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%--------------------------------------------------------------------------
% File : MGT019+2 : TPTP v5.5.0. Released v2.0.0.
% Domain : Management (Organisation Theory)
% Problem : Growth rate of EPs exceeds that of FMs in stable environments
% Version : [PM93] axioms.
% English : The growth rate of efficent producers exceeds the growth rate
% of first movers past a certain time in stable environments.
% Refs : [PM93] Peli & Masuch (1993), The Logic of Propogation Strateg
% : [PM94] Peli & Masuch (1994), The Logic of Propogation Strateg
% : [PB+94] Peli et al. (1994), A Logical Approach to Formalizing
% Source : [PM93]
% Names : LEMMA 1 [PM93]
% : L1 [PB+94]
% Status : CounterSatisfiable
% Rating : 0.00 v4.1.0, 0.20 v4.0.1, 0.00 v3.5.0, 0.33 v3.4.0, 0.00 v2.1.0
% Syntax : Number of formulae : 5 ( 0 unit)
% Number of atoms : 21 ( 1 equality)
% Maximal formula depth : 8 ( 6 average)
% Number of connectives : 17 ( 1 ~ ; 1 |; 8 &)
% ( 0 <=>; 7 =>; 0 <=)
% ( 0 <~>; 0 ~|; 0 ~&)
% Number of predicates : 7 ( 0 propositional; 1-4 arity)
% Number of functors : 5 ( 2 constant; 0-2 arity)
% Number of variables : 11 ( 0 singleton; 9 !; 2 ?)
% Maximal term depth : 2 ( 1 average)
% SPC : FOF_CSA_RFO_SEQ
% Comments : There is no MGT019+1 as Kamps did not send it to me.
%--------------------------------------------------------------------------
%----Subsitution axioms
%----Problem axioms
%----L2. The disbanding rate of first movers exceeds the disbanding
%----rate of efficient producers.
fof(l2,axiom,
( ~ ( ! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)) ) ) )).
%----If EP have lower disbanding rate and not lower founding rate than
%----FM, then EP have higher growth rate.
fof(mp_EP_lower_disbanding_rate,axiom,
( ! [T] :
( ( greater(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))
& greater_or_equal(founding_rate(efficient_producers,T),founding_rate(first_movers,T)) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) )).
%----MP. on "greater or equal to"
fof(mp_greater_or_equal,axiom,
( ! [X,Y] :
( greater_or_equal(X,Y)
=> ( greater(X,Y)
| X = Y ) ) )).
%----A8. The founding rate of first movers does not exceed the founding
%----rate of efficient producers past a certain point in a stable
%----environment.
fof(a8,hypothesis,
( ! [E] :
( ( environment(E)
& stable(E) )
=> ? [To] :
( in_environment(E,To)
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater_or_equal(T,To) )
=> greater_or_equal(founding_rate(efficient_producers,T),founding_rate(first_movers,T)) ) ) ) )).
%----GOAL: L1. The growth rate of efficient producers exceeds the growth
%----rate of first movers past a certain time in stable environments.
fof(prove_l1,conjecture,
( ! [E] :
( ( environment(E)
& stable(E) )
=> ? [To] :
( in_environment(E,To)
& ! [T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& greater_or_equal(T,To) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) ) ) ) )).
%--------------------------------------------------------------------------
|
