TPTP Axioms File: MGT001+0.ax


%--------------------------------------------------------------------------
% File     : MGT001+0 : TPTP v7.5.0. Released v2.4.0.
% Domain   : Management (Organisation Theory)
% Axioms   : Inequalities.
% 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    :

% Status   : Satisfiable
% Syntax   : Number of formulae    :    6 (   0 unit)
%            Number of atoms       :   16 (   3 equality)
%            Maximal formula depth :    6 (   5 average)
%            Number of connectives :   11 (   1 ~  ;   4  |;   2  &)
%                                         (   3 <=>;   1 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    5 (   0 propositional; 2-2 arity)
%            Number of functors    :    0 (   0 constant; --- arity)
%            Number of variables   :   13 (   0 singleton;  13 !;   0 ?)
%            Maximal term depth    :    1 (   1 average)
% SPC      : 

% Comments :
%--------------------------------------------------------------------------
%----Definition of smaller_or_equal (i.t.o. smaller and equal).
fof(definition_smaller_or_equal,axiom,
    ( ! [X,Y] :
        ( smaller_or_equal(X,Y)
      <=> ( smaller(X,Y)
          | X = Y ) ) )).

%%----Definition of smaller_or_equal (i.t.o. greater).
%input_formula(definition_smaller_or_equal, axiom, (
%    ! [X,Y] :
%      ( smaller_or_equal(X,Y)
%    <=> ( ~ greater(X,Y) ) ) )).

%----Definition of greater_or_equal (i.t.o. greater and equal).
fof(definition_greater_or_equal,axiom,
    ( ! [X,Y] :
        ( greater_or_equal(X,Y)
      <=> ( greater(X,Y)
          | X = Y ) ) )).

%%----Definition of greater_or_equal (i.t.o. greater and equal).
%input_formula(definition_greater_or_equal, axiom, (
%    ! [X,Y] :
%      ( greater_or_equal(X,Y)
%    <=> ( ~ greater(Y,X) ) ) )).

%----Definition of smaller (i.t.o. greater).
fof(definition_smaller,axiom,
    ( ! [X,Y] :
        ( smaller(X,Y)
      <=> greater(Y,X) ) )).

%----Our notion of greater is strict (irreflexive and antisymmetric).
fof(meaning_postulate_greater_strict,axiom,
    ( ! [X,Y] : ~ ( greater(X,Y)
        & greater(Y,X) ) )).

%%----Derivable from above.
%input_formula(meaning_postulate_greater_strict2, axiom, (
%    ! [X] :
%      ( ~ greater(X,X) ) )).

%----Our notion of greater is transitive.
fof(meaning_postulate_greater_transitive,axiom,
    ( ! [X,Y,Z] :
        ( ( greater(X,Y)
          & greater(Y,Z) )
       => greater(X,Z) ) )).

%----Hazards of mortality are comparable.
%input_formula(background_ass_a1, axiom, (
%  ! [X,T0,T] :
%    ( organization(X)
%   => ( ( greater(hazard_of_mortality(X,T),hazard_of_mortality(X,T0))
%        | equal(hazard_of_mortality(X,T),hazard_of_mortality(X,T0)) )
%       => smaller(hazard_of_mortality(X,T),hazard_of_mortality(X,T0)) ) ) )).

%----Trichotomy statement for everything.
%input_formula(meaning_postulate_greater_comparable, axiom, (
%    ! [X,Y] :
%      ( greater(Y,X)
%      | equal(X,Y)
%      | greater(X,Y) ) )).
fof(meaning_postulate_greater_comparable,axiom,
    ( ! [X,Y] :
        ( smaller(X,Y)
        | X = Y
        | greater(X,Y) ) )).

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