Examples of Predicate Calculus

Knowledge about Objects

Scheme version:

(turnip turnip6)
(A (?x) ((turnip ?x) -> ((bitter ?x) & (root-vegetable ?x))))
(A (?x) ((root-vegetable ?x) -> ((root ?x) & (vegetable ?x))))
(A (?x) ((vegetable ?x) -> ((food ?x) & (origin ?x plant))))

A way which permits inheritance of attribute values (here a value for taste)

Scheme version:
```
(A (?x) ((turnip ?x) -> (taste ?x bitter)))
```

A (very inefficient) way to handle inheritance exceptions

Scheme version:

(taste turnip8 sweet)
(A (?x) (((turnip ?x) & (~ (eq ?x turnip8))) -> (taste ?x bitter)))

Knowledge about States and Events

One way to represent knowledge about events
If ?g gives ?o to ?r at time ?t, then ?g is near ?r at ?t

Scheme version:
```
(give john mary turnip8 time3)
(A (?g ?r ?o ?t)
   ((give ?g ?r ?o ?t) ->
    (near ?g ?r ?t)))
```

Another way to represent the same thing

Scheme version:

(give give22)
(giver give22 john)
(recipient give22 mary)
(time give22 time3)
(given give22 turnip8)
(A (?g ?r ?e ?t)
   (((give ?e) &
     (giver ?e ?g) &
     (recipient ?e ?r) &
     (time ?e ?t)) ->
    (near ?g ?r ?t)))

Handling time using situations
States take a situation as an argument. Events are functions which return a situation. Note that it is then impossible to assert directly that an event takes place.
If ?g has ?o in situation ?s, then ?g giving ?o to ?r results in a situation in which ?r has ?o.

Scheme version:
```
(A (?g ?r ?o ?s)
   ((have ?g ?o ?s) ->
    (have ?r ?o (give ?g ?r ?o ?s))))
```

Ambiguity in Natural Language

Phyllis didn't drop the class because it met early.

'Phyllis dropped the class and this wasn't because it meets early.'

Scheme version:

(drop drop6)
(dropper drop6 phyllis)
(dropped drop6 q351:w96)
(meet-early meet3)
(meeter meet3 q351:w96)
(~ (cause meet3 drop6))

'Phyllis didn't the drop class and this was because it met early.'

Scheme version:

(fail-to fail7)
(failer fail7 phyllis)
(failed fail7 drop6)
(drop drop6)
(dropper drop6 phyllis)
(dropped drop6 q351:w96)
(meet-early meet3)
(meeter meet3 q351:w96)
(cause meet3 fail7)

Every morning Bob eats an egg.

Scheme version:

(A (?m)
   (morning ?m) ->
   (E (?e ?t)
      ((egg ?e) &
       (eat bob ?e ?t) &
       (during ?t ?m))))

Every morning Bob eats at a walnut table.

Scheme version:

(E (?table)
   ((table ?table) &
    (made-of ?table walnut) &
    (A (?m)
       ((morning ?m) ->
        (E (?time)
          ((eat-at bob ?table ?time) &
           (during ?time ?m)))))))

Last updated: 7 February 1996
URL: http://www.indiana.edu/~gasser/Q351/pc_examples.html
Comments: gasser@salsa.indiana.edu
Copyright 1996, The Trustees of Indiana University