TPTP Problem File: MGT050+1.p
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%--------------------------------------------------------------------------
% File : MGT050+1 : TPTP v8.2.0. Released v2.4.0.
% Domain : Management (Organisation Theory)
% Problem : Unendowed organization's hazard of mortality increases with age
% Version : [Han98] axioms.
% English : An unendowed organization's hazard of mortality increases 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 3 [Han98]
% Status : Theorem
% Rating : 0.14 v8.2.0, 0.11 v8.1.0, 0.06 v7.4.0, 0.10 v7.3.0, 0.03 v7.2.0, 0.00 v7.1.0, 0.04 v7.0.0, 0.13 v6.4.0, 0.15 v6.3.0, 0.12 v6.2.0, 0.16 v6.1.0, 0.27 v6.0.0, 0.17 v5.5.0, 0.19 v5.4.0, 0.25 v5.3.0, 0.30 v5.2.0, 0.20 v5.1.0, 0.19 v5.0.0, 0.25 v4.1.0, 0.17 v4.0.1, 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, 0.14 v3.2.0, 0.27 v3.1.0, 0.22 v2.7.0, 0.17 v2.6.0, 0.33 v2.5.0, 0.17 v2.4.0
% Syntax : Number of formulae : 14 ( 0 unt; 0 def)
% Number of atoms : 57 ( 13 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 49 ( 6 ~; 4 |; 19 &)
% ( 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.
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include('Axioms/MGT001+0.ax').
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%----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 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 external ties does not vary with
%----its age (contra assumption 8).
fof(assumption_11,axiom,
! [X,T0,T] :
( organization(X)
=> external_ties(X,T) = external_ties(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
%----The senescence theorem for unendowed organizations (Barron et
%----al. 1994): an unendowed organization's hazard of mortality
%----increases with its age.
%----From A1, A4-6, and A10-12 (text says D1, A1-4, L5-6; also needs D<,
%----D<=, D>=).
fof(theorem_3,conjecture,
! [X,T0,T] :
( ( organization(X)
& ~ has_endowment(X)
& greater(age(X,T),age(X,T0)) )
=> greater(hazard_of_mortality(X,T),hazard_of_mortality(X,T0)) ) ).
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