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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