Details of Grant 

EPSRC Reference:	GR/L85756/01
Title:	TOPOLOGICAL DUALITY FOR MODAL, TEMPORAL AND PROGRAM LOGICS
Principal Investigator:	Rydeheard, Dr D
Other Investigators:	Simmons, Dr H
Researcher Co-Investigators:
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Department:	Computer Science
Organisation:	Victoria University of Manchester, The
Scheme:	Standard Research (Pre-FEC)
Starts:	01 November 1997	Ends:	31 July 2001	Value (£):	214,531
EPSRC Research Topic Classifications:	Fundamentals of Computing
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
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Summary on Grant Application Form
Modal logics, such as temporal logics, dynamic logics, process logics and logics of non-determinism, are a standard tool of computer science. They are essential to reason about the behaviour of computational systems and are a key component of development methodologies. The semantics of such logics is based on a correspondence between syntax-related (em modal algebras) and semantically motivated (em Kripke structures). Recent work generalises this correspondence to the case where the underlying logic is intuitionistic by introducing a (em topology) on the Kripke structures. This leads to a categorical (em durability theorem) and a complete axiomatisation. The aim of this project is to develop these results and investigate particular cases such as logics of real-time systems and dynamic program logics, to the point where they are ready for application to computer science.
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