TPTP Problem File: MGT047+1.p
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% File : MGT047+1 : TPTP v8.2.0. Released v2.4.0.
% Domain : Management (Organisation Theory)
% Problem : Conditions for changing hazard of mortality
% Version : [Han98] axioms.
% English : An endowed organization's hazard of mortality is constant during
% its period of immunity, jumps when its immunity ends, and
% decreases with further aging but remains above the level during
% the immunity period.
% 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 2 [Han98]
% Status : Theorem
% Rating : 0.39 v8.2.0, 0.36 v8.1.0, 0.33 v7.5.0, 0.34 v7.4.0, 0.33 v7.3.0, 0.34 v7.2.0, 0.31 v7.1.0, 0.30 v6.4.0, 0.35 v6.3.0, 0.29 v6.2.0, 0.36 v6.1.0, 0.43 v6.0.0, 0.35 v5.5.0, 0.41 v5.4.0, 0.46 v5.3.0, 0.52 v5.2.0, 0.40 v5.1.0, 0.38 v4.1.0, 0.35 v4.0.1, 0.39 v4.0.0, 0.38 v3.7.0, 0.35 v3.5.0, 0.32 v3.4.0, 0.26 v3.3.0, 0.36 v3.2.0, 0.45 v3.1.0, 0.44 v2.7.0, 0.50 v2.4.0
% Syntax : Number of formulae : 16 ( 0 unt; 0 def)
% Number of atoms : 74 ( 14 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 63 ( 5 ~; 4 |; 30 &)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 0 prp; 1-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 44 ( 44 !; 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 endowment provides an immunity that lasts until an
%----organization's age exceeds `eta'.
fof(definition_1,axiom,
! [X] :
( has_endowment(X)
<=> ! [T] :
( organization(X)
& ( smaller_or_equal(age(X,T),eta)
=> has_immunity(X,T) )
& ( greater(age(X,T),eta)
=> ~ has_immunity(X,T) ) ) ) ).
%----An organization's hazard of mortality is constant during periods
%----in which it has immunity.
fof(assumption_2,axiom,
! [X,T0,T] :
( ( organization(X)
& has_immunity(X,T0)
& has_immunity(X,T) )
=> hazard_of_mortality(X,T0) = hazard_of_mortality(X,T) ) ).
%----An organization's hazard of mortality is lower during periods in
%----which it has immunity than in periods in which it does not.
fof(assumption_3,axiom,
! [X,T0,T] :
( ( organization(X)
& has_immunity(X,T0)
& ~ has_immunity(X,T) )
=> greater(hazard_of_mortality(X,T),hazard_of_mortality(X,T0)) ) ).
%----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-adolescence theorem (Bruederl and Schuessler
%----1990; Fichman and Levinthal 1991): an endowed organization's
%----hazard of mortality is constant during its period of immunity,
%----jumps when its immunity ends, and decreases with further aging
%----but remains above the level during the immunity period.
%----From D1 and A2-9 (text says D1, A1-4, L1-2; also needs D<, D<=, D>=,
%----MP>str, MP>com).
fof(theorem_2,conjecture,
! [X,T0,T1,T2,T3] :
( ( organization(X)
& has_endowment(X)
& smaller_or_equal(age(X,T0),age(X,T1))
& smaller_or_equal(age(X,T1),eta)
& greater(age(X,T2),eta)
& greater(age(X,T3),age(X,T2)) )
=> ( greater(hazard_of_mortality(X,T2),hazard_of_mortality(X,T3))
& greater(hazard_of_mortality(X,T3),hazard_of_mortality(X,T1))
& hazard_of_mortality(X,T1) = hazard_of_mortality(X,T0) ) ) ).
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