93-4966-9d6a-5a6ff9a6497d

Cirstea, Corina, Adámek, J and Milius, S(eds.) (2006) A modular approach to defining and characterising notions of simulation Information and Computation, 204, (4), pp. 469-502.

Record type: Article

Abstract

We propose a modular approach to defining notions of simulation, and modal logics which characterise them. We use coalgebras to model state-based systems, relators to define notions of simulation for such systems, and inductive techniques to define the syntax and semantics of modal logics for coalgebras. We show that the expressiveness of an inductively defined logic for coalgebras w.r.t. a notion of simulation follows from an expressivity condition involving one step in the definition of the logic, and the relator inducing that notion of simulation. Moreover, we show that notions of simulation and associated characterising logics for increasingly complex system types can be derived by lifting the operations used to combine system types, to a relational level as well as to a logical level. We use these results to obtain Baltag’s logic for coalgebraic simulation, as well as notions of simulation and associated logics for a large class of non-deterministic and probabilistic systems.

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Published date: April 2006
Keywords: Coalgebra, Simulation, Modal logic, Probabilistic system
Organisations: Electronic & Software Systems

Identifiers

Local EPrints ID: 261880
URI: http://eprints.soton.ac.uk/id/eprint/261880
ISSN: 0890-5401
PURE UUID: a0d819ee-2d99-4ac7-aa7d-c86b84a826e9

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Date deposited: 29 Jan 2006
Last modified: 04 Nov 2017 04:35

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Contributors

Author: Corina Cirstea
Editor: J Adámek
Editor: S Milius

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