Extensions to ENGINEERING MATHEMATICS

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;; Extensions to standard-units-and-dimensions
;;     dimensions
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(in-theory 'standard-units-and-dimensions)

(define-instance area-dimension (physical-dimension)
  "The physical dimension of an area is defined as length dimension squared."
  
  :axiom-def (= area-dimension
                (expt length-dimension 2)))

(define-instance pressure-dimension (physical-dimension)
  "the physical dimension of pressure is defined as force over area"
  
  :axiom-def (= pressure-dimension
                (* force-dimension
                   (expt area-dimension -1))))

(define-instance therm^-1-dimension (physical-dimension)
  :axiom-def (= therm^-1-dimension
                (expt thermodynamic-temperature-dimension -1)))

(define-instance work-dimension (physical-dimension)
  :axiom-def (= work-dimension
                (* force-dimension
                   length-dimension)))

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;; Extensions to standard-units-and-dimensions
;;     units
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(in-theory 'standard-units-and-dimensions)

(define-instance megapascal (unit-of-measure)
  " 1 megapascal = 10^6 pascal "
  := (* pascal 1000000)
  :axiom-def (dimension megapascal pressure-dimension)  )

(define-instance watt (unit-of-measure)
  "unit of measure for measuring physical work"
  := (* newton meter)
  :axiom-def (dimension watt work-dimension)  )

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;; Extension to physical quantities by intervals
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(in-theory 'physical-quantities)

(define-relation in-interval (?x ?low ?up)
  "holds if :
                 (?x >= ?low) and
                 (?x <= ?up) and 
if their dimensions are compatible"
  
  :iff-def (and (compatible-quantities ?x ?low)
            (compatible-quantities ?x ?up)
            (=< ?x ?up)
            (>= ?x ?low)))

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;; Mechanical Quantities
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(define-theory mechanical-quantities (standard-units-and-dimensions
                                      scalar-quantities 
                                      vector-quantities)

  "This theory is used to represent mechanical quantities such as
e-module, ... which are extensions to the quantities already
defined in the physical-quantities ontology"
  )

(in-theory 'mechanical-quantities)

(define-class e-module (?x)
  "e-module is a sub-class of vector-quantity of the dimension 3,
containing scalar quantities of the physical dimension pressure"
  
  :def (and (vector-quantity ?x)
            (vector.dimension ?x 3)
            (= (dimension ?x) pressure-dimension)
            )
  )

(define-instance e-module.basis (orthonormal-basis)
  "represents the unit-basis for the e-module class"
  :axiom-def (basis.dimension e-module.basis 3)
  )

(define-class tensile-strength (?x)
  "tensile-strength is a subclass of scalar-quantities associated 
with the physical pressure-dimension"
  :def (and (scalar-quantity ?x)
            (dimension ?x pressure-dimension)
            )
  )
            
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;; Thermal Quantities
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(define-theory thermal-quantities (standard-units-and-dimensions
                                   scalar-quantities) 

  "This theory is used to represent thermal quantities such as
thermal-expansion, ... which are extensions to 
the quantities already defined in the physical-quantities ontology"
  )

(in-theory 'thermal-quantities)

(define-class thermal-expansion (?x)
  
  :def (and (scalar-quantity ?x)
            (dimension ?x therm^-1-dimension))
  )
    
(define-class thermal-conductivity (?x)
  :def (and (scalar-quantity ?x)
            (dimension ?x (* work-dimension
                             (expt area-dimension -1)
                             therm^-1-dimension)))
  )