Allen Relation Between Definite Intervals

Allen Relation Between Definite Intervals

allen_relation(x, y, ...)

# S4 method for numeric,numeric
allen_relation(x, y)

# S4 method for ANY,missing
allen_relation(x)

Arguments

x, y

A numeric vector giving the lower and upper boundaries of the time intervals, respectively. If y is missing, an attempt is made to interpret x in a suitable way (see grDevices::xy.coords()).

...

Currently not used.

Value

A character matrix specifying the Allen relations.

Details

Relation			Converse
precedes	(p)	(P)	preceded by
meets	(m)	(M)	met by
overlaps	(o)	(O)	overlapped by
finished by	(F)	(f)	finishes
contains	(D)	(d)	during
starts	(s)	(S)	started by
equals	(e)

References

Allen, J. F. (1983). Maintaining Knowledge about Temporal Intervals. Communications of the ACM, 26(11): 832-843. doi:10.1145/182.358434 .

Alspaugh, T. (2019). Allen's Interval Algebra. URL: https://thomasalspaugh.org/pub/fnd/allen.html.

See also

Other Allen's intervals: allen_analyze(), allen_complement(), allen_composition(), allen_converse(), allen_illustrate(), allen_intersect(), allen_joint_concurrency(), allen_observe(), allen_observe_frequency(), allen_relation_code(), allen_union()

Author

T. S. Dye, N. Frerebeau

Examples

## Data from Husi 2022
loire <- data.frame(
  lower = c(625, 700, 1200, 1225, 1250, 500, 1000, 1200,
            1325, 1375, 1200, 1300, 1375, 1275, 1325),
  upper = c(750, 825, 1250, 1275, 1325, 700, 1300, 1325,
            1400, 1500, 1300, 1375, 1500, 1325, 1425)
)

## Basic relations
allen_relation(loire$lower, loire$upper)
#>       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
#>  [1,] NA   "o"  "p"  "p"  "p"  "O"  "p"  "p"  "p"  "p"   "p"   "p"   "p"  
#>  [2,] "O"  NA   "p"  "p"  "p"  "M"  "p"  "p"  "p"  "p"   "p"   "p"   "p"  
#>  [3,] "P"  "P"  NA   "o"  "m"  "P"  "d"  "s"  "p"  "p"   "s"   "p"   "p"  
#>  [4,] "P"  "P"  "O"  NA   "o"  "P"  "d"  "d"  "p"  "p"   "d"   "p"   "p"  
#>  [5,] "P"  "P"  "M"  "O"  NA   "P"  "O"  "f"  "m"  "p"   "O"   "o"   "p"  
#>  [6,] "o"  "m"  "p"  "p"  "p"  NA   "p"  "p"  "p"  "p"   "p"   "p"   "p"  
#>  [7,] "P"  "P"  "D"  "D"  "o"  "P"  NA   "o"  "p"  "p"   "F"   "m"   "p"  
#>  [8,] "P"  "P"  "S"  "D"  "F"  "P"  "O"  NA   "m"  "p"   "S"   "o"   "p"  
#>  [9,] "P"  "P"  "P"  "P"  "M"  "P"  "P"  "M"  NA   "o"   "P"   "O"   "o"  
#> [10,] "P"  "P"  "P"  "P"  "P"  "P"  "P"  "P"  "O"  NA    "P"   "M"   "e"  
#> [11,] "P"  "P"  "S"  "D"  "o"  "P"  "f"  "s"  "p"  "p"   NA    "m"   "p"  
#> [12,] "P"  "P"  "P"  "P"  "O"  "P"  "M"  "O"  "o"  "m"   "M"   NA    "m"  
#> [13,] "P"  "P"  "P"  "P"  "P"  "P"  "P"  "P"  "O"  "e"   "P"   "M"   NA   
#> [14,] "P"  "P"  "P"  "M"  "f"  "P"  "O"  "f"  "m"  "p"   "O"   "o"   "p"  
#> [15,] "P"  "P"  "P"  "P"  "M"  "P"  "P"  "M"  "S"  "o"   "P"   "O"   "o"  
#>       [,14] [,15]
#>  [1,] "p"   "p"  
#>  [2,] "p"   "p"  
#>  [3,] "p"   "p"  
#>  [4,] "m"   "p"  
#>  [5,] "F"   "m"  
#>  [6,] "p"   "p"  
#>  [7,] "o"   "p"  
#>  [8,] "F"   "m"  
#>  [9,] "M"   "s"  
#> [10,] "P"   "O"  
#> [11,] "o"   "p"  
#> [12,] "O"   "o"  
#> [13,] "P"   "O"  
#> [14,] NA    "m"  
#> [15,] "M"   NA   

## Complement
(comp <- allen_complement("F")) # "pmoDseSdfOMP"
#> [1] "pmoDseSdfOMP"

## Converse
(conv <- allen_converse(comp)) # "pmoFDseSdOMP"
#> [1] "pmoFDseSdOMP"

## Composition
allen_composition("oFD", "oFDseS") # "pmoFD"
#> [1] "pmoFD"

## Intersection
allen_intersect("pFsSf", "pmoFD") # "pF"
#> [1] "pF"

# Union
allen_union("pFsSf", "pmoFD") # "pmoFDsSf"
#> [1] "pmoFDsSf"