Reasoning with Inequalities

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|= (demo 5)

Now reading from `PL:sources;logic;demos;inequalities.plm'.
Type `?' at the pause prompt for a list of available commands.

;;; -*- Mode: Lisp; Package: STELLA; Syntax: COMMON-LISP; Base: 10 -*-

;;; Version: inequalities.plm,v 1.8 2003/06/05 23:16:14 hans Exp

;;; Reasoning with inequalities
;;; ===========================

;;; This file demonstrates some basic inequality reasoning capabilities.

;;; The best way to view this file is by calling `(demo)' and
;;; selecting it from the menu of example demos.  This demo assumes
;;; familiarity with some basic PowerLoom concepts which are described
;;; in the introductory demo (#1 on the demo menu) and other demos
;;; preceding this one.


;; Standard demo preamble:

|= (in-package "STELLA")
------ pause ------c


|= (defmodule "PL-USER/INEQUALITIES")

|MDL|/PL-KERNEL-KB/PL-USER/INEQUALITIES

|= (in-module "INEQUALITIES")


|= (clear-module "INEQUALITIES")


|= (reset-features)

|l|(:EMIT-THINKING-DOTS :JUST-IN-TIME-INFERENCE)

|= (in-dialect KIF)

:KIF

;; The already familiar `Person' concept with its `age' function:

|= (defconcept Person (?p)
  :documentation "The class of human beings.")

|c|PERSON

|= (deffunction age ((?p Person)) :-> (?a Integer)
  :documentation "?a is ?p's age in years.")

|f|AGE

|= (assert (Person Fred))

|P|(PERSON FRED)

;; Let us assert that Fred is older than thirty using the built-in
;; `>' predicate.  Other comparison predicates such as `>=', `=<', and
;; '<' are also available.  Note the somewhat unusual spelling of `=<'
;; to make it not conflict with the reverse implication sign `<='.

|= (assert (> (age Fred) 30))

|P|(> (AGE FRED) 30)

;; Even though we don't know what Fred's age really is, we can now find
;; out whether he is older than thirty, since we asserted that above:

|= (ask (> (age Fred) 30))

TRUE

;; The built-in inequality reasoning specialists can also answer the
;; following query by exploiting the transitivity of `>':

|= (ask (> (age Fred) 25))

TRUE

;; If the arguments to `>' are known, the result can be computed directly
;; without resorting to inequality inference, for example:

|= (assert (Person Susi))

|P|(PERSON SUSI)

|= (assert (= (age Susi) 16))

|P|(= (AGE SUSI) 16)

;; Since Susi's age is known, PowerLoom can compute directly whether
;; she is older than 12:

|= (ask (> (age Susi) 12))

TRUE

;; And, even though we don't know Fred's age, he must be older than Susi:

|= (ask (> (age Fred) (age Susi)))

TRUE

|= 

Finished demo `PL:sources;logic;demos;inequalities.plm'.

|=