Allen's temporal calculus
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Allen interval calculus

Allen interval calculus is a way to reason about temporal events.

Here's a simple example: given the following facts:

  A patient's fever immediately preceded her cough;
       her cough immediately preceded lab values showing hypokalemia;
       neutrophilia also immediately preceded the hypokalemia.

One can make queries of the relationships between intervals, for example:

When did her neutrophila occur in relationship with her fever?
define (symptoms)
  (set-events '(fever neutrophilia hypokalemia cough))
  (set-temporal-relationship 'fever 'cough '(m))
  (set-temporal-relationship 'cough 'hypokalemia '(m))
  (set-temporal-relationship 'neutrophilia 'hypokalemia '(m))
  (get-temporal-relationship 'neutrophilia 'fever)

Welcome to Racket v5.3.4.
racket@> ,enter "/Users/keith/medsim/temporal-logic/temporal.rkt"
racket@temporal.rkt> (symptoms)
interval fever
interval neutrophilia
interval hypokalemia
interval cough
'(> mi di si oi)

The result list '(> mi di si oi) indicates that several relationships are possible - the episode of neutrophilia either came after the fever (not necessarily immediately after), did come immediately after the fever, started concurrently with the fever, and/or overlapped with the duration of the fever.

Symptom example

This implementation in Racket is based on Stephen Tanimoto's Common Lisp code as described in Chapter 8 ("Commonsense Reasoning") of his book Elements of Artificial Intelligence.

There are 13 possible relationships between intervals, encoded as follows:

 "before"          <
 "after"           >
 "during"          d
 "contains"        di
 "overlaps"        o
 "overlapped-by"   oi
 "meets"           m
 "met-by"          mi
 "starts"          s
 "started-by"      si
 "finishes"        f
 "finished-by"     fi
 "equals"          =