TPTP Problem File: MGT042+1.p
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% File : MGT042+1 : TPTP v8.2.0. Released v2.4.0.
% Domain : Management (Organisation Theory)
% Problem : Conditions for a lower hazard of mortality
% Version : [Han98] axioms.
% English : When an organization lacks immunity, increased collective
% knowledge and superior external ties lower its hazard of
% mortality when internal friction does not increase.
% 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 1 [Han98]
% Status : Theorem
% Rating : 0.28 v8.2.0, 0.22 v8.1.0, 0.19 v7.5.0, 0.22 v7.4.0, 0.20 v7.3.0, 0.24 v7.2.0, 0.21 v7.1.0, 0.17 v7.0.0, 0.27 v6.4.0, 0.31 v6.3.0, 0.29 v6.2.0, 0.32 v6.1.0, 0.40 v6.0.0, 0.26 v5.5.0, 0.37 v5.4.0, 0.43 v5.3.0, 0.56 v5.2.0, 0.45 v5.1.0, 0.43 v5.0.0, 0.42 v4.1.0, 0.35 v4.0.1, 0.30 v4.0.0, 0.29 v3.7.0, 0.30 v3.5.0, 0.26 v3.4.0, 0.47 v3.3.0, 0.50 v3.2.0, 0.64 v3.1.0, 0.78 v2.7.0, 0.67 v2.6.0, 0.83 v2.4.0
% Syntax : Number of formulae : 10 ( 0 unt; 0 def)
% Number of atoms : 54 ( 11 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 49 ( 5 ~; 4 |; 22 &)
% ( 3 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 0 prp; 1-2 aty)
% Number of functors : 6 ( 6 usr; 0 con; 2-2 aty)
% Number of variables : 25 ( 25 !; 0 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : The original text uses mnemonic names:
% Original: C/F/P: Arity: New name:
% zero-symbol c 0 zero
% eta-symbol c 0 eta
% sigma-symbol c 0 sigma
% tau-symbol c 0 tau
% very_low c 0 very_low
% low c 0 low
% mod1 c 0 mod1
% mod2 c 0 mod2
% high c 0 high
% A f 2 age
% H f 2 hazard_of_mortality
% C f 2 capability
% P f 2 position
% K f 2 stock_of_knowledge
% T f 2 external_ties
% F f 2 internal_friction
% O p 1 organization
% EN p 1 has_endowment
% IM p 2 has_immunity
% DS p 3 dissimilar
% AL p 2 is_aligned
% PA p 2 positional_advantage
% FG p 1 fragile_position
% RB p 1 robust_position
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include('Axioms/MGT001+0.ax').
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%----Problem Axioms
%----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) ) ) ) ).
%----Problem theorems
%----When an organization lacks immunity, increased collective
%----knowledge and superior external ties lower its hazard of
%----mortality when internal friction does not increase.
%----From A4, A5, and A6 (text says A1-6; also needs D<, D>=, D<=).
fof(lemma_1,conjecture,
! [X,T0,T] :
( ( organization(X)
& ~ has_immunity(X,T0)
& ~ has_immunity(X,T) )
=> ( ( ( greater(stock_of_knowledge(X,T),stock_of_knowledge(X,T0))
& smaller_or_equal(internal_friction(X,T),internal_friction(X,T0))
& greater_or_equal(external_ties(X,T),external_ties(X,T0)) )
=> smaller(hazard_of_mortality(X,T),hazard_of_mortality(X,T0)) )
& ( ( greater_or_equal(stock_of_knowledge(X,T),stock_of_knowledge(X,T0))
& smaller_or_equal(internal_friction(X,T),internal_friction(X,T0))
& greater(external_ties(X,T),external_ties(X,T0)) )
=> smaller(hazard_of_mortality(X,T),hazard_of_mortality(X,T0)) ) ) ) ).
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