## TPTP Axioms File: SWV008^1.ax

```%------------------------------------------------------------------------------
% File     : SWV008^1 : TPTP v8.1.0. Released v3.6.0.
% Domain   : Software Verification (Security)
% Axioms   : ICL notions of validity wrt S4
% Version  : [Ben08] axioms.
% English  :

% Refs     : [GA08]  Garg & Abadi (2008), A Modal Deconstruction of Access
%          : [Ben08] Benzmueller (2008), Automating Access Control Logics i
%          : [BP09]  Benzmueller & Paulson (2009), Exploring Properties of
% Source   : [Ben08]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of formulae    :    2 (   0 unt;   0 typ;   0 def)
%            Number of atoms       :   12 (   0 equ;   0 cnn)
%            Maximal formula atoms :    8 (   6 avg)
%            Number of connectives :   14 (   0   ~;   0   |;   0   &;  14   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   7 avg;  14 nst)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :    2 (   0   ^   2   !;   0   ?;   2   :)
% SPC      :

% Comments : Requires LCL008^0.ax SWV008^0.ax
%          : THF0 syntax
%------------------------------------------------------------------------------
%----We add the reflexivity and the transitivity axiom to obtain S4.
thf(refl_axiom,axiom,
! [A: \$i > \$o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ A ) @ A ) ) ).

thf(trans_axiom,axiom,
! [B: \$i > \$o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ B ) @ ( mbox @ rel @ ( mbox @ rel @ B ) ) ) ) ).

%------------------------------------------------------------------------------
```