Can we connect with FOL or Second Order Logic the reification construct of E13 Attribute Assignment and S4 Observation with the named graph construction of I1 Argumentation?
posted by Martin on 2/12/2016
In the 37th joined meeting of the CIDOC CRM SIG and ISO/TC46/SC4/WG9 and the 30th FRBR - CIDOC CRM Harmonization meeting, it was assigned to Christian -Emil to analyze and see if FOL representation is possible between the E13 Attribute Assignment and S4 Observation with the named graph construction of I1 Argumentation and also it was noted that a link is needed between the temporal constraint belief and the argumentation that motivated it.
Berlin, December 2016
Posted by Christian Emil on 27/3/2017
Issue 322: Can we connect with FOL or Second Order Logic the reification construct of E13 Attribute Assignment and S4 Observation with the named graph construction of I1 Argumentation? (posted by Martin on 2/12/2016 ) and assigned to CEO.
The problem seems to boil down to the lack of a generic way to identify sets of CRM statements on the logical level. In this rather long text I have tried to clarify the issue for myself (at least). I have not reached a satisfying solution. I may have tried to solve another question than the issue which is somewaht looseluy specified. It would be nice with a discussion about this issue.
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Conclusion
In CRM we can make statements about instances of classes identified with unique identifiers (see 2 CRM in First Order Logic (FOL)) in this text. However, we cannot make statements about statements, that is, pair of instances connected by a property. This is also true for FOL interpretations of CRM.
The CRM statements in an instance of a E13 reification (E39, E13, P140, P140 , etc) can be modeled as an instance of I4 Proposition Set. Similar for S4 Observation. In an FOL-KB interpretation of CRM(Sci/Inf) the instance of I4 will be identified with a unique identifier, say n. In an RDF(S) implementation this identifier, n, can be used to name the corresponding graph. Therefore we can use the belief construct to assign a truth value to this instance of I4 identified with the name n of the graph for the reification construct.
The self-reference used Kurt Gödel in his famous theorem involved an encoding trick, that is, a systematic way to enumerate terms, predicates, propositions etc. Then it was possible to construct a self-referencing proposition.
We can interpret CRM statements as named (RDF) graphs and use the name of a graph as the identifier for the corresponding instance of I4. This is a similar trick to that of Gödel (mutatis muntandis) enabling higher order statements. But it corresponds to writing down the CRM statements on a paper, give the paper a unique identification number and then use this number as an identifier for the instance of I4 representing the information carried by the paper.
A better solution would of course be to create an enumeration function for creating unique identifiers for all finite sets of CRM statements.
Then it may be possible to identify an E13 construct as a given instance of I4.
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My notes
1 The class E13 Attribute assignment
‘E13 Attribute assignment’ was introduced quite early in the development of CRM as an alternative to the basic reification of property instances found in RDF. It is a very general construct consisting of a class E13 Attribute assignment (subclass of E7 Activity) and two properties:
P140 assigned attribute to (was attributed by): E1 CRM Entity
P141 assigned (was assigned by): E1 CRM Entity
The construct can be used to reify instances of all properties in CRM and declare connection of some type between instances of all pairs of class in CRM.
In CRM E13 Attribute Assignment is specialized into four subclasses representing
· E14 Condition Assessment
· E15 Identifier Assignment
· E16 Measurement
· E17 Type Assignment
The four subclasses represent declarative events we usually do not think of as reification. Perhaps all declarative events in CRM should be subclasses of E13 Attribute Assignment, (for example E8 Acquisition, but this is irrelevant here).
An instance of E13 Attribute Assignment fixes in time when a given relation was declared. This construct does in general not give any information about extent in time the relation is valid. The only exception is the E14 Condition Assessment where an instance of E3 Condition State (subclass of E2 Temporal Entity) is assigned to an instance of E18 Physical Thing. The corresponding instance of Ε3 Condition State must occur in time before the instance of E14 Condition Assessment since we cannot foresee the future. This is the opposite of the I1 Argumentation construct found in CRMInf, see below.
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2 CRM in First Order Logic (FOL)
Roughly, the FOL representation of CRM consists of axioms constructed from the definition of CRM. The axioms will have universally quantified variables. The concrete instances of the classes in CRM are represented as names. The facts are the axioms where the (universally quantified/free) variables are replaced by the names. In a KB (Knowledge Base) K the set of axioms is called the TBOX of K and the set of facts the ABOX of K. The names denote real world objects. In different interpretations (models of the theory) the names can denote different real world objects (physical, abstract, temporal entities).
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3 Implementation
Information organized compliant with CRM can be implemented in RDF(S). An RDF(S) based CRM Knowledge Base is one among many possible implementations (models) for a FOL description of CRM. By implementation (model) is meant that there is a mapping from the valid terms in the CRM-FOL KB into the content of the triplestore/graph database preserving the validity of axioms and terms resulting from the use of deduction rules. The names representing instances of classes will be names/URIs and literals and the terms will be graphs.
In RDF it is possible to give names to (sub) graphs. Through its name a graph can be used as subject or object in an RDF-triple. The named graph mechanism is extremely powerful. Seen from a CRM-FOL point of view, the named graph mechanism is on the implementation level and does not have a counterpart in the CRM-FOL description. In FOL it is not possible to quantify over predicates or terms, that is, a variable can never be instantiated by a predicate.
One should remember that this is a (important) detail on the implementation level and not a mechanism expressed at the logical (FOL) level. From the logical/formal ontological level, named graphs may or may not make implementations easier.
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4 Names and identifiers in CRM
In CRM all class instances can be given zero or many appellations (instances of E41 Appellation) or identifiers (instances of E42 Identifier) through the property P1 Identifies. These names and identifiers are on the real world descriptive level. That is, an instance of E42 Identifier will typically be a shelf mark, an inventory number, ISBN, or a URL:
“This class comprises strings or codes assigned to instances of E1 CRM Entity in order to identify them uniquely and permanently within the context of one or more organisations. Such codes are often known as inventory numbers, registration codes, etc. and are typically composed of alphanumeric sequences. The class E42 Identifier is not normally used for machine-generated identifiers used for automated processing unless these are also used by human agents.”
From “the Formalization of CRM – first attempt 2015 by Carlo Meghini Martin Doerr:
“ The individuals in the domain of the CRM are 1) CRM-entities which includes appellations and 2) primitive values.
The CRM models these individuals as objects, identified by object identifiers. We note tht the CRM identifiers have the following features: 1) at any time, each identifier denotes only one object 2) at any time, no two identifiers denote the same object 3) each identifier denotes the same object throughout the whole KB lifetime”
In an instance of a CRM KB the object identifiers are on a meta level and not necessarily instances of E42 Identifier identifying the object through P2.
5 The CRMInf class I1 Argumentation
Instances of I1 Argumentation is used to express that an actor believes/declares/concludes that a given set of propositions (an instance of I4 Proposition Set) is true, false, probable, etc. (an instance of E6 Belief value) for a certain amount of time given by an instance of I2 Belief, a subclass of E2 Temporal Entity. The classes and properties involved are
I1 Argumentation
J2 concluded that (was concluded by) I2 Belief
I2 Belief (subclass of E2 Temporal Entity)
J4 that (is subject of) I4 Proposition Set
J5 holds to be I6 Belief Value
I4 Proposition Set (subclass of E73 Information Object)
The construct (I1 Argumentation, I2 Belief, I6 Belief Value, and I4 Proposition Set) is different from E13 Attribute assignment. It states that someone at a given point in time (timespan) conclude that from this point (directly after the timespan ends) and onwards (for a given time) the actor in question believes that a given set of propositions has a given truth value.
The class I4 Proposition Set is identified as
“This class comprises the sets of formal, binary propositions that an I2 Belief is held about. It could be implemented as a named graph, a spreadsheet or any other structured data-set. Regardless of the specific syntax employed, the effective propositions it contains should be made up of unambiguous identifiers, concepts of a formal ontology and constructs of logic”
The example from the CRMInf definition of I4:
“Type 29 bowls are from the 1st Century AD (expressed as CRM statements)”
can be modeled as instances of I4 Proposition Set. So can the statements in representing an E13 Attribute assignment, e.g. the examples from the definition of P140, P141 in CRM 6.2.2):
“01 June 1997 Identifier Assignment of the silver cup donated by Martin Doerr (E15) assigned attribute to silver cup 232 (E19)
01 June 1997 Identifier Assignment of the silver cup donated by Martin Doerr (E15) assigned object identifier 232”
6 The CRMSci class S4 Observation
The class S4 is a subclass of E13 Attribute assignment and the properties O8 observed and O8 observed value are subproperties of P140 assigned attribute to and P141 assigned respectively:
S4 Observation
Subclass of: E13 Attribute Assignment
(Subclass of I4 Argumentation when CRMInf is included)
O8 observed (was observed by): S15 Observable Entity (subproperty of P140)
O9 observed property type (property type was observed by): S9 Property Type
O16 observed value (value was observed by): E1 CRM Entity (subproperty of P141)
7 The Issue 322
The issue is formulated as “Can we connect with FOL or Second Order Logic the reification construct of E13 Attribute Assignment and S4 Observation with the named graph construction of I1 Argumentation?”
In CRM we can make statements about instances of classes identified with unique identifiers (see 2 CRM in First Order Logic (FOL)) in this text. However, we cannot make statements about statements, that is, pair of instances connected by a property. This is also true for FOL interpretations of CRM.
The CRM statements in an instance of a E13 reification (E39, E13, P140, P140 , etc) can be modeled as an instance of I4 Proposition Set. Similar for S4 Observation. In an FOL-KB interpretation of CRM(Sci/Inf) the instance of I4 will be identified with a unique identifier, say n. In an RDF(S) implementation this identifier, n, can be used to name the corresponding graph. Therefore we can use the belief construct to assign a truth value to this instance of I4 identified with the name n of the graph for the reification construct..
The self-reference used Kurt Gödel in his famous theorem involved an encoding trick, that is, a systematic way to enumerate terms, predicates, propositions etc. Then it was possible to construct a self-referencing proposition.
We can interpret CRM statements as named (RDF) graphs and use the name of a graph as the identifier for the corresponding instance of I4. This is a similar trick to that of Gödel (mutatis muntandis) enabling higher order statements. It corresponds to write down the CRM statements on a paper, give the paper a unique identification number and then use this number as an identifier for the instance of I4 representing the information carried by the paper. A better solution would be to create an enumeration function for creating unique identifiers for all finite sets of CRM statements.
In the 38th joined meeting of the CIDOC CRM SIG and ISO/TC46/SC4/WG9 and the 31st FRBR - CIDOC CRM Harmonization meeting, the crm-sig discussed CEO’s email that I1 is subclass of E13 but does not use or reference its properties and made the following comments:
- To put a type on E13 which references the properties, so that you can specify the relation attributed
- Either delete E13 or get this logical formulation.
- Could there be an automated inference that would translate E13 to I1 and vice versa?
- Need logical representation of named graphs at instance level.
- It is needed a named graph logic specialist
HW is assigned to CEO, Carlo for logical representation of named graphs at instance level.
Heraklion, April 2017
In the 40th joined meeting of the CIDOC CRM SIG and ISO/TC46/SC4/WG9 and the 33nd FRBR - CIDOC CRM Harmonization meeting, the crm-sig discussed about the old HW assignment of Carlo and CEO for logical representation of named graphs at instance level.
In the flow of this discussion a comment was posed about “how to describe what can be observed”. It is accepted that what we observe is actually a ‘situation’ a bundle of properties. So class ‘observable entity’ is wrong. It is needed a logical construct that certain kinds of things can be result of an observation
HW assigned to CEO to communicate with Carlo in order to follow up the proposed by Carlo First Order Theory for the representation of named graphs at instance level. Achilles’ reading example in CRMtex (TX5 Reading) is good starting point.
Cologne, January 2018
In the 53rd CIDOC CRM & 46th FRBRoo SIG meeting, CEO gave a brief summary of the state of the issue. He personally thinks that connecting the reification construct of E13 Attribute Assignment and S4 Observation with the named graph construction of I1 Argumentation should not be dealt with in SO Logic. Could be done in other logical systems. He will turn in this HW in time for the meeting in Rome.
HW: CEO
May 2022
In the 54th CIDOC CRM & 47th FRBR/LRMoo SIG Meeting, Martin Doerr gave an overview of the issue. The idea is that an Attribute Assignment essentially talks about a single property instance, which forms a parallel to pointing to a named graph that contains one property instance. I1 Argumentation which results in an instance of I2 Belief cannot be a subclass of E13. There is also a problem with S4 Observation if the reification construct deals with more than one property simultaneously (what is now referred to as Situation).
An open-ended discussion followed, where Christian-Emil Ore maintained that the CRM set of properties that are equivalent to a named graph can be represented as a set of propositions and the connection between them in FOL. One can always name that and say that the predicate “X” stands for a proposition, in CRM an instance of E89. On the other hand, the scope note of I4 Proposition Set explicitly refers to binary propositions and formal ontology concepts, which seems too restrictive. Logical constructs does not specify the order or mode of the logical system the statements are expressed in. This could yield propositions that are incompatible with the CRM. The scope note needs redrafting.
The idea is that CRMinf can be connected to CRM compatible knowledge base through such statements. As CRMinf stands now, it seems that many things that we regard as premises and conclusions won’t be formulated in properties that have been defined in a formal ontology. In general, the scope of CRMinf should be broader than what can now be expressed. The reference to name graphs should explicitly only leave room for named graphs that contain 1+ property instances alone (rather than instances of properties and classes or just the one property instance permitted by E13).
If there are any formalizations in FOL that can be used to declare the E13 reification of a single property as a specific case of a named graph, it would be interesting to look at it.
Decision: close the issue, start a new one, where to redraft the scope note of I4 Proposition Set based on the comments above. “Definition of I4 Proposition Set and what an instance of I2 Belief is about”.
Everyone in agreement. Issue closed.