Relational Networks as a Computational Semantic Model
This post is, in large part, revised and adapted from the “Computation” section of Literary Morphology.
In the middle and late 1960s researchers in cognitive science began investigating natural language semantics using computational techniques. One of the first, and most influential of these was a relational network model proposed by Ross Quillian (1968). His basic idea is an old one, that the meaning of a word resides in its relations with other words, and it is perhaps on that account that Umberto Eco adopted it as his semantic model in A Theory of Semiotics (1976, pp. 121 ff.).
Following Quillian’s path-breaking work a number of researchers developed their own relational network models. My teacher, the late David Hays, was one of them. This post provides a quick introduction to the network formalism and that takes a ‘blitz’ though the work I on did on Shakespeare’s Sonnet 129 using Hays’s network model. This work is reported in more technical detail in Benzon 1976, 1978, and 1981.
Networks, Path Tracing, and Pattern Matching
One of the primary objects of literary computation is simply to compose meaning, on the fly, from the succession of words in the text. This is not the only computational process – we must also consider the sound and rhythm of those words, we must consider style – but that is what I want to concentrate on here. Following a wide-spread convention, though not a universal one, let us think of lexemes (that is, words) as being organized in a relational (or cognitive or semantic) network (see Figure 1) where the nodes are concepts and the links between the nodes are relations between the concepts. Thus dog would be linked to animal through an ISA link (dog is an animal) and to eat by an AGENT (AGT) link, while in the same subnetwork liver is linked to eat by a PATIENT (PAT) link (dog eats liver), and so forth through all the types of concepts and relationships.
Figure 1: Relational Network of Lexemes
The network fragment depicted in Figure 1 is small and quite simple in form. The networks used in computer simulations of human thinking are quite large, but like that in Figure 1, they a composed of simple parts connected to one another in simple ways. In the work I did with David Hays we distinguished between sensorimotor schemas, on the one hand, and cognitive networks on the other (Benzon 1976, 1978, Hays 1976, 1981). Things like dog, pine tree, walk, salt, and so forth, things one can apprehend with the sense, would be characterized by sensorimotor schemas. Sensory schemas regulate how one sees, hears, smells, touches, and tastes things while motor schemas regulate one’s physical interaction with them.
These schemas, in turn, provide the definitional foundation for nodes in the cognitive network. Thus the dog, eat, and liver nodes in Figure 1 would be associated with corresponding sensorimotor schemas. We also had mechanisms for defining abstract concepts over patterns in cognitive networks (Hays 1976, Benzon and Hays 1990).
These days we would say that our account of semantics was embodied. Words are given meaning by perceptual and motor schemes or patterns defined over those schemas.
For our immediate purposes, however, the important point is that two general classes of operations can be defined in networks, path tracing and pattern matching (Hays 1977). In Figure 2 we see some network in which a particular path is highlighted. It might, for example, might trace the opening of Shakespeare’s sonnet 129, “The expense of spirit in a waste of shame/Is lust in action …“ Each node would correspond to a word, or perhaps a grammatical relation, and the path in total corresponds to the pattern of network activation set up by the ‘incoming’ string of words.
Figure 2: Path Tracing
In Figure 3 two areas of the network are highlighted, each consisting of five nodes where the pattern of connection is the same in each network. Though these two subnetworks have different orientations and overall proportions in the 2D representation of the network, those are irrelevant; what matters is the pattern of connectivity, and that is the same in each network. Each consists of four nodes connected by five links in the same configuration. Hence the patterns match. Of course, pattern matching implies a second order network, or some other meta-structure, to recognize the match (Hays 1981).
Figure 3: Pattern Matching
Continuing with Shakespeare’s sonnet, one of those fragments might represent the basic lust sequence at the heart of the sonnet while the other embodies the simile that is introduced in lines seven and eight: “. . . a swallow'd bait/On purpose laid to make the taker mad.” Both of these actions involve a three part sequence and so the network fragments representing those sequences have the same form (see Figure 4).
Figure 4: Lust and Madness
Working in this way we could construct a relational network as the basis for performing the sonnet’s meaning. The meaning of the poem would then arise in the interaction between the text and such a network, where the network is implemented in someone’s brain. Think of that meaning is an ongoing and evolving pattern of resonance in millions upon millions of neurons. Such networks, of course, may differ from one individual to another and even where highly similar, may have different emotional resonance.
Constituent Structure
Language strings are said to be organized into longer and shorter strings, where longer strings are constituted by shorter strings. In long written texts we recognize units such as chapters, paragraphs, sentences, phrases, and individual word. All of which is to say that language strings have a pattern of constituency over longer and shorter strings.
The idea of constituency has a natural interpretation in the network notation I discussed above. Consider Figure 5:
Figure 5: Path with Three Constituents
The diagram depicts the same path displayed in Figure 2, but it has been broken into three segments. Each of those segments is a constituent of the entire path. Each of those segments could, in principle, be divided into constituents and, by the same token, the entire path could be a constituent in some longer path.
There is psychological evidence that the constituent structure of sentences reflects the way the mind parses them for processing (Neisser 1966: 259 ff., Taylor 1976: 105 ff.). I am simply, and perhaps rashly, extending this notion to the entire text (as does Cureton 1992, pp. 179 ff.). The meaning of a text may or may not, ultimately, be a single gestalt. But the process of arriving at that meaning has a structure in which partial meanings are “computed” and, in turn, combined into more comprehensive meanings, until the entire text has been comprehended.
Consider Shakespeare’s sonnet which, as an Elizabethan sonnet, conforms to a formula in which three quatrains are followed by a couplet, thus:
Figure 6: Structure of an Elizabethan Sonnet
The rhyme scheme is: abab cdcd efef gg. Note that this scheme reinforces the boundaries between the quatrains.
Each branch of this tree indicates the “processing” of a portion of the poem; that is to say, each ‘spans’ a certain path in the network. One processes section 1.11 and then 1.12, which completes 1.1. Sections 1.2 and 1.3 are processed in turn and, when complete, one has a ‘partial result’ corresponding to the meaning of the three quatrains minus whatever modification is induced by the final couplet. One then processes the final couplet and combines that partial result with the partial result for the quatrains to arrive at the poem’s meaning.
All competent readers will segment the text in the same way; they will recognize the same pattern of constituents, namely that dictated by the form laid out in Figure 6. Thus they will arrive at the same structure of partial meanings being organized into more inclusive meanings culminating in the meaning of the entire text. Where competent readers will differ is in the meanings evoked at the lowest level of this constituent structure. The important point, however, is that the varying meanings different readers bring to the words and phrases in a text are processed in a computational structure that is the same for all competent readers.
Description and Explanation
It is one thing to describe the semantic structure of a text by using a network model. It is something rather different to explain that structure. In Figure 7 I’ve taken the lust and madness networks from Figure 4 and added identifiers for the nodes:
Figure 7: Lust and Madness, Again
Node L designates the whole of the lust sequence, L1, L2, and L3; while node B designates the whole of the swallowed-bait sequence, B1, B2, and B3. Now, let us take Shakespeare’s poem and follow it through these two sequences. To do that I’ve simply indicated the appropriate network structure by placing the appropriate identifier in brackets BEFORE the portion of the poem that is derived from that network structure (see poem below, with lines separated into quatrains).
The first line and a half of the poem is about the entire lust sequence, not any one part of it. Then, in the middle of the second line, it shifts our attention to the first part of the sequence:
[L] The expense of spirit in a waste of shame
Is lust in action, and [L1] till action, lust
Is perjured, murderous, bloody, full of blame,
Savage, extreme, rude, cruel, not to trust;
[L2] Enjoyed no sooner but [L3] despised straight,
[L1] Past reason hunted, and [L2] no sooner had,
[L3]Past reason hated as [B2] a swallowed bait
[B1] On purpose laid [B3] to make the taker mad:
[L1] Mad in pursuit and [L2] in possession so,
[L3] Had, [L2] having, and [L3] in quest to have, [L] extreme;
[L2] A bliss in proof, and [L3] proved, a very woe,
[L1] Before, a joy proposed, [L3] behind, a dream.
At the beginning of the second quatrain we have another shift in focus and, in the second half of the quatrain, we shift attention to the swallowed-bait simile. The third quatrain returns to the lust sequence and moves rapidly through it back and forth.
That exhausts those two sequences, as it were; but the poem still has two more lines to go:
All this the world well knows; yet none knows well
To shun the heaven that leads men to this hell.
This that the world well knows, I take to be the entire pattern of activity evoked by the first twelve lines of the poem taken as a single object of conception and contemplation. All of it in one big conceptual lump. That being the case, we need further network structure suitable for expressing the world’s knowledge as it were.
But this isn’t the time and place to do that, though I’ve sketched such structures in my older work (Benzon 1976, 1978, 1993). it is sufficient for my present purpose simply to note that it is required.
What I’m really after at the moment is to distinguish between description and explanation. For the purposes of making that distinction let us assume that network structure, as well as all the structure needed to account for the inner details evoked by Shakespeare’s language. Let us further assume that all the details of the language itself—meter and rhyme and so forth—have been accounted for.
All that gets us is a description of what happens in the mind (considered as a cognitive network) when reading Shakespeare’s Sonnet 129. Note that these networks are, in principle, independent of this poem, or of any other text that might be based on them. When Jack says of Jill, I want her, he’s invoking the first episode of the the lust sequence. And when, at the end of the evening and Jack has gone home, Jill thinks, what a let-down that was, she’s invoking the third episode of the sequence.
Thus Shakespeare’s sonnet is just one of many utterances that calls on that fragment of conceptual structure. To assert that his sonnet evokes or activates that part of the general cognitive network is simply to describe the conceptual basis of his language. But it doesn’t explain how it is that Shakespeare managed to create exquisite poetry on that basis.
But why does the poem evoke those concepts, in just that order, with words sounding just so? Until we can answer those questions we’ve not explained how this poem works; we don’t know what makes it a poem. We just have a description of what has been done, with no sense of what is essential and what incidental.
That’s an awful lot of work for a description. Alas, I see no way around it. That’s what this cognitive conceptual universe is like. Full of pesky details.
By way of consolation I note that, when Watson and Crick announced that the DNA molecule and the form of a double-helix, that too was just a description. I do not of course mean to imply that my account of Shakespeare’s sonnet is an intellectual achievement of that order. It most certainly is not. My point is simply that descriptions are not to be sneezed at simply because they are descriptions. Some descriptions have inherent interest.
ADDENDUM: Objectified Semantics: This kind of semantic model is an objectified semantics. A cognitive or relational network of this sort is a fully objectified conceptual object. It can be described and analyzed in mathematical and computational terms.
Whether or not such an objectified model can be said to be true of the world, that is a different matter. That requires empirical evidence, which may or may not be forthcoming. Objectification facilitates empirical investigation, but it is not equivalent to it nor thus a substitute for it. Objectification does not imply objectivity.
This semantic model is thus as dumb as rocks.
Meaning, that’s something else. Meaning arises within a subject who is interacting with the world, directly or through a text. A relational network is part of the neural / mental equipment that produces meaningful experience, but the network cannot itself be identified with meaning.
References
Benzon, W. L. (1976) "Cognitive Networks and Literary Semantics." MLN, 91, 952-982.
Benzon, W. L. (1978) “Cognitive Science and Literary Theory,” Ph. D. dissertation, State University of New York at Buffalo. Ann Arbor: University Microfilms, 78-10602.
Benzon, W. L. (1981) “Lust in Action: An Abstraction.” Language and Style, 14, 251-270.
Benzon, W. L. (1993) "The Evolution of Narrative and the Self." Journal of Social and Evolutionary Systems, 16, 129-155.
Benzon, W. L., and D. G. Hays. (1990) "The Evolution of Cognition." Journal of Social and Biological Structures, 13, 297-320.
Cureton, R. D. (1992). Rhythmic Phrasing in English Verse. London and New York, Longman.
Eco, Umberto (1976). A Theory of Semiotics. Bloomington: Indiana University Press.
Hays, D. G. (1976). "On Alienation: An Essay in the Psycholinguistics of Science." Theories of Alienation. R. R. Geyer and D. R. Scheitzer. Leiden, Martinus Nijhoff: 169-187.
Hays, D. G. (1977). "Types of Processes on Cognitive Networks." Proceedings of the International Conference on Computational Linguistics, Pisa August 27 - September 1, 1973. A. Zampolli and N. Calzolari. Firenze, Leo S. Olschki Editore: 523-532.
Hays, D. G. (1981). Cognitive Structures. New Haven, HRAF Press.
Neisser, U. (1966) Cognitive Psychology. New York: Appleton-Century-Crofts.
Quillian, M. R. (1968). "Semantic Memory." In M. Minsky, ed. Semantic Information Processing. Cambridge, MA: MIT Press, 216-270.
Taylor, I. (1976) Introduction to Psycholinguistics. New York: Holt, Rinehart and Winston.
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