%--------------------------------------------------------------------------
% File     : MGT048+1 : TPTP v9.0.0. Released v2.4.0.
% Domain   : Management (Organisation Theory)
% Problem  : Capability decreases monotonically with its age
% Version  : [Han98] axioms.
% English  : An organization's capability decreases monotonically with its age.

% Refs     : [Kam00] Kamps (2000), Email to G. Sutcliffe
%          : [CH00]  Carroll & Hannan (2000), The Demography of Corporation
%          : [Han98] Hannan (1998), Rethinking Age Dependence in Organizati
% Source   : [Kam00]
% Names    : LEMMA 5 [Han98]

% Status   : Theorem
% Rating   : 0.06 v8.1.0, 0.03 v7.1.0, 0.00 v6.4.0, 0.04 v6.3.0, 0.08 v6.1.0, 0.10 v6.0.0, 0.09 v5.5.0, 0.07 v5.4.0, 0.11 v5.3.0, 0.19 v5.2.0, 0.05 v5.0.0, 0.00 v3.3.0, 0.07 v3.2.0, 0.18 v3.1.0, 0.11 v2.7.0, 0.17 v2.5.0, 0.00 v2.4.0
% Syntax   : Number of formulae    :   10 (   0 unt;   0 def)
%            Number of atoms       :   34 (   7 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :   25 (   1   ~;   4   |;   9   &)
%                                         (   3 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   0 prp; 1-2 aty)
%            Number of functors    :    4 (   4 usr;   0 con; 2-2 aty)
%            Number of variables   :   25 (  25   !;   0   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments : See MGT042+1.p for the mnemonic names.
%--------------------------------------------------------------------------
include('Axioms/MGT001+0.ax').
%--------------------------------------------------------------------------
%----Problem Axioms
%----Increased knowledge elevates an organization's capability; and
%----increased accumulation of organizational internal frictions
%----diminishes its capability.
fof(assumption_5,axiom,
    ! [X,T0,T] :
      ( organization(X)
     => ( ( ( greater(stock_of_knowledge(X,T),stock_of_knowledge(X,T0))
            & smaller_or_equal(internal_friction(X,T),internal_friction(X,T0)) )
         => greater(capability(X,T),capability(X,T0)) )
        & ( ( smaller_or_equal(stock_of_knowledge(X,T),stock_of_knowledge(X,T0))
            & greater(internal_friction(X,T),internal_friction(X,T0)) )
         => smaller(capability(X,T),capability(X,T0)) )
        & ( ( stock_of_knowledge(X,T) = stock_of_knowledge(X,T0)
            & internal_friction(X,T) = internal_friction(X,T0) )
         => capability(X,T) = capability(X,T0) ) ) ) ).

%----Case: liability of senescence (Ass. 10-12 replacing A7-9)!
%----
%----An organization's stock of knowledge does not vary with its age
%----(contra assumption 7).
fof(assumption_10,axiom,
    ! [X,T0,T] :
      ( organization(X)
     => stock_of_knowledge(X,T) = stock_of_knowledge(X,T0) ) ).

%----The quality of an organization's internal friction increases
%----monotonically with its age (contra assumption 9).
fof(assumption_12,axiom,
    ! [X,T0,T] :
      ( ( organization(X)
        & greater(age(X,T),age(X,T0)) )
     => greater(internal_friction(X,T),internal_friction(X,T0)) ) ).

%----Problem theorems
%----Case C: liability of senescence.
%----
%----An organization's capability decreases monotonically with its age.
%----From A5, A10, A12 (also needs D<=).
%----
%----Text says mistakenly: capability(X,T) > capability(X,T0)
fof(lemma_5,conjecture,
    ! [X,T0,T] :
      ( ( organization(X)
        & greater(age(X,T),age(X,T0)) )
     => smaller(capability(X,T),capability(X,T0)) ) ).

%--------------------------------------------------------------------------