Associative Networks
- Information Models in Graph Notation

Here are some notations/meta-models for modeling of static semantic/conceptual/information aspects. The Importance of Labeling the Links. [SemNet 294ff] «Associationists from Aristotle to the present day have assumed that there can be an association from one word to another. The set of associations to a given word will contain many members that will differ in strength, and many of the words in the set will themselves be be associatvely related. It is therefore natural to think of words as associated by a network of undifferentiated links varying in strength. ... Although such a network may be explanatorily useful for studies of word association, it is obviously a poor instrument for semantics because a mere associative link from one word to another tells one nothing about the intensional relation between the words. ... The decisive step in converting an associative network into a potential semantic machine was the introduction of labels on the links between words. The importance of representing the relation between entities was recognized by Selz in 1913 (cited by Humphrey, 1951), but Selz lacked an appopriate language in which to make his theory wholly explicit. With the advent of programming languages, and particularly list-processing languages such as IPL abd LISP, the way was clear for the invention of semantic networks. ... LISP allows one to set up a whole series of property names and their specific values associated with a symbolic atom such as poodle ... In describing such information, it is natural to represent it in graphical form: Superordinate Size Dog <-------------- Poodle --------> Small | Hair v Curly Early semantic networks (Qillian, 1968; Raphael, 1968) were probably inspired in part by this feature of IPL and LISP.» Cf. Connectionist networks - they can be seen as associative networks with dynamics (reacting & learning) [cf. Conn 19]. [SemNet] P N Johnson-Laird, D J Herrmann, R Chaffin: Only Connections: A Critque of Semantic Networks; Psychological Bulletin 96(2); APA 1984. [CGPPF] Eileen C Way: Conceptual Graphs - Past, Present, and Future; in Tepfenhart, Dich, Sowa (eds): Conceptual Structures: Current Practices (ICCS'94) LNAI 835.

Class diagrams
A. The class diagrams of the UML classifier box (node) a. Interface b. Class in "stereotypes" «type» «implementationClass» «metaclass» «utility» c. Association class object box (node) a (composite) object association line (edge between classifiers) a type of links association path - - - - connects association class with its association line link (edge between objects) generalization -------|> realizes - - - -|> dependency - - - -> constraint - - - - e.g. {or} constraint
navigation bar: Class Inclusion relations inclusion diagrams in information engineering arrows in class diagrams
B. The type view of the Syntropy modeling notation
C. Betrand Meyer's Business Object Notation (BON) -> Paige, Ostroff: A Comparison of the Business Object Notation and the Unified Modeling Language; York Univ., 1999.

Sowa's Conceptual Graphs (1984 in "Conceptual Structures: Information Processing in Mind and Machine")

-> Conceptual Graphs: fundamental notions (1992) box (node) concepts - represent entities, attributes, states, and events circle (node) relations - show how the concepts are interconnected edge connects a relation and a concept Conceptual graphs are: bi-partite, undirected, non-relational (ie. several edges between the same nodes) «Conceptual graphs form a knowledge representation language based on linguistics, psychology, and philosophy» [Sowa 1984]. «[A] conceptual graph has no meaning in isolation. Only through the semantic network are its concepts and relations linked to context, language, emotion, and perception» [Sowa 1984]. «The very beginning of the theory of conceptual graphs can be traced to a term paper that John Sowa wrote for Marvin Minsky in 1968. ... At that time, Minsky's and Papert's book Perceptrons had just come out, and that plkus articles from Minsky's edited book, Semantic Information Processing were part of the course. Included in the readings were Quillian's classic paper on networks. The only other graph-based representation that influenced Sowa at that time, was Hays' Depdency theory (1964). Sowa ... hit upon the perfect metaphor to express his notion of knowledge representation: Tinker-toys. He wanted a language which contained various formatted blocks that could join and be recombined in different ways to create new structures. ... It was not until the 1970's that Sowa began seriously working on conceptual graphs as a knowledge representation language for database design and development at IBM ... The first published paper on conceptual graphs appeared in 1976 ... The formation rules and graph unification procedure were added at this time, inspired by lectures given at IBM by Alan Robinson. Actor nodes were added to the theory to support database query, and the joins and projections of conceptual graphs were seen as the intensional counterparts of the joins and projections of database relations. ... [T]here was a rule of detachment, which allowed conceptual relations to be removed from a graph. ... However, the inclusion of detachment means that the formation rules are not strictly specialization rules: a graph might be more general after an application of the formation rules than it was before. It was to preserve the specialization property of the canonical formation rules that detachment was [later] replaced with simplification. Simplification will not specialize a graph further, but it will not generalize it. And strict specialization rules are needed to defe a generalization hierarchy. The current form of the rules guarantees that any graph resulting from their application will be either the same or more specialized. [From 1976 to 1984] Sowa discovered and incorporated Pierce's existential graphs, the -calculus for definitions was developed, and the formation rules were changed into the current form.» [CGPPF]

Chen's Entity/Relationship (ER) models & notation

box (node) an entity (type) ellipse (node) an attribute (type/name) multi-arrow an relationship (type/name) triangle (pseudo-node of multi-arrow) makes a relationship explicit other arrows with special meaning ... The original ER is from [Chen 1976]. Several (notational) variants of ER were developed. For example Barker's notation (metamodel of Barker ER in ORM; comparison with ORM) On normal forms: [Scot A. Becker: Data Schema Normalization; Conceptual Modeling 9; June 1999]

Hasse diagrams

node: element of the poset edge between a (higher in the diagram) and b (lower in the diagram): a is larger than b represent partial ordered sets (posets) as a vertically oriented graph

Information Engineering (ER)
[when?] first by Clive Finkelstein in Australia, and CACI in the UK, later by James Martin. [Halpin] [T Halpin: Entity Relationship Modeling from an ORM perspective: Part 3; Conceptual Modeling 13; Apr 2000 navigation bar: Class Inclusion relations inclusion diagrams in information engineering arrows in class diagrams	Notation variants for the subtype relationship

Object-Role-Modelling (ORM)

``ORM originated in the mid-1970s as a semantic modeling method, one of the early versions being NIAM (Natural language Information Analysis Method)'' [ORM1] developed in Europe [see page 6 in T Halpin: Subtyping: conceptual and logical issues; Database Newsletter 23/6]. ``[T]he most popular version of ORM [is] supported in modeling and query tools such as Visio's InfoModeler and ActiveQuery'' [ORM1]. more references: terHofstede one paper (and similars); P. van Bommel, A.H.M. ter Hofstede, and Th.P. van der Weide. Semantics and verification of object-role models. Information Systems, 16(5):471-- 495, October 1991. The meta model: categories of types, entity type & relationship, type & role & relationship

ORM (b) compared to Barker ER (a):

Semantic networks
More text is found below at semantic network theories. A. Quillian's semantic networks of word meaning as a representation of the lexicon (1968) [SemNet] (cf) «Quillian's (1968) theory anticipated most of the features of subsequent semantic networks. He assumed that memory for meaning is no different from memory for perceptual or other nonlinguistic information, and he postulated a semantic network as a model for lexical memory. The network is composed of links between two sorts of nodes: type nodes, which represent concepts, and token nodes, which represent instances of concepts by virtue of the links to their respective type nodes. The meaning of a word is defined by an initital configuration of token nodes attached to the type node representing the word, and each of the token nodes is linked to its respective type node» [SemNet 294ff].
type (node) a concept token (node) instance of a concept token--->type «from a token to its type node» type---->token «from a type to a superordinate token» (eg. "(plant)" ---> "put" [I don't understand this...]) token--->token «from a token to another token representing a modifying property» (eg. "put" ---> "for" «to represent the fact that seeds are put in the ground for them to grow») token--+->token1 `->token2 `->token3 «from a token to a conjunction or disjunction of tokens» (eg. the "object" put by planting is "seed", "plant", or "thing") .->token1 token==| `->token3 «from a token to two other tokens so as to act as a label on a link between them» (eg. object <--in--> earth)	(plant) | v .-> SUBJECT -> person put ==| | | .-----> OBJECT ----+-> seed | `-> IN ==| ^ OR `-> plant | `-> earth | `-> thing v | for --> grow -------------' Example "to plant" (without instance links)
«The amount of information in a network is potentialy so vast that Quillian assumed that facts are stored explicitly only if they cannot be generated from the network. Hence, general information need be represented only at a superordinate level without being attached to all the subordinate nodes to which it applies. ... Poodle --> Dog --> Animal There is no need to represent the fact that a poodle is an animal ...» [SemNet 294ff]. B. Linday, Norman, and Rumelhart's semantic networks (1972) [SemNet] for sentence meaning «The semantic network as we have described it so far constitutes a theory about the organization and processing of the mental lexicon: Representations of words are stored in a network, and the semantic relations between words are represented by labelled links between the items in the network. ... The next major step in the evolution of network theory was to show how the meaning of any sentence could be represented as a semantic network. ... If a sentence uses a verb to establish a relation between the entities denoted by noun phrases, then the semantic representation of the sentence can take the form of a small-scale semantic network that captures the relation (expressed by the verb) between the entities (denoted by the noun phrases). The full semantic representations of the words in the sentence are, of course, encoded separately in the main network corresponding to the mental lexicon.»
concept (node) a concept (not represented by a word, and other than an event), linked by ISA (set inclusion), IS (attributing properties), HAS (attributing proper parts) event (node) an event concept (not event instance) - is linked to actions, actors, and objects involved in the event primary (node) corresponds to a word in the language (Quillian's type) secondary (node) a specific use of a primary token (Quillian's token), or an individual event linked with ACT to event node links [T]he labels on links from nodes are based on the cases (e.g., agent, pbject, recipient) of Fillmore's (1968) Case grammar.	TOUCH ^ time | location isa PAST <-----(touch)--------> p -----> PARK || actor isa |`-----------> h -----> HIPPIE | object isa `------------> d -----> DEBUTANTE Example "In a park a hippie touched a debutante" (with a letter inserted for unlabelled nodes)
Semantic Network Theories The semantic networks described above are theories of the representation of word/sentence meaning. «Such a theory about representation becomes a full-fledged theory of [linguistic] performance only when processes for using the representation ... are specified. Indeed, as Quillian suggested, certain aspects of meaning may be represented by such processes rather than directly in the network. A natural assumption, however, is that when people evaluate the relation between two concepts, they do so by searching through the network for a path between them. Quillian wrote a computer program that operates in this way» [SemNet 294ff]. «First, network theories are designed primarily to elucidate intensional relations, in particular, the relations between the meanings of words. ... Seconds, ... semantic networks are constructed on the assumption that the representation and evaluation of intensional relations can be considered independently from extensional relations ... Third, comprehensive network theories are based on a formalism containing three components: a parser, a semantic memory consisting of a network of links between nodes, and a set of interpretative processes that operate on the network. Intensional relations between ords are represented within the semantic network by labelled links between the nodes. The parser uses this information to construct network representations of sentences. The interpretative processes carry out such tasks as updating the semantic network, making inferences from sentences, and searching the semantic network to establish the intensional properties of expressions and intensional relations between them. ... Fourth. there is a general, although not absolute, commitment to parsimony. If information about the meaning of a word can be inferred by traversing links, then it is not redundantly specified in the network. Hence, general facts can be stored at the level of a superset rather than for each subset to which they apply» [SemNet 302].
1973: Anderson and Bower's Human Associative Memory (HAM). «All the semantic information is represented by the configuration of the links and the labels on them; the nodes themselves have no semantic labels.» Representation of "In a park a hippie touched a debutante" (tree shown left to right, instead of normally top down, and with some mnemonic node labels added):	location isa word .-------------(p)-----(P)------ PARK () time isa word context / `-------------(a)-----(A)------ PAST / () \ subject isa word fact \ .-------------(h)-----(H)------ HIPPIE () \ relation isa word predicate \ .----------(t)-----(T)------ TOUCH () object isa word `----------(d)-----(D)------ DEBUTANTE
1972-1977, «Linday, Norman, and Rumelhart developed a theory of long-term memory and comprehension ...» (cf. description of nodes and links) «Like Quillian, the LNR group assumes that ... general properties are stored at just one node ... However, this generic information is treated as aset of values that can be assumed by default (e.g., typically, birds fly) rather than as necessarily true. Hence, the system can absorb exceptions (e.g., penguins do not fly) without risk of inconsistency. In their later work, the LNR group argued that [their old style of representation] is superficial, and that a deeper level of representation is required in order to capture the full meaning of sentences. These deeper representations decompose the superficial ones into their appropriate semantic primitives.» Eg. "John gave Fido to Mary" (shown left to right instead of top down)	agent isa DO-------------------()----- JOHN / event / subject isa / .----------()----- JOHN CAUSE POSSESS object isa \ from / `----------()----- FIDO result \ / CHANGE \ subject isa to \ .----------()----- MARY POSSESS object isa `----------()----- FIDO
1976: Anderson's ACT succeeds HAM. «[S]entences are no longer divided into facts and contexts; the notation is now more uniform and closely related to the standard theory of transformational grammar. ... Unlike the LNR system, ACT does not decompose the meanings of words into a network of primitives, but rather analyzes their semantics by using productions.» Representation of "In a park a hippie touched a debutante" (net shown left to right, instead of normally top down):	relation predicate .----------AT TIME ()----------() argument \ `----------PAST \ subject \ relation \ predicate .----------TOUCH ()-----------() argument / \ `----------DEBUTANTE / \ subject / `-------------------HIPPIE / / relation / .----------AT PLACE ()----------() argument predicate `----------PARK

Syntax trees, parse trees, constituent graphs

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