## TPTP Axioms File: SWV008^1.ax

```%------------------------------------------------------------------------------
% File     : SWV008^1 : TPTP v7.5.0. 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 unit;   0 type;   0 defn)
%            Number of atoms       :   20 (   0 equality;   4 variable)
%            Maximal formula depth :    7 (   7 average)
%            Number of connectives :   14 (   0   ~;   0   |;   0   &;  14   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&;   0  !!;   0  ??)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +)
%            Number of symbols     :    6 (   0   :;   0  :=)
%            Number of variables   :    2 (   0 sgn;   2   !;   0   ?;   0   ^)
%                                         (   2   :;   0  :=;   0  !>;   0  ?*)
% 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 ) ) ) ) )).

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