%--------------------------------------------------------------------------
% File     : MGT046+1 : TPTP v9.0.0. Released v2.4.0.
% Domain   : Management (Organisation Theory)
% Problem  : Unendowed organization's hazard of mortality declines with age
% Version  : [Han98] axioms.
% English  : An unendowed organization's hazard of mortality declines
%            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    : THEOREM 1 [Han98]

% Status   : Theorem
% Rating   : 0.12 v9.0.0, 0.14 v8.2.0, 0.08 v7.5.0, 0.09 v7.4.0, 0.10 v7.3.0, 0.07 v7.2.0, 0.03 v7.1.0, 0.00 v7.0.0, 0.07 v6.4.0, 0.08 v6.2.0, 0.12 v6.1.0, 0.17 v6.0.0, 0.13 v5.5.0, 0.11 v5.4.0, 0.14 v5.3.0, 0.22 v5.2.0, 0.10 v5.0.0, 0.12 v4.1.0, 0.09 v4.0.0, 0.08 v3.7.0, 0.10 v3.5.0, 0.11 v3.4.0, 0.16 v3.3.0, 0.21 v3.2.0, 0.27 v3.1.0, 0.22 v2.7.0, 0.17 v2.4.0
% Syntax   : Number of formulae    :   14 (   0 unt;   0 def)
%            Number of atoms       :   58 (  12 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :   50 (   6   ~;   4   |;  20   &)
%                                         (   3 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   0 prp; 1-2 aty)
%            Number of functors    :    7 (   7 usr;   0 con; 2-2 aty)
%            Number of variables   :   36 (  36   !;   0   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments : See MGT042+1.p for the mnemonic names.
%--------------------------------------------------------------------------
include('Axioms/MGT001+0.ax').
%--------------------------------------------------------------------------
%----Problem Axioms
%----An unendowed organization never possesses immunity.
fof(assumption_1,axiom,
    ! [X,T] :
      ( ( organization(X)
        & ~ has_endowment(X) )
     => ~ has_immunity(X,T) ) ).

%----When an organization lacks immunity, superior capability and
%----position imply a lower hazard of mortality.
fof(assumption_4,axiom,
    ! [X,T0,T] :
      ( ( organization(X)
        & ~ has_immunity(X,T0)
        & ~ has_immunity(X,T) )
     => ( ( ( greater(capability(X,T),capability(X,T0))
            & greater_or_equal(position(X,T),position(X,T0)) )
         => smaller(hazard_of_mortality(X,T),hazard_of_mortality(X,T0)) )
        & ( ( greater_or_equal(capability(X,T),capability(X,T0))
            & greater(position(X,T),position(X,T0)) )
         => smaller(hazard_of_mortality(X,T),hazard_of_mortality(X,T0)) )
        & ( ( capability(X,T) = capability(X,T0)
            & position(X,T) = position(X,T0) )
         => hazard_of_mortality(X,T) = hazard_of_mortality(X,T0) ) ) ) ).

%----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) ) ) ) ).

%----Improved ties with external actors enhance an organization's position.
fof(assumption_6,axiom,
    ! [X,T0,T] :
      ( organization(X)
     => ( ( greater(external_ties(X,T),external_ties(X,T0))
         => greater(position(X,T),position(X,T0)) )
        & ( external_ties(X,T) = external_ties(X,T0)
         => position(X,T) = position(X,T0) ) ) ) ).

%----Case: liability of Newness (Ass. 7-9).
%----
%----An organization's stock of knowledge increases monotonically with
%----its age.
fof(assumption_7,axiom,
    ! [X,T0,T] :
      ( ( organization(X)
        & greater(age(X,T),age(X,T0)) )
     => greater(stock_of_knowledge(X,T),stock_of_knowledge(X,T0)) ) ).

%----The quality of an organization's external ties increases
%----monotonically with its age.
fof(assumption_8,axiom,
    ! [X,T0,T] :
      ( ( organization(X)
        & greater(age(X,T),age(X,T0)) )
     => greater(external_ties(X,T),external_ties(X,T0)) ) ).

%----The quality of an organization's internal friction does not vary
%----with its age.
fof(assumption_9,axiom,
    ! [X,T0,T] :
      ( organization(X)
     => internal_friction(X,T) = internal_friction(X,T0) ) ).

%----Problem theorems
%----The liability-of-newness theorem (Stinchcombe 1965): an unendowed
%----organization's hazard of mortality declines monotonically with
%----its age.
%----From A1 and A4-9 (text says D1, A1-4, L1-2; also needs D<=, D>=).
fof(theorem_1,conjecture,
    ! [X,T0,T] :
      ( ( organization(X)
        & ~ has_endowment(X)
        & greater(age(X,T),age(X,T0)) )
     => smaller(hazard_of_mortality(X,T),hazard_of_mortality(X,T0)) ) ).

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