TPTP Axioms File: LCL007+4.ax


%------------------------------------------------------------------------------
% File     : LCL007+4 : TPTP v7.5.0. Released v3.3.0.
% Domain   : Logic Calculi (Propositional modal)
% Axioms   : Axiomatization of S1-0
% Version  : [Fey50] axioms.
% English  :

% Refs     : [Fey50] Feys (1950), Les systemes formalises de modalites aris
%          : [Hal]   Halleck (URL), John Halleck's Logic Systems
%          : [She06] Shen (2006), Automated Proofs of Equivalence of Modal
% Source   : [Hal]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of formulae    :   14 (  14 unit)
%            Number of atoms       :   14 (   0 equality)
%            Maximal formula depth :    1 (   1 average)
%            Number of connectives :    0 (   0 ~  ;   0  |;   0  &)
%                                         (   0 <=>;   0 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   14 (  14 propositional; 0-0 arity)
%            Number of functors    :    0 (   0 constant; --- arity)
%            Number of variables   :    0 (   0 singleton;   0 !;   0 ?)
%            Maximal term depth    :    0 (   0 average)
% SPC      : 

% Comments : Requires LCL006+1, LCL007+0, LCL007+1
%------------------------------------------------------------------------------
%----Modal definitions
fof(s1_0_op_possibly,axiom,op_possibly).

fof(s1_0_op_or,axiom,op_or).

fof(s1_0_op_implies,axiom,op_implies).

fof(s1_0_op_strict_implies,axiom,op_strict_implies).

fof(s1_0_op_equiv,axiom,op_equiv).

fof(s1_0_op_strict_equiv,axiom,op_strict_equiv).

%----Modal rules
fof(s1_0_modus_ponens_strict_implies,axiom,modus_ponens_strict_implies).

fof(s1_0_substitution_strict_equiv,axiom,substitution_strict_equiv).

fof(s1_0_adjunction,axiom,adjunction).

%----Modal axioms
fof(s1_0_axiom_m1,axiom,axiom_m1).

fof(s1_0_axiom_m2,axiom,axiom_m2).

fof(s1_0_axiom_m3,axiom,axiom_m3).

fof(s1_0_axiom_m4,axiom,axiom_m4).

fof(s1_0_axiom_m5,axiom,axiom_m5).

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