%------------------------------------------------------------------------------ % File : AGT033^1 : TPTP v7.1.0. Bugfixed v5.4.0. % Domain : Agents % Problem : Someone possibly likes someone else % Version : [Ben11] axioms. % English : % Refs : [Ben11] Benzmueller (2011), Email to Geoff Sutcliffe % : [Ben11] Benzmueller (2011), Combining and Automating Classical % Source : [Ben11] % Names : Ex_12_3 [Ben11] % Status : Theorem % Rating : 0.25 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v5.5.0, 0.33 v5.4.0 % Syntax : Number of formulae : 118 ( 0 unit; 45 type; 33 defn) % Number of atoms : 481 ( 38 equality; 183 variable) % Maximal formula depth : 15 ( 6 average) % Number of connectives : 336 ( 4 ~; 4 |; 9 &; 309 @) % ( 0 <=>; 10 =>; 0 <=; 0 <~>) % ( 0 ~|; 0 ~&) % Number of type conns : 203 ( 203 >; 0 *; 0 +; 0 <<) % Number of symbols : 49 ( 45 :; 0 =) % Number of variables : 111 ( 3 sgn; 34 !; 6 ?; 71 ^) % ( 111 :; 0 !>; 0 ?*) % ( 0 @-; 0 @+) % SPC : TH0_THM_EQU_NAR % Comments : % Bugfixes : v5.4.0 - Added missing axioms for symmetry of B %------------------------------------------------------------------------------ %----Include embedding of quantified multimodal logic in simple type theory include('Axioms/LCL013^0.ax'). %------------------------------------------------------------------------------ thf(a1,type,( a1: $i > $i > $o )). thf(a2,type,( a2: $i > $i > $o )). thf(a3,type,( a3: $i > $i > $o )). thf(jan,type,( jan: mu )). thf(piotr,type,( piotr: mu )). thf(cola,type,( cola: mu )). thf(pepsi,type,( pepsi: mu )). thf(beer,type,( beer: mu )). thf(likes,type,( likes: mu > mu > $i > $o )). thf(very_much_likes,type,( very_much_likes: mu > mu > $i > $o )). thf(possibly_likes,type,( possibly_likes: mu > mu > $i > $o )). thf(axiom_a1_1,axiom, ( mvalid @ ( mbox @ a1 @ ( likes @ jan @ cola ) ) )). thf(axiom_a1_2,axiom, ( mvalid @ ( mbox @ a1 @ ( likes @ piotr @ pepsi ) ) )). thf(axiom_a1_3,axiom, ( mvalid @ ( mforall_ind @ ^ [X: mu] : ( mbox @ a1 @ ( mimplies @ ( mdia @ a1 @ ( likes @ X @ pepsi ) ) @ ( likes @ X @ cola ) ) ) ) )). thf(axiom_a1_4,axiom, ( mvalid @ ( mforall_ind @ ^ [X: mu] : ( mbox @ a1 @ ( mimplies @ ( mdia @ a1 @ ( likes @ X @ cola ) ) @ ( likes @ X @ pepsi ) ) ) ) )). thf(axiom_a2_1,axiom, ( mvalid @ ( mbox @ a2 @ ( likes @ jan @ pepsi ) ) )). thf(axiom_a2_2,axiom, ( mvalid @ ( mbox @ a1 @ ( likes @ piotr @ cola ) ) )). thf(axiom_a2_3,axiom, ( mvalid @ ( mbox @ a1 @ ( likes @ piotr @ beer ) ) )). thf(axiom_a2_4,axiom, ( mvalid @ ( mforall_ind @ ^ [X: mu] : ( mbox @ a2 @ ( mimplies @ ( likes @ X @ pepsi ) @ ( likes @ X @ cola ) ) ) ) )). thf(axiom_a2_5,axiom, ( mvalid @ ( mforall_ind @ ^ [X: mu] : ( mbox @ a2 @ ( mimplies @ ( likes @ X @ cola ) @ ( likes @ X @ pepsi ) ) ) ) )). thf(axiom_a3_1,axiom, ( mvalid @ ( mbox @ a3 @ ( likes @ jan @ cola ) ) )). thf(axiom_a3_2,axiom, ( mvalid @ ( mdia @ a3 @ ( likes @ piotr @ pepsi ) ) )). thf(axiom_a3_3,axiom, ( mvalid @ ( mdia @ a1 @ ( likes @ piotr @ beer ) ) )). thf(axiom_a3_4,axiom, ( mvalid @ ( mforall_ind @ ^ [X: mu] : ( mforall_ind @ ^ [Y: mu] : ( mbox @ a3 @ ( mimplies @ ( mand @ ( likes @ X @ Y ) @ ( mand @ ( mbox @ a1 @ ( likes @ X @ Y ) ) @ ( mbox @ a2 @ ( likes @ X @ Y ) ) ) ) @ ( very_much_likes @ X @ Y ) ) ) ) ) )). thf(axiom_user_communication_1,axiom, ( mvalid @ ( mforall_ind @ ^ [X: mu] : ( mforall_ind @ ^ [Y: mu] : ( mimplies @ ( mbox @ a3 @ ( very_much_likes @ X @ Y ) ) @ ( very_much_likes @ X @ Y ) ) ) ) )). thf(axiom_user_communication_2,axiom, ( mvalid @ ( mforall_ind @ ^ [X: mu] : ( mforall_ind @ ^ [Y: mu] : ( mimplies @ ( mdia @ a3 @ ( very_much_likes @ X @ Y ) ) @ ( likes @ X @ Y ) ) ) ) )). thf(axiom_user_communication_3,axiom, ( mvalid @ ( mforall_ind @ ^ [X: mu] : ( mforall_ind @ ^ [Y: mu] : ( mimplies @ ( mdia @ a1 @ ( likes @ X @ Y ) ) @ ( possibly_likes @ X @ Y ) ) ) ) )). thf(axiom_user_communication_4,axiom, ( mvalid @ ( mforall_ind @ ^ [X: mu] : ( mforall_ind @ ^ [Y: mu] : ( mimplies @ ( mdia @ a2 @ ( likes @ X @ Y ) ) @ ( possibly_likes @ X @ Y ) ) ) ) )). thf(axiom_user_communication_5,axiom, ( mvalid @ ( mforall_ind @ ^ [X: mu] : ( mforall_ind @ ^ [Y: mu] : ( mimplies @ ( mdia @ a3 @ ( likes @ X @ Y ) ) @ ( possibly_likes @ X @ Y ) ) ) ) )). thf(axioms_B_a1,axiom, ( msymmetric @ a1 )). thf(axioms_B_a2,axiom, ( msymmetric @ a2 )). thf(axioms_B_a3,axiom, ( msymmetric @ a3 )). thf(axioms_D_a1,axiom, ( mserial @ a1 )). thf(axioms_D_a2,axiom, ( mserial @ a2 )). thf(axioms_D_a3,axiom, ( mserial @ a3 )). thf(subrel,type,( subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o )). thf(subrel_def,definition, ( subrel = ( ^ [R1: $i > $i > $o,R2: $i > $i > $o] : ! [X: $i,Y: $i] : ( ( R1 @ X @ Y ) => ( R2 @ X @ Y ) ) ) )). thf(axiom_I_a1_a2,axiom, ( subrel @ a1 @ a2 )). thf(axiom_I_a1_a3,axiom, ( subrel @ a1 @ a3 )). thf(axiom_I_a2_a3,axiom, ( subrel @ a2 @ a3 )). thf(cond4s,type,( cond4s: ( $i > $i > $o ) > ( $i > $i > $o ) > $o )). thf(cond4s_def,definition, ( cond4s = ( ^ [R1: $i > $i > $o,R2: $i > $i > $o] : ! [U: $i,V: $i,W: $i] : ( ( ( R1 @ U @ V ) & ( R2 @ V @ W ) ) => ( R2 @ U @ W ) ) ) )). thf(axioms_Is_a1_a1,axiom, ( cond4s @ a1 @ a1 )). thf(axioms_Is_a1_a2,axiom, ( cond4s @ a1 @ a2 )). thf(axioms_Is_a1_a3,axiom, ( cond4s @ a1 @ a3 )). thf(axioms_Is_a2_a1,axiom, ( cond4s @ a2 @ a1 )). thf(axioms_Is_a2_a2,axiom, ( cond4s @ a2 @ a2 )). thf(axioms_Is_a2_a3,axiom, ( cond4s @ a2 @ a3 )). thf(axioms_Is_a3_a1,axiom, ( cond4s @ a1 @ a1 )). thf(axioms_Is_a3_a2,axiom, ( cond4s @ a2 @ a2 )). thf(axioms_Is_a3_a3,axiom, ( cond4s @ a3 @ a3 )). thf(axioms_5_a1,axiom, ( meuclidean @ a1 )). thf(axioms_5_a2,axiom, ( meuclidean @ a2 )). thf(axioms_5_a3,axiom, ( meuclidean @ a3 )). thf(conj,conjecture, ( mvalid @ ( mexists_ind @ ^ [X: mu] : ( mexists_ind @ ^ [Y: mu] : ( possibly_likes @ X @ Y ) ) ) )). %------------------------------------------------------------------------------