# Issue 357: FOL representation for shortcuts

Closing the issue 276, the sig assigned HW to CEO to check all shortcuts FOL formulation.

Heraklion, October 2018

posted by CEO on 10/1/2018

<HW>

Dear all

I searched for 'shortcut, and picked out all property definition containing the term. The attached file contains all these. Of course, not all contain shortcut defintions, but I have kept them in the file for reference. For the properties being defined as short cuts, I have added a FOL-definition and also done som minor corrections in the scope note.

I have formulated the FOL descriptions as definintions:

P8(x,y) ≡ ($z)[E53(z) ˄ P7(x,z) ˄ P156(y,z)]

By doing so I have assumed that all the short cuts are strong, which they are with a few exceptions, for example

P7(x,y) ≡ ($z)[ E2(x) ∧ E53(z) ∧ P161(x,z) ˄ P89(z,y)]

Since P161 has a superclass of E4 Period as domain, we have to add the E2(x) clause to ensure implication from right to left. If the clause is dropped the shortcut is of the ? type in (not strong, not weak).

In the 41st joined meeting of the CIDOC CRM SIG and ISO/TC46/SC4/WG9 and the 34th FRBR - CIDOC CRM Harmonization meeting, CEO has been assigned with checking all shortcuts FOL formulation.

Lyon, May 2018

posted by Christian Emil on 21/10/2019

Dear all

Here is the homework of ISSUE .

Best,

Christian-Emil

The number of shortcuts has changed due to deprecation of properties and a few new. The eventual change of E4 isa E92 to a property etc, will result in 4 new shortcuts marked as red text below. One existing shortcut has to be redefined, marked in read as well.

In the long discussion of formalizing shortcuts in FOL, the two terms strong shortcut and weak shortcut were introduce. A shortcut is weak when the existence of a long path implies an instance of the shortcut. In a graph the instantiation of the long path should automatically introduce a triple for the shortcut. It should be noted that there can be more than one instantiation of a long path.

A strong shortcut is a weak shortcut where the instantiation of the shortcut implies the existence of a long path. As long as the long path need not to be unique, I think this is ok in FOL. However, this may contradict the open world view ad also the timelessness of some properties like P1, P2. To make things simple I have defined all shortcuts as weak shortcuts. That is, the long path implies the short.

I have removed the “declaration” of class for intermediate nodes in the path where these are implied from the propertydefintion:

P105(x,y) ⊂ [E30(z) ˄ P104(x,z) ˄ P75(y,z)] becomes P105(x,y) ⊂ [P104(x,z) ˄ P75(y,z)]

since P104(x,z) ⊃ E30(z) and also P75(y,z) ⊃ E30(z).

The CRMbase document has no FOL description of the shortcuts. In 2015 when we started this work the intension was to add a line to those properties that are shortcuts, e.g.

In First Order Logic:

P105(x,y) ⊃ E72(x)

P105(x,y) ⊃ E39(y)

Shortcut: P105(x,y) ⊂ [ P104(x,z) ˄ P75(y,z)]

To add this is pure editorial work, the sig should just decide yes or no.

1. P1 is identified by (identifies), is a shortcut for the path from ‘E1 CRM Entity’ through ‘P140i was attributed by’, ‘E15 Identifier Assignment’, ‘P37 assigned’,‘E42 Identifier’, ‘P139 has alternative form’ to ‘E41 Appellation’.

P1(x,y) ⊂ [P140(z.x) ˄ P141(z,y)]

2. P2: Type assignment events allow a more detailed path from ‘E1 CRM Entity’ through ‘P41i was classified by’, ‘E17 Type Assignment’, ‘P42 assigned’, to ‘E55 Type’ for assigning types to objects compared to the shortcut offered by P2 has type (is type of).

P2(x,y) ⊂ )[ P41(z.x) ˄ P42(z,y)]

3. [P7 took place at (witnessed)] It is a shortcut of the more fully developed path from E4 Period through P161 has spatial projection, E53 Place, P89 falls within to E53 Place. E4 Period is a subclass of E92 Spacetime Volume. By the definition of P161 has spatial projection an instance of E4 Period takes place on all its spatial projections, that is, instances of E53 Place. Something happening at a given place can also be considered to happen at a larger place containing the first. For example, the assault on the Bastille July 14th 1789 took place in the area covered by Paris in 1789 but also in the area covered by France in 1789.

P7(x,y) ⊂ [E4(x) ˄ P161(x,z) ˄ P89(z,y)]

P7(x,y) ⊂ [Pyyy(x,w) ˄ P161(w,z) ˄ P89(z,y)]

4. P8 took place on or within (witnessed) is a shortcut of the more fully developed path from ‘E4 Period’ through ‘P7 took place at’, ‘E53 Place’, ‘P156i is occupied by’, to ‘E18 Physical Thing’

P8(x,y) ⊂ [P7(x,z) ˄ P156(y,z)]

5. [P9 consists of (forms part of)] This property associates an instance of E4 Period with another instance of E4 Period that is defined by a subset of the phenomena that define the former. Therefore the spacetime volume of the latter must fall within the spacetime volume of the former.P9 consists of (forms part of) shortcut of long path via E92 STV

P9(x,y) ⊂ [Pyyy(x,z) ˄ P132(z,w) ˄ Pyyy(y,w) ]

6. P43: It is a shortcut of the more fully developed path from ‘E70 Thing’ through ‘P39 measured’, ‘E16 Measurement’, ‘P40 observed dimension’, to ‘E54 Dimension’. It offers no information about how and when an E54 Dimension was established, nor by whom.

P43(x,y) ⊂ [P39(z,x) ˄ P40(z,y)]

7. P44: It is a shortcut of the more fully developed path from ‘E18 Physical Thing’ through ‘P34 concerned’, ‘E14 Condition Assessment’, ‘P35 has identified’, to ‘E3 Condition State’. It offers no information about how and when the E3 Condition State was established, nor by whom.

P44(x,y) ⊂ [P34(z,x) ˄ P35(z,y)]

8. P46 is composed of (forms part of) shortcut via E92 Spacetime Volume

P46(x,y) ⊂ [E92(z) ˄ P92(w) ˄ Pxxx(x,z) ˄ P132(z,w) ˄ Pxxx(y,w)]

9. P49 has former or current keeper (is former or current keeper of) is a shortcut for the more detailed path from ‘E18 Physical Thing’ through ‘P30 transferred custody of’, ‘E10 Transfer of Custody’, ‘P28 custody surrendered by’ or ‘P29 custody received by’ to ‘ E39 Actor’.

P49(x,y) ⊂ [P30(z,x) ˄ [P28(z,y) ˅ P29(z,y) ]]

10. P50 has current keeper (is current keeper of) is a shortcut for the more detailed path from ‘E18 Physical Thing’ through, ‘P30i custody transferred through’, ‘E10 Transfer of Custody’, ‘P29 custody received by’ ,to ‘E39 Actor’.

P50(x,y) ⊂ [P30(z,x) ˄ P29(z,y)]

11. P51 has former or current owner (is former or current owner of) is a shortcut for the more detailed path from ‘E18 Physical Thing’ through ‘P24i changed ownership through’, ‘E8 Acquisition’, ‘P23 transferred title from’, or ‘P22 transferred title to’,to ‘E39 Actor.’

P51(x,y) ⊂ [P24(z,x) ˄ [P23(z,y) ˅ P22(z,y) ]]

12. P52 has current owner (is current owner of) is a shortcut for the more detailed path from ‘E18 Physical Thing through’, ‘P24i changed ownership through, ‘E8 Acquisition’, ‘P22 transferred title to’, to ‘E39 Actor’, if and only if this acquisition event is the most recent.

P52(x,y) ⊂ [P24(z,x) ˄ P22(z,y) ]

13. P53 has former or current location (is former or current location of) is a shortcut. A more detailed representation can make use of the fully developed (i.e. indirect) path from ‘E19 Physical Object’, though, ‘P25i moved by’, ‘E9 Move’, ‘P26 moved to’ or ‘P27 moved from’, to ‘ E53 Place’.

P53(x,y) ⊂ [P25(z,x) ˄ [P26(z,y) ˅ P27(z,y) ]]

14. P55 has current location (currently holds) is a shortcut. A more detailed representation can make use of the fully developed (i.e. indirect) path from ‘E19 Physical Object’,through, ‘P25i moved by’, ‘E9 Move’, ‘P26 moved to’, to, ‘E53 Place’if and only if this Move is the most recent

P55(x,y) ⊂ [P25(z,x) ˄ P26(z,y)]

15. P56 bears feature (is found on) is a shortcut. A more detailed representation can make use of the fully developed (i.e. indirect) path ‘E19 Physical Object’,through, ‘P59 has section’, ‘E53 Place’, ‘P53i is former or current location of’, to, ‘E26 Physical Feature’.

P56(x,y) ⊂ [P59(x,z) ˄ P53(y,z)]

16. [P62 depicts (is depicted by)]This property is a shortcut of the more fully developed path from E24 Physical Human-Made Thing through P65 shows visual item, E36 Visual Item, P138 represents, E1CRM Entity. P138.1 mode of representation “depiction” allows the nature of the depiction to be refined.

P62(x,y) ⊂ [P65(x,z) ˄ P138(z,y)]

17. P105 right held by (has right on) is a shortcut of the fully developed path E72 Legal Object,P104 is subject to, E30 Right, P75i is possessed by, E39 Actor.

P105(x,y) ⊂ [P104(x,z) ˄ P75(y,z)]

18. [P107 has current or former member (is current or former member of)] This property is a shortcut of the more fully developed path E74 Group, P144i gained member by, E85 Joining, P143 joined , E39 Actor

P107(x,y) ⊂ [P107(x,y) ˄ E55(z)]

19. [P152 has parent (is parent of)] This property is, among others, a shortcut of the fully developed paths from ‘E21Person’ through ‘P98i was born’, ‘E67 Birth’, ‘P96 by mother’ to ‘E21 Person’, and from ‘E21Person’ through ‘P98i was born’, ‘E67 Birth’, ‘P97 from father’ to ‘E21 Person’.

P152(x,y) ⊂ [E67(z) ˄ [P98(z,x) ˄ P96(z,y) ˅ P98(z,x) ˄ P97(z,y)]]

20. P156 occupies is a shortcut via E92 Spacetime Volume

P156(x,y) ⊂ [Pxxx(x,z) ˄ P161(z,y)]

21. P164 during (was time-span of) shortcut via E92 Spacetime Volume

P164(x,y) ⊂ [Pyyy(x,z) ˄ P161(z,w)]

22. [P167 at (was place of) ] It is a shortcut of the more fully developed path from E93 Presence through P161 has spatial projection, E53 Place, P89 falls within (contains) to E53 Place.

P167(x,y) ⊂ [E93(x) ˄ P161(x,z) ˄ P89(z,y)]

23. P171 at some place within is a shortcut of the fully developed path E53 Place, P89 falls within, E53 Place, P168 place is defined by, E94 Space Primitive through a not represented declarative Place as defined in CRMgeo (Doerr and Hiebel 2013) to a Space Primitive

P171(x,y) ⊂ [P89(x,z) ˄ P168(z,y)]

24. [P172 contains] This property is a shortcut of the fully developed path: E53 Place, P89i contains, E53 Place, P168 place is defined by, E94 Space Primitive

P172(x,y) ⊂ [P89(z,x) ˄ P168(z,y)]

Posted by Mark Fichtner on 24/10/2019

Am Mo., 21. Okt. 2019 um 18:57 Uhr schrieb Christian-Emil Smith Ore <c.e.s.ore@iln.uio.no>:

Dear all

Here is the homework of ISSUE .

Best,

Christian-Emil

The number of shortcuts has changed due to deprecation of properties and a few new. The eventual change of E4 isa E92 to a property etc, will result in 4 new shortcuts marked as red text below. One existing shortcut has to be redefined, marked in read as well.

In the long discussion of formalizing shortcuts in FOL, the two terms strong shortcut and weak shortcut were introduce. A shortcut is weak when the existence of a long path implies an instance of the shortcut. In a graph the instantiation of the long path should automatically introduce a triple for the shortcut. It should be noted that there can be more than one instantiation of a long path.

A strong shortcut is a weak shortcut where the instantiation of the shortcut implies the existence of a long path. As long as the long path need not to be unique, I think this is ok in FOL. However, this may contradict the open world view ad also the timelessness of some properties like P1, P2. To make things simple I have defined all shortcuts as weak shortcuts. That is, the long path implies the short.

I have removed the “declaration” of class for intermediate nodes in the path where these are implied from the propertydefintion:

I don't think that this is a good thing to do as due to open world assumption it will be misleading. It will be "smarter" for interns like us, but more difficult for externals. Furthermore the scope note becomes less complete by that.

P105(x,y) ⊂ [E30(z) ˄ P104(x,z) ˄ P75(y,z)] becomes P105(x,y) ⊂ [P104(x,z) ˄ P75(y,z)]

since P104(x,z) ⊃ E30(z) and also P75(y,z) ⊃ E30(z).

The CRMbase document has no FOL description of the shortcuts. In 2015 when we started this work the intension was to add a line to those properties that are shortcuts, e.g.

In First Order Logic:

P105(x,y) ⊃ E72(x)

P105(x,y) ⊃ E39(y)

Shortcut: P105(x,y) ⊂ [ P104(x,z) ˄ P75(y,z)]

To add this is pure editorial work, the sig should just decide yes or no.

1. P1 is identified by (identifies), is a shortcut for the path from ‘E1 CRM Entity’ through ‘P140i was attributed by’, ‘E15 Identifier Assignment’, ‘P37 assigned’,‘E42 Identifier’, ‘P139 has alternative form’ to ‘E41 Appellation’.

P1(x,y) ⊂ [P140(z.x) ˄ P141(z,y)]

The naming is difficult and I don't understand your solution in any way...... I usually would propose:

P1(x,a) ⊂ [P140(y,x) ˄ E15(y) ^ P37(y,z) ^ E42(z) ^ P139(z,a) ^ E41(a) ]

or easier using i for inverse:

P1(x,a) ⊂ [P140i(x,y) ˄ E15(y) ^ P37(y,z) ^ E42(z) ^ P139(z,a) ^ E41(a)]

or following your logic:

P1(x,a) ⊂ [P140(y,x) ^ P37(y,z) ^ P139(z,a) ]

2. P2: Type assignment events allow a more detailed path from ‘E1 CRM Entity’ through ‘P41i was classified by’, ‘E17 Type Assignment’, ‘P42 assigned’, to ‘E55 Type’ for assigning types to objects compared to the shortcut offered by P2 has type (is type of).

P2(x,y) ⊂ )[ P41(z.x) ˄ P42(z,y)]

P2(x,y) ⊂ [ P41(z,x) ˄ P42(z,y)] is ok - I would prefer P2(x,y) ⊂ [ P41(z,x) ˄ P42(z,y) ^ E17(z)] or P2(x,y) ⊂ [ P41i(x,z) ˄ P42(z,y) ^ E17(z)]

3. [P7 took place at (witnessed)] It is a shortcut of the more fully developed path from E4 Period through P161 has spatial projection, E53 Place, P89 falls within to E53 Place. E4 Period is a subclass of E92 Spacetime Volume. By the definition of P161 has spatial projection an instance of E4 Period takes place on all its spatial projections, that is, instances of E53 Place. Something happening at a given place can also be considered to happen at a larger place containing the first. For example, the assault on the Bastille July 14th 1789 took place in the area covered by Paris in 1789 but also in the area covered by France in 1789.

P7(x,y) ⊂ [E4(x) ˄ P161(x,z) ˄ P89(z,y)]

P7(x,y) ⊂ [Pyyy(x,w) ˄ P161(w,z) ˄ P89(z,y)]

I really have a bad feeling with the scope note here. What is described here is not the typical shortcut but an implication or a rule. I guess these should be handled differently. Furthermore this is probably not precise enough as the part with "E53 Place, P89 falls within, E53 Place" is transitive - I don't know how to express that in an easy way here and I don't think that there is an easy way to do that with FOL at all.

Nethertheless:

P7(x,y) ⊂ [E4(x) ˄ P161(x,z) ˄ P89(z,y)] is ok - I would prefer P7(x,y) ⊂ [E4(x) ˄ P161(x,z) ˄ E53(z) ^ P89(z,y) ^ E53(y)]

4. P8 took place on or within (witnessed) is a shortcut of the more fully developed path from ‘E4 Period’ through ‘P7 took place at’, ‘E53 Place’, ‘P156i is occupied by’, to ‘E18 Physical Thing’

P8(x,y) ⊂ [P7(x,z) ˄ P156(y,z)]

Fully agree on P8(x,y) ⊂ [P7(x,z) ˄ P156(y,z)]

more developed: P8(x,y) ⊂ [P7(x,z) ˄ E53(z) ^ P156(y,z)]

inverse: P8(x,y) ⊂ [P7(x,z) ˄ E53(z) ^ P156i(z,y)]

5. [P9 consists of (forms part of)] This property associates an instance of E4 Period with another instance of E4 Period that is defined by a subset of the phenomena that define the former. Therefore the spacetime volume of the latter must fall within the spacetime volume of the former.P9 consists of (forms part of) shortcut of long path via E92 STV

P9(x,y) ⊂ [Pyyy(x,z) ˄ P132(z,w) ˄ Pyyy(y,w) ]

Thats rather the same problem as with 3.

6. P43: It is a shortcut of the more fully developed path from ‘E70 Thing’ through ‘P39 measured’, ‘E16 Measurement’, ‘P40 observed dimension’, to ‘E54 Dimension’. It offers no information about how and when an E54 Dimension was established, nor by whom.

P43(x,y) ⊂ [P39(z,x) ˄ P40(z,y)]

Agree on P43(x,y) ⊂ [P39(z,x) ˄ P40(z,y)]

Longer: P43(x,y) ⊂ [P39(z,x) ˄ E16(z) ^ P40(z,y)]

Inverse: P43(x,y) ⊂ [P39i(x,z) ˄ E16(z) ^ P40(z,y)]

As P39 is defined with Range E1 the question is also if we want to specify here that we need to be more specific here. Although this follows from the definition of P43 anyway it may be good to state it again (as it does not follow from the definition of P39), leading to:

P43(x,y) ⊂ [E70(x) ^ P39(z,x) ˄ E16(z) ^ P40(z,y)]

7. P44: It is a shortcut of the more fully developed path from ‘E18 Physical Thing’ through ‘P34 concerned’, ‘E14 Condition Assessment’, ‘P35 has identified’, to ‘E3 Condition State’. It offers no information about how and when the E3 Condition State was established, nor by whom.

P44(x,y) ⊂ [P34(z,x) ˄ P35(z,y)]

Agree on P44(x,y) ⊂ [P34(z,x) ˄ P35(z,y)]

Longer: P44(x,y) ⊂ [P34(z,x) ˄ E14(z) ^ P35(z,y)]

Inverse: P44(x,y) ⊂ [P34i(x,z) ˄ E14(z) ^ P35(z,y)]

8. P46 is composed of (forms part of) shortcut via E92 Spacetime Volume

P46(x,y) ⊂ [E92(z) ˄ P92(w) ˄ Pxxx(x,z) ˄ P132(z,w) ˄ Pxxx(y,w)]

9. P49 has former or current keeper (is former or current keeper of) is a shortcut for the more detailed path from ‘E18 Physical Thing’ through ‘P30 transferred custody of’, ‘E10 Transfer of Custody’, ‘P28 custody surrendered by’ or ‘P29 custody received by’ to ‘ E39 Actor’.

P49(x,y) ⊂ [P30(z,x) ˄ [P28(z,y) ˅ P29(z,y) ]]

Agree on P49(x,y) ⊂ [P30(z,x) ˄ [P28(z,y) ˅ P29(z,y) ]]

Longer: P49(x,y) ⊂ [P30(z,x) ˄ E18(z) ^ [P28(z,y) ˅ P29(z,y) ]]

Inverse: P49(x,y) ⊂ [P30i(x,z) ˄ E18(z) ^ [P28(z,y) ˅ P29(z,y) ]]

10. P50 has current keeper (is current keeper of) is a shortcut for the more detailed path from ‘E18 Physical Thing’ through, ‘P30i custody transferred through’, ‘E10 Transfer of Custody’, ‘P29 custody received by’ ,to ‘E39 Actor’.

P50(x,y) ⊂ [P30(z,x) ˄ P29(z,y)]

Agree on P50(x,y) ⊂ [P30(z,x) ˄ P29(z,y)]

Longer: P50(x,y) ⊂ [P30(z,x) ˄ E10(z) ^ P29(z,y)]

Inverse: P50(x,y) ⊂ [P30i(x,z) ˄ E10(z) ^ P29(z,y)]

11. P51 has former or current owner (is former or current owner of) is a shortcut for the more detailed path from ‘E18 Physical Thing’ through ‘P24i changed ownership through’, ‘E8 Acquisition’, ‘P23 transferred title from’, or ‘P22 transferred title to’,to ‘E39 Actor.’

P51(x,y) ⊂ [P24(z,x) ˄ [P23(z,y) ˅ P22(z,y) ]]

Agree on P51(x,y) ⊂ [P24(z,x) ˄ [P23(z,y) ˅ P22(z,y) ]]

Longer: P51(x,y) ⊂ [P24(z,x) ˄ E8(z) ^ [P23(z,y) ˅ P22(z,y) ]]

Inverse: P51(x,y) ⊂ [P24i(x,z) ˄ E8(z) ^ [P23(z,y) ˅ P22(z,y) ]]

Too much work to be this detailed without knowing if it is relevant, so I skip it from now on as I mostly agree on the parts below here.

12. P52 has current owner (is current owner of) is a shortcut for the more detailed path from ‘E18 Physical Thing through’, ‘P24i changed ownership through, ‘E8 Acquisition’, ‘P22 transferred title to’, to ‘E39 Actor’, if and only if this acquisition event is the most recent.

P52(x,y) ⊂ [P24(z,x) ˄ P22(z,y) ]

Yes

13. P53 has former or current location (is former or current location of) is a shortcut. A more detailed representation can make use of the fully developed (i.e. indirect) path from ‘E19 Physical Object’, though, ‘P25i moved by’, ‘E9 Move’, ‘P26 moved to’ or ‘P27 moved from’, to ‘ E53 Place’.

P53(x,y) ⊂ [P25(z,x) ˄ [P26(z,y) ˅ P27(z,y) ]]

Yes

14. P55 has current location (currently holds) is a shortcut. A more detailed representation can make use of the fully developed (i.e. indirect) path from ‘E19 Physical Object’,through, ‘P25i moved by’, ‘E9 Move’, ‘P26 moved to’, to, ‘E53 Place’if and only if this Move is the most recent

P55(x,y) ⊂ [P25(z,x) ˄ P26(z,y)]

Yes

15. P56 bears feature (is found on) is a shortcut. A more detailed representation can make use of the fully developed (i.e. indirect) path ‘E19 Physical Object’,through, ‘P59 has section’, ‘E53 Place’, ‘P53i is former or current location of’, to, ‘E26 Physical Feature’.

P56(x,y) ⊂ [P59(x,z) ˄ P53(y,z)]

Yes

16. [P62 depicts (is depicted by)]This property is a shortcut of the more fully developed path from E24 Physical Human-Made Thing through P65 shows visual item, E36 Visual Item, P138 represents, E1CRM Entity. P138.1 mode of representation “depiction” allows the nature of the depiction to be refined.

P62(x,y) ⊂ [P65(x,z) ˄ P138(z,y)]

Yes

17. P105 right held by (has right on) is a shortcut of the fully developed path E72 Legal Object,P104 is subject to, E30 Right, P75i is possessed by, E39 Actor.

P105(x,y) ⊂ [P104(x,z) ˄ P75(y,z)]

Yes

18. [P107 has current or former member (is current or former member of)] This property is a shortcut of the more fully developed path E74 Group, P144i gained member by, E85 Joining, P143 joined , E39 Actor

P107(x,y) ⊂ [P107(x,y) ˄ E55(z)]

Yes

19. [P152 has parent (is parent of)] This property is, among others, a shortcut of the fully developed paths from ‘E21Person’ through ‘P98i was born’, ‘E67 Birth’, ‘P96 by mother’ to ‘E21 Person’, and from ‘E21Person’ through ‘P98i was born’, ‘E67 Birth’, ‘P97 from father’ to ‘E21 Person’.

P152(x,y) ⊂ [E67(z) ˄ [P98(z,x) ˄ P96(z,y) ˅ P98(z,x) ˄ P97(z,y)]]

Why do you have the E67(z) here and nowhere else? I am unsure with the brackets here, I would prefer:

P152(x,y) ⊂ [E67(z) ˄ P98(z,x) ˄ [P96(z,y) ˅ P97(z,y)]]

20. P156 occupies is a shortcut via E92 Spacetime Volume

P156(x,y) ⊂ [Pxxx(x,z) ˄ P161(z,y)]

We will see ;)

21. P164 during (was time-span of) shortcut via E92 Spacetime Volume

P164(x,y) ⊂ [Pyyy(x,z) ˄ P161(z,w)]

We will see, too.

22. [P167 at (was place of) ] It is a shortcut of the more fully developed path from E93 Presence through P161 has spatial projection, E53 Place, P89 falls within (contains) to E53 Place.

P167(x,y) ⊂ [E93(x) ˄ P161(x,z) ˄ P89(z,y)]

All the below are the same as 3 again - I am unsure here.

23. P171 at some place within is a shortcut of the fully developed path E53 Place, P89 falls within, E53 Place, P168 place is defined by, E94 Space Primitive through a not represented declarative Place as defined in CRMgeo (Doerr and Hiebel 2013) to a Space Primitive

P171(x,y) ⊂ [P89(x,z) ˄ P168(z,y)]

24. [P172 contains] This property is a shortcut of the fully developed path: E53 Place, P89i contains, E53 Place, P168 place is defined by, E94 Space Primitive

P172(x,y) ⊂ [P89(z,x) ˄ P168(z,y)]