Knowledge Graph Considered Harmful for Ontology

Abstract

The time of knowledge graph has come. Linked Data is now rephrased to knowledge graph, and no one has doubt on the future of it. However, will the time of ontology come in the next step? There exists a long history of ontology ever since the ancient Greece, and now the terminology has become popular with the advent of OWL. Nevertheless, the ontology does not seem to happen so as Linked Data did. There is a serious gap on the semantic representation between the ontology and the knowledge graph, and the gap originates semantic networks. In this paper, we pursue the history of knowledge representation, point out the serious semantic gap contained in knowledge graph. We propose an alternative representation language for ontological knowledge in Semantic Webs.

Keywords

• New KM
• RDF
• OWL
• knowledge graph
• knowledge representation
• Frame-based
• Case-based

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The purpose of this essay is to cause a stir in the community of Semantics Webs just as Dijkstra did in software engineering.1 It seems that the time of Linked Open Data (LOD) has come. Ones have become to rephrase \Linked Data" to \knowledge graph", since knowledge graph has been used as technical terminology in the domain of semantic search by Google, IBM, etc.. Because the both is roughly the same technology from the technical viewpoint. On the other hand, the term of \ontology" exists ever since the age of ancient Greece, and the engineering of ontologies has been pursued since 1970s as a part of computer science and Arti cial Intelligence, then it has become popular today with OWL. However, we have yet a serious gap between the representation of knowledge graph and ontology. More precisely, we have theoretical, practical, and sociotechnological di culties such as how to understand the subsumption concept described in RDF Semantics [ 2 ] with respect to the ambiguous IS-A concept [ 3, 4 ], how to represent structural link [ 3, 5 ] in the form of knowledge graph, and how to discriminate the notion of class and individual in human mind. 1 See, https://en.wikipedia.org/wiki/Considered_harmful

The following is a fallible example which novices easily fall into erros.2

Wine a owl:Class ; rdfs:subClassOf food:PotableLiquid ; *madeFromGrape WineGrape .

Instead, it should be exactly coded in turtle as follows.

Wine a owl:Class ;

rdfs:subClassOf food:PotableLiquid , [ a owl:Restriction ; owl:onProperty madeFromGrape ; owl:allValuesFrom WineGrape ] .

The cause of this mistake is three fold; rstly, the abstract syntax of RDF (namely RDF graph) does not t to the description of ontologies; secondly, it it hard to understand the concept of subsumption and property inheritance; thirdly, most people are sluggish to study hard, some one tends to take an easier way even if it is impossible to reach the nal goal.

Contrary to the error sentence mentioned above, the following code is completely correct with respect to individuals.

ElyseZinfundel a Zinfundel ;

hasMaker Elyse ; hasSugar Dry.

In this case, Zinfundel is a class, but ElyseZinfundel, Elyse, and Dry are individuals. There is no inheritance on properties. Actually, at the error case shown above, it should be coded with the meanings that every wine (as instance) is made from some wine-grape (as instance), and it must be described at the class level on wine. Otherwise, it is forced to describe the property values on every instances. It should be here noticed that Wine and WineGrape are classes.

Such a kind of problems was involved in the beginning of semantic networks. Woods [ 3 ] pointed out the semantical ambiguity of network links and introduced the distinction of assertional link and structural link. At the nal step of KL-ONE family, Clark developed a knowledge representation language, KM (Knowledge Machine) [ 9, 10 ]. According to the style in KM-like representation, the error sentence mentioned above may be paraphrased into the followings.

Wine is a owl:Class and rdfs:subClassOf food:PotableLiquid . every Wine is madeFromGrape a WineGrape .

Note that these sentences are not English, rather an arti cial knowledge representation language. It is a sort of syntax sugar of the turtle syntax and preserves 2 This example is taken from Wine Ontology [ 6 ], and where an asterisk is attached to the head of wrong lines.

RDF and OWL semantics. We can translate KM-like sentences into turtle sentences, just as turtle sentences can be translated into RDF/XML format without the loss of information.

It is conceived that Description Logics inherited the heritage of semantic networks and frame systems [ 4 ]. In fact, many features of KL-ONE family came into OWL. In this paper, we pursue the history of knowledge representation, speci cally focusing on the development of class notion and subsumption concept, then point out the problem of knowledge graph representation for OWL. Finally, we propose a new representation language, the New KM, a successor of KM by Clark and SWCLOS (Semantic Web processor on top of Common Lisp Object System) [ 11, 12 ].

The rest of this paper is organized as follows. In section 2, we present a brief history of the knowledge representation on semantic networks and frame systems, focusing on class-instance notions and the inheritance concept. section 3 presents an idea of New KM, which is a uni ed successor of KM by Clark and our own Semantic Web Processor, SWCLOS. Finally, we conclude some remarks and the future work. 2 2.1

Historical Views on Knowledge Representation

Semantic Networks to Description Logic and OWL The study of semantic networks was started as an associative link network at 1966 by Quillian's work [ 7, 8 ], for the purpose of making arti cial memory for words and meanings. At the time, such an associative link structure was taken as a rm base in modeling human memory. However, many problems that were involved in such simple networks were soon exposed by many researchers.3 Human epistemology is more complex than the association.

Woods [ 3 ] analyzed the semantics of semantic networks and introduced the distinction between structural links, which present propositional statements on things, and assertional links on assertional relation among things. He addressed the following network structure.

N12368

SUPERC MOD

TELEPHONE BLACK

The meanings of this sentence may be interpreted in two ways. In OWL, it would be written distinctively as follows, into a proposition in TBox (left side) or an assertion in ABox (right side).

N12368 owl:intersectionOf ( TELEPHONE N12368 a TELEPHONE ; hasColor BLACK . 3 The original by Quillian was not so simple as the successors. The original had devices of type, token, plane, and notions of class, subclass, and modi cation. [ 13 ] [ a owl:Restriction ; owl:onProperty hasColor ; owl:hasValue BLACK ] ) .

The former insists the class of black-colored telephone, but the latter asserts the existence of a telephone whose color is accidentally black. On the idea that the notation must be speci ed more precisely, he started the discussion on the problem involved in semantic networks. However, the issues, in the viewpoints at the present, were confused and spread out widely in distinct levels, from semantics to pragmatics, from denotational levels to logical levels.

Up to the mid of 1970s, semantic networks constitute the primer knowledge representation and many attempts revealed that they never lived up to researcher's expectations. Brackman [ 13 ] demonstrated complex semantic networks that contain both conceptual networks and their particulars, and showed special existences a set of links that allows the speci cation of a concept as a set of attribute de nitions in conjunction with a structural interrelation between those attributes, see details in [ 13 ].

At 1979, Brackman [ 14 ] presented a comprehensive survey on semantic networks. He investigated the work by Quillian, Woods, Brackman, Collins, Carbonell, Winston, expanding to Fillmore, Simmons, Hendrix, Rumelhart, Schank, Heidom, Anderson, Shapiro, Cercone, Phillip Hayes, Norman, and Szolovits, then clari ed ve levels of characteristics on semantic networks, \implementational," \logical," \epistemological," \conceptual," and \linguistic" levels. Due to limitations of space, we summarize the result at Table 1. Note that we can capture that

RDFS and OWL fall into epistemological level, which was discovered by Brackman as a missing level in his comprehensive investigation. Usual ontologies that are built using RDFS and OWL are at conceptual level. As an instantiation of such an epistemological level, he advocated more elaborated \Structured Inheritance Networks", in which Role/Filler Description and Structural Description are derived.

Eventually, Brackman [ 15 ] published KL-ONE at 1985, and after that many KL-ONE-ish systems succeeded. They are, as a whole, called KL-ONE family. All systems of KL-ONE family, except KM [ 9, 10 ] is listed at [ 16 ].

The class-instance notion gradually emerged in the development of KLONE family. In the original KL-ONE, the notion of class was the production of a classi er, and did not provide any explicit primitives for the classinstance indication. This situation is carried over Description Logics and OWL. In CLASSIC [ 17 ], the operators for individuals were identical to that for classes, but the function cl-create-ind was provided to create an individual under a CLASSIC-description. Moreover, LOOM [ 18 ] prepared 17 operators (functions/macros/slots) for instances. Ideas of objects and mixin classes were borrowed from CLOS (Common Lisp Object System) and provided the mixininheritance functionality.

KM [ 9, 10 ] is, which is not regarded so, the last system in the line of KL-ONE family in thought. It has a frame-like syntax as well as CLASSIC and LOOM. However, it presented an easier way to encode the inheritance attributes for instances at classes. The following is actual programming code in KM of Buy event.

(every Buy has (buyer ((a Agent))) (object ((a Thing))) (seller ((a Agent))) (money ((the cost of (the object of Self)))) (subevent1 ((a Give with (agent ((the buyer of Self))) (object ((the money of Self))) (rcpt ((the seller of Self)))))) (subevent2 ((a Give with (agent ((the seller of Self))) (object ((the object of Self))) (rcpt ((the buyer of Self))))))) This code axiomatize that two agents appear as buyer and seller, every event of Buy is accompanied by two distinctive Give events in which one event for a buyer the money is received by the buyer, in the other event for a seller the object is received by seller. In the above example, the event money is instantiated as the cost of the event. KM denotes two fundamental types, instances and classes. A class has the extension of the individuals, and properties of individuals of a class are expressed of the form: (every <class> has (<slots1> (<expr11> <expr12> ... )) (<slots2> (<expr21> <expr22> ... )) ...

) Thus, \(every ..." form describes properties for individuals of a class to be inherited in accordance with superclass-subclass relation. On the other hand, the form without \every" but with \superclasses" attribute for classes denotes superclasses of a subjective class with other properties for the class per se. (<class> has (superclasses (<superclass1> <superclas2> ... )) (<slots1> (<expr11> <expr12> ... )) (<slots2> (<expr21> <expr22> ... )) ...

) This grammar greatly reduces the burden of awkward expression in knowledge graph. We propose such a grammar for RDF and OWL in Section 3. 2.2

Frames to RDFS Minsky [ 19 ] published the idea of framework of human cognitive mechanisms at 1974.

We can think of a frame as a network of nodes and relations. The top levels of a frame are xed, and represent things that are always true about the supposed situation. The lower levels have many terminals { slots that must be lled by speci c instances or data. [. . . ] Collections of related frames are linked together into frame-systems. The e ects of important actions are mirrored by transformations between the frames of a system. [Minskey, 1974] As Minsky mentioned in his paper, the basic idea of frame is not his invention and his presentation was not complete, but he pointed out several important notions of frame systems such as sharing terminals, a frame and subframes, variables, attachments, default assignment, and so on. He talked the image of frame-based cognition in many scenes, vision, linguistics, memory acquisition, retrieval of knowledge, and control. Minsky's prevision had become the source of many frame systems after that.

KRL and FRL were the rst two systems embodied Minsky's idea. Especially, Bobrow's KRL[ 20 ] gave some inspiration to KL-ONE family, where the appearance of network disappeared and frame-like forms, e.g., UNIT, appeared. The followings are an example of event description described in KRL. [Event234 UNIT Individual <SELF (a Give with object = (a Pen) giver = (Person2 (which IsHusbandOf Person3)} recipient = Person1)>] [Give UNIT Specialization <SELF (an Event)> <object (a Thing)> <giver (a Person)> <recipient (a Person)>] [Lawyer UNIT Specialization

<SELF (a Person)>] [Pen UNIT Basic

<SELF (a PhysicalObject)>] [Lawyer UNIT Specialization

<SELF (a Person)] [Person1 UNIT Individual

<SELF (a Person with firstName = "David")>] [Person2 UNIT Individual <SELF {(a Person with firstName = "Jonathan")

(which IsHusbandOf Person3)}>] [Person3 UNIT Individual <SELF {(a Person with firstName = "Ellen")

(a Lawyer)}>]

KRL allowed to explicitly express both classes and individuals in a uniform pattern named UNIT. It is obvious that \(a Pen)" denotes an instance of class Pen. The form \(a <class> with <slot-name> = <slot-value>)" indicates an instance of <class> has <slot-value> to the <slot-name> in both class and individual descriptions.

FRL [ 21, 22 ] was an implementation for several representation techniques suggested by Minsky and additional functionalities that are, today, conceived common in frame systems. Namely, local procedure attachments, IF-NEEDED, IF-ADDED, and IF-REMOVED were demonstrated in addition to basic functionalities of default value and inheritance along AKO (a kind of). However, the semantics of the inheritance, which should be turned into the subsumption from the viewpoint of RDF Semantics [ 2 ], is not formalized, whereas it worked practically.

Schank's Memory Organization Package (MOP) [ 23 ] was a very unique package for Case-Based Reasoning (CBR). It is possible to deem it a successor of frame systems, but the most strong impact of MOP on Semantic Webs is that it has made clear the bunch of slots (a set of pairs of property-name and propertyvalue) of an instance de ne the class of the instance. In other words, the intension (slots) decides the extension (class). Actually, we utilized the algorithm of slots->mop in MOP onto building Agriculture Activity Ontology (AAO) [ 24 ] with SWCLOS. However, the MOP has no structural di erence between classes and instances and the actual deference of MOP between them is just the ag for instance/class is true or false.

Common Lisp Object System (CLOS) [ 25, 26 ] is the rst genuine class-based object system, in which the instance object structure is completely di erent from the class object structure, and we need the de nition of a class before the instance object creation. We can de ne Wine class in pure CLOS as follows. (defclass Wine (food:PotableLiquid) ((madeFromGrape :accessor madeFromGrape :type WineGrape)) (:metaclass owl:Class))

Furthermore, if rdfs:label is de ned as slot at the metaclass owl:Class with the meta-object protocol [27], we can add the rdfs:label slot of class Wine meta-object as follows.

(make-instance 'owl:Class :name 'Wine rdfs:label "Wine") 3

A Brief Overview of New Knowledge Machine Along with the progression and popularization of Linked Open Data, more comprehensible and comprehensive tools are required for new entrants from ordinary people. It is easy to write down knowledge graphs at instance levels, but it is di cult to expand the knowledge graph to the ontology. It is obvious that we need new guides who lead starters in LODs to the ontologies. For the purpose of that, we are now tackling to develop a new platform of Semantic Webs that covers from LODs to ontologies. It will be an amalgam of a database for knowledge graph, gently guiding for novices, straight-forward representation of knowledge, etc. In this section, we give rough sketches of several parts of the tools. 3.1

Light Weight Database and Indexing in Knowledge Graph The new platform has an interface to RDF stores, AllegroGraph, Virtuoso, Stardog, and so on. In addition, we have developed an internal graph memory as cache based on DTREE and the uni cation4. It demonstrated that Princeton WordNet [28] was absorbed on memory for the machine of Intel Core i7-4770, 16GB. In this module, we can perform simple information retrievals on one shot via simple pattern matching that is similar to SPARQL queries. 4 See Paradigms of Arti cial Intelligence Programming by Peter Norvig Section 14.8. In addition to domain and range constraints in RDFS, which was already equipped on SWCLOS, we are going to implement exible hierarchical structure adjustment. Schank's MOP provided the functionality of instance adjustment but not class adjustment. We will expand such adjustment to the class level. The rules of instantiation will work e ectively at the class level. We are developing a new KM language for Semantic Webs, which imitates the behavior of Clark's KM. Note that RDF semantics and OWL semantics are strictly preserved in the New KM. Especially, it will allows to represent metalevel ontologies [29] like:

Species is a owl:Class and rdfs:subClassOf owl:Class . EndangeredSpecies is rdfs:subClassOf Species .

Eagle is a owl:Class and is a EndangeredSpecies .

Harry is a Eagle . 4

Conclusion and Future Work This paper introduced a new knowledge representation machine, the New KM, which is a successor of SWCLOS, Schank's MOP, and Clark's KM, and more. It will ease the di culties of entering Linked Open Data and proceeding to ontologies and meta-modeling of ontologies.

This paper pursued the history of knowledge representation from the beginning of semantic networks and frame systems, focusing on the evolution of class-instance notion and the implementation on representation languages. This paper rediscovered the ve levels of semantic networks. We found that the highest level, Linguistic level, in which we can investigate any concepts and words as networks, is left as unexplored domain. The comprehensive platform based on RDF and OWL will be indispensable to build extensive ontologies from comprehensive web resources like Wikipedia, and others. 27. Kiczales, Gregor, Jim des Rivieres, Daniel G. Boblow: The Art of the Meaobject

Protocol, MIT (1991) 28. Koide, Seiji, Hideaki Takeda: RDFization of Japanese Electronic Dictionaries and

LOD, 2nd Workshop on Linked Data in Linguistics (LDL-3024), (2013) 29. Koide, Seiji, Hideaki Takeda: Inquiry into RDF and OWL Semantics, JIST 2016, 25{31, Springer (2016)

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