LEGAL RELATIONS Learning Program
by Layman E. Allen and Sandra L. Bartlett


Equivalent
Level 0, Level 1, and Level n LEGAL RELATIONS

Overview

Level 0 (LR.0): Deontic LEGAL RELATIONS
Deontic Sets
Negation of Deontic Sets

Level 1 (LR.1.C): CONDITIONAL LEGAL RELATIONS
CONDITIONAL Deontic Sets
Negation of CONDITIONAL Deontic Sets

Level 1 (LR.1.P): POWER (Capacitive) LEGAL RELATIONS
POWER Sets
Negation of POWER Sets

Level n LEGAL RELATIONS
Level n CONDITIONAL LEGAL RELATIONS
Level n POWER LEGAL RELATIONS

Symbols

┌─► LRa
└─► LRb
means LEGAL RELATION LRa is equivalent to LEGAL RELATION LRb.


┌─◄ ┌─► LRq
│ └─► LRr
│    
└─► ┌─► LRu
  └─► LRv
means IF the top pair of LEGAL RELATIONS are equivalent, THEN the bottom pair of LEGAL RELATIONS are equivalent.


Sets of Equivalent Level 0 (LR.0): Deontic LEGAL RELATIONS

Deontic Sets

 Notation Versions    Abbreviations
┌─►p1_DUTY_p2_state  ┌─►1D2s
├─►p2_RIGHT_p1_state  ├─►2R1s
├─►NOT(p1_PRIVILEGE_p2_NOTstate)  ├─►N1PV2Ns
├─►NOT(p2_NO-RIGHT_p1_state)  ├─►N2N-R1s
├─►OBLIGATORY((state_DONE-BY_p1)_DONE-FOR_p2)  ├─►O_(sD21)D42
└─►OBLIGATORY((state_DONE-FOR_p2)_DONE-BY_p1)  └─►O_(sD42)D21
 
 Text Versions    
┌─►Person1 has a DUTY to person2 to bring about the state of affairs.
├─►Person2 has a RIGHT that person1 bring about the state of affairs.
├─►IT IS NOT SO THAT person1 has a PRIVILEGE with respect to person2 to NOT bring about the state of affairs
├─►IT IS NOT SO THAT person2 has a NO-RIGHT that person1 bring about the state of affairs.
├─►IT IS OBLIGATORY THAT state of affairs DONE-BY person1 is DONE-FOR person2.
└─►IT IS OBLIGATORY THAT state of affairs DONE-FOR person2 is DONE-BY person1.
 
 
 Notation Versions    Abbreviations
┌─►p1_DUTY_p2_NOTstate  ┌─►1D2Ns
├─►p2_RIGHT_p1_NOTstate  ├─►2R1Ns
├─►NOT(p1_PRIVILEGE_p2_state)  ├─►N1PV2s
├─►NOT(p2_NO-RIGHT_p1_NOTstate)  ├─►N2N-R1Ns
├─►OBLIGATORY((NOTstate_DONE-BY_p1)_DONE-FOR_p2)  ├─►O_(NsD21)D42
└─►OBLIGATORY((NOTstate_DONE-FOR_p2)_DONE-BY_p1)  └─►O_(NsD42)D21
 
 Text Versions    
┌─►Person1 has a DUTY to person2 to NOT bring about the state of affairs.
├─►Person2 has a RIGHT that person1 NOT bring about the state of affairs.
├─►IT IS NOT SO THAT person1 has a PRIVILEGE with respect to person2 to bring about the state of affairs
├─►IT IS NOT SO THAT person2 has a NO-RIGHT that person1 NOT bring about the state of affairs.
├─►IT IS OBLIGATORY THAT NOT state of affairs DONE-BY person1 is DONE-FOR person2.
└─►IT IS OBLIGATORY THAT NOT state of affairs DONE-FOR person2 is DONE-BY person1.
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Negation of Deontic Sets

 Notation Versions    Abbreviations
┌─►NOT(p1_DUTY_p2_state)  ┌─►N1D2s
├─►NOT(p2_RIGHT_p1_state)  ├─►N2R1s
├─►p1_PRIVILEGE_p2_NOTstate  ├─►1PV2Ns
├─►p2_NO-RIGHT_p1_state  ├─►2N-R1s
├─►NOT(OBLIGATORY((state_DONE-BY_p1)_DONE-FOR_p2))  ├─►NO_(sD21)D42
└─►NOT(OBLIGATORY((state_DONE-FOR_p2)_DONE-BY_p1))  └─►NO_(sD42)D21
 
 Text Versions    
┌─►IT IS NOT SO THAT person1 has a DUTY to person2 to bring about the state of affairs.
├─►IT IS NOT SO THAT person2 has a RIGHT that person1 bring about the state of affairs.
├─►Person1 has a PRIVILEGE with respect to person2 to NOT bring about the state of affairs
├─►Person2 has a NO-RIGHT that person1 bring about the state of affairs.
├─►IT IS NOT SO THAT IT IS OBLIGATORY THAT state of affairs DONE-BY person1 is DONE-FOR person2.
└─►IT IS NOT SO THAT IT IS OBLIGATORY THAT state of affairs DONE-FOR person2 is DONE-BY person1.
 
 
 Notation Versions    Abbreviations
┌─►NOT(p1_DUTY_p2_NOTstate)  ┌─►N1D2Ns
├─►NOT(p2_RIGHT_p1_NOTstate)  ├─►N2R1Ns
├─►p1_PRIVILEGE_p2_state  ├─►1PV2s
├─►p2_NO-RIGHT_p1_NOTstate  ├─►2N-R1Ns
├─►NOT(OBLIGATORY((NOTstate_DONE-BY_p1)_DONE-FOR_p2))  ├─►NO_(NsD21)D42
└─►NOT(OBLIGATORY((NOTstate_DONE-FOR_p2)_DONE-BY_p1))  └─►NO_(NsD42)D21
 
 Text Versions    
┌─►IT IS NOT SO THAT person1 has a DUTY to person2 to NOT bring about the state of affairs.
├─►IT IS NOT SO THAT person2 has a RIGHT that person1 NOT bring about the state of affairs.
├─►Person1 has a PRIVILEGE with respect to person2 to bring about the state of affairs
├─►Person2 has a NO-RIGHT that person1 NOT bring about the state of affairs.
├─►IT IS NOT SO THAT IT IS OBLIGATORY THAT NOT state of affairs DONE-BY person1 is DONE-FOR person2.
└─►IT IS NOT SO THAT IT IS OBLIGATORY THAT NOT state of affairs DONE-FOR person2 is DONE-BY person1.
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Sets of Equivalent Level 1 (LR.1.C): CONDITIONAL LEGAL RELATIONS

CONDITIONAL Deontic Sets

 Notation Versions    Abbreviations
┌─►CONDc(p1_DUTY_p2_state)  ┌─►Cc1D2s
├─►CONDc(p2_RIGHT_p1_state)  ├─►Cc2R1s
├─►CONDc(NOT(p1_PRIVILEGE_p2_NOTstate))  ├─►CcN1PV2Ns
├─►CONDc(NOT(p2_NO-RIGHT_p1_state))  ├─►CcN2N-R1s
├─►CONDc(OBLIGATORY((state_DONE-BY_p1)_DONE-FOR_p2))  ├─►CcO_(sD21)D42
└─►CONDc(OBLIGATORY((state_DONE-FOR_p2)_DONE-BY_p1))  └─►CcO_(sD42)D21
 
 Text Versions    
┌─►CONDITIONAL (realized upon fulfillment of condition c)
│   person1 has a DUTY to person2 to bring about the state of affairs.
├─►CONDITIONAL (realized upon fulfillment of condition c)
│   person2 has a RIGHT that person1 bring about the state of affairs.
├─►CONDITIONAL (realized upon fulfillment of condition c)
│   IT IS NOT SO THAT person1 has a PRIVILEGE with respect to person2 to
│   NOT bring about the state of affairs
├─►CONDITIONAL (realized upon fulfillment of condition c)
│   IT IS NOT SO THAT person2 has a NO-RIGHT that person1 bring about the state of affairs.
├─►CONDITIONAL (realized upon fulfillment of condition c)
│   IT IS OBLIGATORY THAT state of affairs DONE-BY person1 is DONE-FOR person2.
└─►CONDITIONAL (realized upon fulfillment of condition c)
   IT IS OBLIGATORY THAT state of affairs DONE-FOR person2 is DONE-BY person1.
 
 
 Notation Versions    Abbreviations
┌─►CONDc(p1_DUTY_p2_NOTstate)  ┌─►Cc1D2Ns
├─►CONDc(p2_RIGHT_p1_NOTstate)  ├─►Cc2R1Ns
├─►CONDc(NOT(p1_PRIVILEGE_p2_state))  ├─►CcN1PV2s
├─►CONDc(NOT(p2_NO-RIGHT_p1_NOTstate))  ├─►CcN2N-R1Ns
├─►CONDc(OBLIGATORY((NOTstate_DONE-BY_p1)_DONE-FOR_p2))  ├─►CcO_(NsD21)D42
└─►CONDc(OBLIGATORY((NOTstateDONE-FOR_p2)_DONE-BY_p1))  └─►CcO_(NsD42)D21
 
 Text Versions    
┌─►CONDITIONAL (realized upon fulfillment of condition c)
│   person1 has a DUTY to person2 to NOT bring about the state of affairs.
├─►CONDITIONAL (realized upon fulfillment of condition c)
│   person2 has a RIGHT that person1 NOT bring about the state of affairs.
├─►CONDITIONAL (realized upon fulfillment of condition c)
│   IT IS NOT SO THAT person1 has a PRIVILEGE with respect to person2 to bring about the state of affairs.
├─►CONDITIONAL (realized upon fulfillment of condition c)
│   IT IS NOT SO THAT person2 has a NO-RIGHT that person1 NOT bring about the state of affairs.
├─►CONDITIONAL (realized upon fulfillment of condition c)
│   IT IS OBLIGATORY THAT NOT state of affairs DONE-BY person1 is DONE-FOR person2.
└─►CONDITIONAL (realized upon fulfillment of condition c)
   IT IS OBLIGATORY THAT NOT state of affairs DONE-FOR person2 is DONE-BY person1.
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Negation of CONDITIONAL Deontic Sets

 Notation Versions    Abbreviations
┌─►NOT(CONDc(p1_DUTY_p2_state))  ┌─►NCc1D2s
├─►NOT(CONDc(p2_RIGHT_p1_state))  ├─►NCc2R1s
├─►NOT(CONDc(NOT(p1_PRIVILEGE_p2_NOTstate)))  ├─►NCcN1PV2Ns
├─►NOT(CONDc(NOT(p2_NO-RIGHT_p1_state)))  ├─►NCcN2N-R1s
├─►NOT(CONDc(OBLIGATORY((state_DONE-BY_p1)_DONE-FOR_p2)))  ├─►NCcO_(sD21)D42
└─►NOT(CONDc(OBLIGATORY((state_DONE-FOR_p2)_DONE-BY_p1)))  └─►NCcO_(sD42)D21
 
 Text Versions    
┌─►IT IS NOT SO THAT CONDITIONAL (realized upon fulfillment of condition c)
│   person1 has a DUTY to person2 to bring about the state of affairs.
├─►IT IS NOT SO THAT CONDITIONAL (realized upon fulfillment of condition c)
│   person2 has a RIGHT that person1 bring about the state of affairs.
├─►IT IS NOT SO THAT CONDITIONAL (realized upon fulfillment of condition c)
│   IT IS NOT SO THAT person1 has a PRIVILEGE that person2 NOT bring about the state of affairs.
├─►IT IS NOT SO THAT CONDITIONAL (realized upon fulfillment of condition c)
│   IT IS NOT SO THAT person2 has a NO-RIGHT that person1 bring about the state of affairs.
├─►IT IS NOT SO THAT CONDITIONAL (realized upon fulfillment of condition c)
│   IT IS OBLIGATORY THAT state of affairs DONE-BY person1 is DONE-FOR person2.
└─►IT IS NOT SO THAT CONDITIONAL (realized upon fulfillment of condition c)
   IT IS OBLIGATORY THAT state of affairs DONE-FOR person2 is DONE-BY person1.
 
 
 Notation Versions    Abbreviations
┌─►NOT(CONDc(p1_DUTY_p2_NOTstate))  ┌─►NCc1D2Ns
├─►NOT(CONDc(p2_RIGHT_p1_NOTstate))  ├─►NCc2R1Ns
├─►NOT(CONDc(NOT(p1_PRIVILEGE_p2_state)))  ├─►NCcN1PV2s
├─►NOT(CONDc(NOT(p2_NO-RIGHT_p1_NOTstate)))  ├─►NCcN2N-R1Ns
├─►NOT(CONDc(OBLIGATORY((NOTstate_DONE-BY_p1)_DONE-FOR_p2)))  ├─►NCcO_(NsD21)D42
└─►NOT(CONDc(OBLIGATORY((NOTstate_DONE-FOR_p2)_DONE-BY_p1)))  └─►NCcO_(NsD42)D21
 
 Text Versions    
┌─►IT IS NOT SO THAT CONDITIONAL (realized upon fulfillment of condition c)
│   person1 has a DUTY to person2 to NOT bring about the state of affairs.
├─►IT IS NOT SO THAT CONDITIONAL (realized upon fulfillment of condition c)
│   person2 has a RIGHT that person1 NOT bring about the state of affairs.
├─►IT IS NOT SO THAT CONDITIONAL (realized upon fulfillment of condition c)
│   IT IS NOT SO THAT person1 has a PRIVILEGE that person2 bring about the state of affairs.
├─►IT IS NOT SO THAT CONDITIONAL (realized upon fulfillment of condition c)
│   IT IS NOT SO THAT person2 has a NO-RIGHT that person1 NOT bring about the state of affairs.
├─►IT IS NOT SO THAT CONDITIONAL (realized upon fulfillment of condition c)
│   IT IS OBLIGATORY THAT NOT state of affairs DONE-BY person1 is DONE-FOR person2.
└─►IT IS NOT SO THAT CONDITIONAL (realized upon fulfillment of condition c)
   IT IS OBLIGATORY THAT NOT state of affairs DONE-FOR person2 is DONE-BY person1.
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Sets of Equivalent Level 1 (LR.1.P): POWER (Capacitive) LEGAL RELATIONS

POWER Sets

 Notation Versions   Abbreviations
┌─►p1_POWER_LRa  ┌─►1_P_LRa
├─►LRa_LIABILITY_p1   ├─►LRa_LB_1
├─►NOT(p1_DISABILITY_LRa)                                                        ├─►N1_DB_LRa
└─►NOT(LRa_IMMUNITY_p1)  └─►N(LRa_I_1)
 
 Text Versions    
┌─►Person1 has POWER to create LEGAL RELATION LRa.
├─►LEGAL RELATION LRa has LIABILITY of being created by person1.
├─►IT IS NOT SO THAT
│   person1 has a DISABILITY to create LEGAL RELATION LRa.
└─►IT IS NOT SO THAT
   LEGAL RELATION LRa has IMMUNITY from being created by person1.
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Negation of POWER Sets

 Notation Versions    Abbreviations
┌─►NOT(p1_POWER_LRa)  ┌─►N1_P_LRa
├─►NOT(LRa_LIABILITY_p1)  ├─►N(LRa_LB_1)
├─►p1_DISABILITY_LRa                                                            ├─►1_DB_LRa
└─►LRa_IMMUNITY_p1  └─►LRa_I_1
 
 Text Versions    
┌─►IT IS NOT SO THAT
│   person1 has POWER to create LEGAL RELATION LRa.
├─►IT IS NOT SO THAT
│   LEGAL RELATION LRa has LIABILITY of being created by person1.
├─►Person1 has a DISABILITY to create LEGAL RELATION LRa.
└─►LEGAL RELATION LRa has IMMUNITY from being created by person1.
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Level n LEGAL RELATIONS

Level n CONDITIONAL LEGAL RELATIONS

    Notation Versions                          Abbreviations
┌─◄ ┌─► LRa  ┌─◄ ┌─►LRa
│   └─► LRb  │   └─►LRb
│          │        
└─► ┌─► CONDc(LRa)  └─► ┌─►CcLRa
    └─► CONDc(LRb)      └─►CcLRb
IF LRa is equivalent to LRb,
THEN CONDcLRa is equivalent to CONDcLRb.
IF LRa is equivalent to LRb,
THEN CcLRa is equivalent to CcLRb.
 
    Text Versions      
┌─◄ ┌─► LEGAL RELATION LRa
│   └─► LEGAL RELATION LRb
│                   
└─► ┌─► CONDITIONAL (realized upon fulfillment of condition c) LEGAL RELATION LRa
    └─► CONDITIONAL (realized upon fulfillment of condition c) LEGAL RELATION LRb
IF LEGAL RELATION LRa is equivalent to LEGAL RELATION LRb,
THEN CONDITIONAL (realized upon fulfillment of condition c) LEGAL RELATION LRa is equivalent to CONDITIONAL (realized upon fulfillment of condition c) LEGAL RELATION LRb.
 
 
Example 1       
    Notation Versions       Abbreviations
┌─◄ ┌─► p3_POWER_CONDc1(p2_DUTY_p1_state)  ┌─◄ ┌─►3_P_Cc12D1s
│   └─► p3_POWER_CONDc2(p1_RIGHT_p2_state)  │   └─►3_P_Cc21R2s
│          │        
└─► ┌─► CONDc3(p3_POWER_CONDc1(p2_DUTY_p1_state))  └─► ┌─►Cc33_P_Cc12D1s
    └─► CONDc3(p3_POWER_CONDc2(p1_RIGHT_p2_state))      └─►Cc33_P_Cc21R2s
 
    Text Versions      
┌─◄ ┌─► Person3 has POWER to create CONDITIONAL (realized upon fulfillment of condition c1)
│   │   person2 has a DUTY to person1 to bring about the state of affairs.
│   └─► Person3 has POWER to create CONDITIONAL (realized upon fulfillment of condition c2)
│       person1 has a RIGHT that person2 bring about the state of affairs.
│                   
└─► ┌─► CONDITIONAL (realized upon fulfillment of condition c3)
   │   person3 has POWER to create CONDITIONAL (realized upon fulfillment of condition c1)
   │   person2 has a DUTY to person1 to bring about the state of affairs.
    └─► CONDITIONAL (realized upon fulfillment of condition c3)
      person3 has POWER to create CONDITIONAL (realized upon fulfillment of condition c2)
      person1 has a RIGHT that person2 bring about the state of affairs.
 
 
Example 2       
    Notation Versions       Abbreviations
┌─◄ ┌─► CONDc1(p3_POWER_p2_DUTY_p1_state)  ┌─◄ ┌─►Cc13_P_2D1s
│   └─► CONDc2(p3_POWER_p1_RIGHT_p2_state)  │   └─►Cc23_P_1R2s
│          │        
└─► ┌─► CONDc3(CONDc1(p3_POWER_p2_DUTY_p1_state))  └─► ┌─►Cc3Cc13_P_2D1s
    └─► CONDc3(CONDc2(p3_POWER_p1_RIGHT_p2_state))      └─►Cc3Cc23_P_1R2s
 
    Text Versions      
┌─◄ ┌─► CONDITIONAL (realized upon fulfillment of condition c1) person3 has a POWER to create
│   │   person2 has a DUTY to person1 to bring about the state of affairs.
│   └─► CONDITIONAL (realized upon fulfillment of condition c2)person3 has a POWER to create
│       person1 has a RIGHT that person2 bring about the state of affairs.
│                   
└─► ┌─► CONDITIONAL (realized upon fulfillment of condition c3)
   │   CONDITIONAL (realized upon fulfillment of condition c1) person3 has a POWER to create
   │   person2 has a DUTY to person1 to bring about the state of affairs.
    └─► CONDITIONAL (realized upon fulfillment of condition c3)
      CONDITIONAL (realized upon fulfillment of condition c2) person3 has a POWER to create
      person1 has a RIGHT that person2 bring about the state of affairs.
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Level n POWER LEGAL RELATIONS

    Notation Versions                      Abbreviations
┌─◄ ┌─► LRa  ┌─◄ ┌─►LRa
│   └─► LRb  │   └─►LRb
│          │        
└─► ┌─► p1_POWER_LRa  └─► ┌─►1_P_LRa
    └─► p1_POWER_LRb      └─►1_P_LRb
IF LRa is equivalent to LRb,
THEN p1_POWER_LRa is equivalent to p1_POWER_LRb.		 IF LRa is equivalent to LRb,
THEN 1_P_LRa is equivalent to 1_P_LRb.
 
    Text Versions   
┌─◄ ┌─► LEGAL RELATION LRa
│   └─► LEGAL RELATION LRb
│                   
└─► ┌─► Person1 has POWER to create LEGAL RELATION LRa.
    └─► Person1 has POWER to create LEGAL RELATION LRb.
IF LEGAL RELATION LRa is equivalent to LEGAL RELATION LRb, THEN
person1 has POWER to create LEGAL RELATION LRa is equivalent to
person1 has POWER to create LEGAL RELATION LRb.
 
 
Example 1       
    Notation Versions       Abbreviations
┌─◄ ┌─► p3_POWER_CONDc1(p2_DUTY_p1_state)  ┌─◄ ┌─►3_P_Cc12D1s
│   └─► p3_POWER_CONDc2(p1_RIGHT_p2_state)  │   └─►3_P_Cc21R2s
│          │        
└─► ┌─► p4_POWER_p3_POWER_CONDc1(p2_DUTY_p1_state)  └─► ┌─►4_P_3_P_Cc12D1s
    └─► p4_POWER_p3_POWER_CONDc2(p1_RIGHT_p2_state)      └─►4_P_3_P_Cc21R2s
 
    Text Versions      
┌─◄ ┌─► Person3 has POWER to create CONDITIONAL (realized upon fulfillment of condition c1)
│   │   person2 has a DUTY to person1 to bring about the state of affairs.
│   └─► Person3 has POWER to create CONDITIONAL (realized upon fulfillment of condition c2)
│       person1 has a RIGHT that person2 bring about the state of affairs.
│                   
└─► ┌─► Person4 has POWER to create
    │   person3 has POWER to create CONDITIONAL (realized upon fulfillment of condition c1)
    │   person2 has a DUTY to person1 to bring about the state of affairs.
    └─► Person4 has POWER to create
      person3 has POWER to create CONDITIONAL (realized upon fulfillment of condition c2)
      person1 has a RIGHT that person2 bring about the state of affairs.
 
 
Example 2       
    Notation Versions       Abbreviations
┌─◄ ┌─► CONDc1(p3_POWER_p2_DUTY_p1_state)  ┌─◄ ┌─►Cc13_P_2D1s
│   └─► CONDc2(p3_POWER_p1_RIGHT_p2_state)  │   └─►Cc23_P_1R2s
│          │        
└─► ┌─► p4_POWER_CONDc1(p3_POWER_p2_DUTY_p1_state)  └─► ┌─►4_P_Cc13_P_2D1s
    └─► p4_POWER_CONDc2(p3_POWER_p1_RIGHT_p2_state)      └─►4_P_Cc23_P_1R2s
 
    Text Versions      
┌─◄ ┌─► CONDITIONAL (realized upon fulfillment of condition c1) person3 has a POWER to create
│   │   person2 has a DUTY to person1 to bring about the state of affairs.
│   └─► CONDITIONAL (realized upon fulfillment of condition c2)person3 has a POWER to create
│       person1 has a RIGHT that person2 bring about the state of affairs.
│                   
└─► ┌─► Person4 has POWER to create
   │   CONDITIONAL (realized upon fulfillment of condition c1) person3 has a POWER to create
   │   person2 has a DUTY to person1 to bring about the state of affairs.
    └─► Person4 has POWER to create
      CONDITIONAL (realized upon fulfillment of condition c2) person3 has a POWER to create
      person1 has a RIGHT that person2 bring about the state of affairs.
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