%------------------------------------------------------------------------------
% File     : LCL007+1 : TPTP v9.0.0. Released v3.3.0.
% Domain   : Logic Calculi (Propositional modal)
% Axioms   : Propositional modal logic definitions
% Version  : [She06] axioms.
% English  :

% Refs     : [Hal]   Halleck (URL), John Halleck's Logic Systems
%          : [She06] Shen (2006), Automated Proofs of Equivalence of Modal
% Source   : [She06]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of formulae    :    4 (   0 unt;   0 def)
%            Number of atoms       :    8 (   4 equ)
%            Maximal formula atoms :    2 (   2 avg)
%            Number of connectives :    4 (   0   ~;   0   |;   0   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    5 (   4 usr;   4 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   0 con; 1-2 aty)
%            Number of variables   :    6 (   6   !;   0   ?)
% SPC      : 

% Comments :
%------------------------------------------------------------------------------
%----Definitions
fof(op_possibly,axiom,
    ( op_possibly
   => ! [X] : possibly(X) = not(necessarily(not(X))) ) ).

fof(op_necessarily,axiom,
    ( op_necessarily
   => ! [X] : necessarily(X) = not(possibly(not(X))) ) ).

fof(op_strict_implies,axiom,
    ( op_strict_implies
   => ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ) ).

fof(op_strict_equiv,axiom,
    ( op_strict_equiv
   => ! [X,Y] : strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X)) ) ).

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