A spatio-temporal specification language and its completeness & decidability

Li, Tengfei; Liu, Jing; Sun, Haiying; Chen, Xiang; Zhang, Lipeng; Sun, Junfeng

doi:10.1186/s13677-020-00209-3

Journal of Cloud Computing

Advances, Systems and Applications

Table 1 Logics for specifying spatio-temporal properties

From: A spatio-temporal specification language and its completeness & decidability

Spatio-Temporal Logic	Temporal representation			Spatial representation			Applications
	Temporal Logic	Temporal Operator	Temporal Domain	Spatial Logic	Spatial Operator	Spatial Domain
STSL [15]	STL	Threshold predicate, Boolean connectives,Globally, eventually, until with interval	Dense time	S4 _u	spatial intersection, union, complementary, interior, closure + universal, existential	Both changeable and unchangeable spatial terms in topometric space	Runtime verification for cyber-physical systems
STLCS [58]	CTL	Boolean connectives, branching next, globally, eventually, until	Branching time	SLCS	next, surrounded, reachability, touch, everywhere, somewhere	Discrete closure space	Public transport systems
SpaTeL [59]	STL	Threshold predicate, Boolean connectives,Globally, eventually, until with interval	Dense time	TSSL	next, globally, eventually, until bounded with direction	Quad transition system	Networked dynamical systems
SSTL [60]	STL	Globally, eventually, until with interval	Dense time	Spatial modality	somewhere, everywhere, until, surround	Discrete space	Turing reaction diffusion system and bike-sharing system
STREL [61]	STL	Globally, eventually, until and since with interval	Dense time	Spatial modality	reachability, escape, somewhere, everywhere, until, surround	Euclidean spatial model	Mobile Ad hoc sensor network
DTL [62]	LTL	Boolean connectives, linear next, globally, eventually, until	Discrete time	S4	spatial intersection, union, complementary, interior, closure	Topological space	Dynamic topological systems
MLSL [63]	ITL	equal, before, meets, overlap, during, starts, finishes, temporal interval chop	Dense time	Shape Calculus	claimed by, reserved by, occupied by, horizontal chop, vertical chop	Traffic snapshots	Multi-lane motorway traffic
\(\mathcal {L}_{DS}\) [64]	HML	modal diamond operator 〈μ〉 and branching temporal operators	Discrete time	π-calculus	composition, guarantee, hiding, revelation, next	Mobile agent	Distributed concurrent systems
PSTL [65]	PTL	Boolean connectives,next, globally, eventually, until	Discrete time	S4 _u	intersection, union, complementary, interior, closure, universal, existential	Topological space	Geographical region
MTSL [31]	MTL	Boolean connectives, Globally, eventually, until with interval	Bounded time	S4 _u	intersection, union, complementary, interior, closure, universal, existential	Topological space	Train control systems

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