%--------------------------------------------------------------------------
% File     : MGT058+1 : TPTP v9.0.0. Released v2.4.0.
% Domain   : Management (Organisation Theory)
% Problem  : An organization's position cannot be both fragile and robust
% Version  : [Han98] axioms.
% English  :

% 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 10 [Han98]

% Status   : Theorem
% Rating   : 0.12 v9.0.0, 0.14 v8.2.0, 0.11 v8.1.0, 0.08 v7.5.0, 0.09 v7.4.0, 0.10 v7.2.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.08 v6.2.0, 0.12 v6.1.0, 0.13 v6.0.0, 0.09 v5.5.0, 0.04 v5.4.0, 0.07 v5.3.0, 0.15 v5.2.0, 0.05 v5.0.0, 0.04 v4.1.0, 0.09 v4.0.1, 0.13 v4.0.0, 0.12 v3.7.0, 0.05 v3.4.0, 0.16 v3.3.0, 0.14 v3.2.0, 0.18 v3.1.0, 0.22 v2.7.0, 0.33 v2.5.0, 0.17 v2.4.0
% Syntax   : Number of formulae    :    9 (   0 unt;   0 def)
%            Number of atoms       :   32 (   4 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :   27 (   4   ~;   4   |;   8   &)
%                                         (   5 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   0 prp; 1-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   19 (  18   !;   1   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments : See MGT042+1.p for the mnemonic names.
%--------------------------------------------------------------------------
include('Axioms/MGT001+0.ax').
%--------------------------------------------------------------------------
%----Problem Axioms
%--- Case: Fragile and robust positions in drifting environments.
%--- Retracting A16!
%----
%----An organization's position is fragile if and only if it does not
%----provide advantage after age `sigma'.
%----
%----Added case:  ( smaller_or_equal(age(X,T),sigma)
%----            => positional_advantage(X,T) )
fof(definition_3,axiom,
    ! [X] :
      ( fragile_position(X)
    <=> ! [T] :
          ( ( smaller_or_equal(age(X,T),sigma)
           => positional_advantage(X,T) )
          & ( greater(age(X,T),sigma)
           => ~ positional_advantage(X,T) ) ) ) ).

%----An organization's position is robust if and only if it provides
%----positional advantage only after age `tau'.
%----
%----Text says fragile_position(X) instead of robust_position(X).
%----Interchanged ~ positional_advantage(X,T) and positional_advantage(X,T).
fof(definition_4,axiom,
    ! [X] :
      ( robust_position(X)
    <=> ! [T] :
          ( ( smaller_or_equal(age(X,T),tau)
           => ~ positional_advantage(X,T) )
          & ( greater(age(X,T),tau)
           => positional_advantage(X,T) ) ) ) ).

%----Problem theorems
%----An organization's position cannot be both fragile and robust.
%----From D3-4 (also needs D<, D<=, D>=, MP>com).
%----
%----Requires several additions to the antecedent.
fof(lemma_10,conjecture,
    ! [X] :
      ( ( organization(X)
        & ? [T0] : age(X,T0) = zero
        & greater_or_equal(sigma,zero)
        & greater_or_equal(tau,zero) )
     => ~ ( fragile_position(X)
          & robust_position(X) ) ) ).

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