---
title: "Implementing Systemic Classification by Unification — Mellish 1988"
description: "He then defines subsumption relative to those axioms, so the possible descriptions form a lattice. 21 references, cited by 20 papers here."
authors: ["C. S. Mellish"]
year: 1988
venue: "Computational Linguistics"
source: "https://aclanthology.org/J88-1004/"
licence: "CC BY-NC-SA 3.0 (ACL Anthology, before 2016)"
licence_url: "https://creativecommons.org/licenses/by-nc-sa/3.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/mellish-1988-implementing-systemic-classification-unification/"
---
[Elamur Research](https://md.research.elamur.ai/free/en/) · [this page in HTML](https://research.elamur.ai/free/en/papers/mellish-1988-implementing-systemic-classification-unification/)

[home](https://md.research.elamur.ai/free/en/) / [papers](https://md.research.elamur.ai/free/en/papers/) / [1988](https://md.research.elamur.ai/free/en/papers/1988/) / Implementing Systemic Classification by Unification

# Implementing Systemic Classification by Unification

**Authors:** C. S. Mellish · **Year:** 1988 · **Venue:** [Computational Linguistics](https://md.research.elamur.ai/free/en/venues/cl/) ([Computational Linguistics 1988](https://md.research.elamur.ai/free/en/venues/cl/1988/)) · **Licence:** [CC BY-NC-SA 3.0 (ACL Anthology, before 2016)](https://creativecommons.org/licenses/by-nc-sa/3.0/)

**Links:** [Publisher's page](https://aclanthology.org/J88-1004/) · [PDF](https://aclanthology.org/J88-1004.pdf) · [OpenAlex](https://openalex.org/W1483469057)

**Citations:** 83 citations (OpenAlex, 2026-10-14) · [20](https://md.research.elamur.ai/free/en/papers/mellish-1988-implementing-systemic-classification-unification/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
Mellish asks whether the inferences licensed by Halliday's system networks (which property combinations entail or exclude others) can be computed with ordinary first-order term unification, the basic operation of logic programming. He first gives the four network connectives a precise logical reading as unary-predicate axioms. These cover choice systems, simultaneous choices, and conjunctive and disjunctive entry conditions. He then defines subsumption relative to those axioms, so the possible descriptions form a lattice. Parsing and generation rely on incremental description refinement, which needs only two operations: conjunction (greatest lower bound) and subsumption tests. The paper therefore looks for structure-preserving mappings from these description spaces into the lattice of Generalised Atomic Formulae (GAF). There, unification builds conjunctions, unification failure signals incompatibility, and the instantiation ordering tests subsumption. A general "brute force" encoding works but requires repeated variables. Without repeated variables, networks with disjunctive entry conditions cannot be faithfully encoded. This gives a principled way to build feature co-occurrence checks directly into unification-based systems.

## Key points
- System network connectives (choice "|", simultaneous "{", conjunctive "}" and disjunctive "]" entry conditions) are translated into first-order axioms, using an "at most one of" (AMO) operator for choice systems.
- Subsumption is defined relative to the network's axioms, a special case of Buntine's (1986) generalised subsumption. Incremental description refinement (a term from Bobrow and Webber, 1980) reduces to repeated greatest-lower-bound steps starting from "true".
- In the GAF lattice (Reynolds 1970), unification (Robinson 1965) is the meet operation. Mapping property names to fixed terms lets conjunction, incompatibility, and subsumption checks all run through standard unification.
- Repetition-free terms (GAFo) always decide compatibility pairwise. Networks containing "]" violate this property: in the paper's example, the set {a1, b2, c} is inconsistent although every pair in it is consistent. Such networks therefore need repeated variables, whereas the portion of Winograd's verb network examined can be encoded componentwise.
- Compared with related work, Kasper's (1986) FUG translation yields disjunctive functional descriptions, and Gazdar et al.'s repetition-free unification does not preserve global constraints. Mellish instead builds the constraints into the terms. The work was supported by SERC grant GR/D/08876.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

## Institutions

- [University of Sussex](https://md.research.elamur.ai/free/en/universities/university-of-sussex/) — University, Brighton, United Kingdom · 22 works · 3,332 citations

📚 Shelves (6): [🖥️ Computer Science](https://md.research.elamur.ai/free/en/shelves/computer-science/) · 16,667 works · [🤖 Artificial Intelligence](https://md.research.elamur.ai/free/en/shelves/computer-science/artificial-intelligence/) · 16,194 works · [🎭 Arts and Humanities](https://md.research.elamur.ai/free/en/shelves/arts-and-humanities/) · 16,039 works · [🗣️ Language and Linguistics](https://md.research.elamur.ai/free/en/shelves/arts-and-humanities/language-and-linguistics/) · 15,891 works · [💭 Psychology](https://md.research.elamur.ai/free/en/shelves/psychology/) · 1,552 works · [💭 Experimental and Cognitive Psychology](https://md.research.elamur.ai/free/en/shelves/psychology/experimental-and-cognitive-psychology/) · 870 works

## Cite

Cite as: C. S. Mellish. 1988. Implementing Systemic Classification by Unification. Computational Linguistics.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@article{mellish1988implementing,
  title = {{Implementing Systemic Classification by Unification}},
  author = {C. S. Mellish},
  journal = {Computational Linguistics},
  year = {1988},
  url = {https://aclanthology.org/J88-1004/}
}
```

- [← previous An Architecture for Anaphora Resolution](https://md.research.elamur.ai/free/en/papers/rich-1988-architecture-anaphora-resolution/)
- [next → Aspect, Aspectual class, and the Temporal Structure of Narrative](https://md.research.elamur.ai/free/en/papers/nakhimovsky-1988-aspect-aspectual-class-temporal-structure/)
- [↑ back to papers of 1988](https://md.research.elamur.ai/free/en/papers/1988/)

## References

21 references, 0 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

1. Birkhoff, Garrett. 1963 Lattice Theory. American Mathematical Society. [find](https://scholar.google.com/scholar?q=Birkhoff%2C+Garrett%2E+1963+Lattice+Theory%2E+American+Mathematical+Society%2E)
2. Bundy, Alan; Byrd, Lawrence and Mellish, Chris. 1982 Special Purpose, but Domain Independent, Inference Mechanisms. In Steels, Luc and Campbell, John, Eds., Progress in Artificial Intelligence. John Wiley, Chichester, UK: 93-111. [find](https://scholar.google.com/scholar?q=Bundy%2C+Alan%3B+Byrd%2C+Lawrence+and+Mellish%2C+Chris%2E+1982+Special+Purpose%2C+but+Domain+Independent%2C+Inference+Mechanisms%2E+In+Steels%2C+Luc+and+Campbell%2C+John%2C+Eds%2E%2C+Progress+in+Artificial+Intelligence%2E+John+W)
3. Buntine, Wray. 1986 Generalised Subsumption and its Applications to Induction and Redundancy. In Steels, Luc and DuBoulay, Ben, Eds., Procs of the Seventh European Conference on Artificial Intelligence. [find](https://scholar.google.com/scholar?q=Buntine%2C+Wray%2E+1986+Generalised+Subsumption+and+its+Applications+to+Induction+and+Redundancy%2E+In+Steels%2C+Luc+and+DuBoulay%2C+Ben%2C+Eds%2E%2C+Procs+of+the+Seventh+European+Conference+on+Artificial+Intelligenc)
4. Codish, Michael and Shapiro, Ehud. 1986 Compiling OR-Parallelism into AND-Parallelism. In Shapiro, Ehud, Ed., Procs of the Third International Conference on Logic Programming. Springer Verlag. [find](https://scholar.google.com/scholar?q=Codish%2C+Michael+and+Shapiro%2C+Ehud%2E+1986+Compiling+OR%2DParallelism+into+AND%2DParallelism%2E+In+Shapiro%2C+Ehud%2C+Ed%2E%2C+Procs+of+the+Third+International+Conference+on+Logic+Programming%2E+Springer+Verlag%2E)
5. Dahl, Veronica. 1977 Un Systeme Deductif d'Interrogation de Banques de Donnes en Espagnol. PhD dissertation, Groupe d'Intelligence Artificielle, University of Marseille-Luminy. [find](https://scholar.google.com/scholar?q=Dahl%2C+Veronica%2E+1977+Un+Systeme+Deductif+d%27Interrogation+de+Banques+de+Donnes+en+Espagnol%2E+PhD+dissertation%2C+Groupe+d%27Intelligence+Artificielle%2C+University+of+Marseille%2DLuminy%2E)
6. Gazdar, Gerald; Klein, Ewan;Pullum, Geoffrey and Sag, Ivan. 1985 Generalised Phrase Structure Grammar. Blackwell. [find](https://scholar.google.com/scholar?q=Gazdar%2C+Gerald%3B+Klein%2C+Ewan%3BPullum%2C+Geoffrey+and+Sag%2C+Ivan%2E+1985+Generalised+Phrase+Structure+Grammar%2E+Blackwell%2E)
7. Gazdar, Gerald; Pullum, Geoffrey; Carpenter, Robert; Klein, Ewan; Hukari, Thomas and Levine, Robert. (to appear) Category Structures. Computational Linguistics. [find](https://scholar.google.com/scholar?q=Gazdar%2C+Gerald%3B+Pullum%2C+Geoffrey%3B+Carpenter%2C+Robert%3B+Klein%2C+Ewan%3B+Hukari%2C+Thomas+and+Levine%2C+Robert%2E+%28to+appear%29+Category+Structures%2E+Computational+Linguistics%2E)
8. Hudson, Richard A. 1971 English Complex Sentences: An Introduction to Systemic Grammar. North Holland. [find](https://scholar.google.com/scholar?q=Hudson%2C+Richard+A%2E+1971+English+Complex+Sentences%3A+An+Introduction+to+Systemic+Grammar%2E+North+Holland%2E)
9. Kasper, Robert. 1986 Systemic Grammar and Functional Unification Grammar. In Benson, J. and Greaves, W., Eds., Selected papers from the Twelfth International Systemics Workshop. Ablex, Norwood, NJ, USA. [find](https://scholar.google.com/scholar?q=Kasper%2C+Robert%2E+1986+Systemic+Grammar+and+Functional+Unification+Grammar%2E+In+Benson%2C+J%2E+and+Greaves%2C+W%2E%2C+Eds%2E%2C+Selected+papers+from+the+Twelfth+International+Systemics+Workshop%2E+Ablex%2C+Norwood%2C+NJ%2C+US)
10. Kay, Martin. 1984 Functional Unification Grammar: A Formalism for Machine Translation. In Procs of COLING-84. [find](https://scholar.google.com/scholar?q=Kay%2C+Martin%2E+1984+Functional+Unification+Grammar%3A+A+Formalism+for+Machine+Translation%2E+In+Procs+of+COLING%2D84%2E)
11. Kress, Gunther, Ed. 1976 Halliday: System and Function in Language. Oxford University Press. [find](https://scholar.google.com/scholar?q=Kress%2C+Gunther%2C+Ed%2E+1976+Halliday%3A+System+and+Function+in+Language%2E+Oxford+University+Press%2E)
12. McCord, Michael C. 1986 Design of a Prolog-based Machine Translation System. In Shapiro, Ehud, Ed., Procs of the Third International Conference on Logic Programming. Springer Verlag. [find](https://scholar.google.com/scholar?q=McCord%2C+Michael+C%2E+1986+Design+of+a+Prolog%2Dbased+Machine+Translation+System%2E+In+Shapiro%2C+Ehud%2C+Ed%2E%2C+Procs+of+the+Third+International+Conference+on+Logic+Programming%2E+Springer+Verlag%2E)
13. Mellish, Chris S. (forthcoming) Version Spaces, Description Spaces and Unification. Research paper, Dept of Artificial Intelligence, University of Edinburgh. [find](https://scholar.google.com/scholar?q=Mellish%2C+Chris+S%2E+%28forthcoming%29+Version+Spaces%2C+Description+Spaces+and+Unification%2E+Research+paper%2C+Dept+of+Artificial+Intelligence%2C+University+of+Edinburgh%2E)
14. Patten, Terry A. 1986 Interpreting Systemic Grammar as a Computational Representation: A Problem Solving Approach to Text Generation. PhD thesis, University of Edinburgh. [find](https://scholar.google.com/scholar?q=Patten%2C+Terry+A%2E+1986+Interpreting+Systemic+Grammar+as+a+Computational+Representation%3A+A+Problem+Solving+Approach+to+Text+Generation%2E+PhD+thesis%2C+University+of+Edinburgh%2E)
15. Reynolds, John C. 1970 Transformational Systems and the Algebraic Structure of Atomic Formulas. In Meltzer, Bernard and Michie, Donald, Eds., Machine Intelligence 5. Edinburgh University Press. [find](https://scholar.google.com/scholar?q=Reynolds%2C+John+C%2E+1970+Transformational+Systems+and+the+Algebraic+Structure+of+Atomic+Formulas%2E+In+Meltzer%2C+Bernard+and+Michie%2C+Donald%2C+Eds%2E%2C+Machine+Intelligence+5%2E+Edinburgh+University+Press%2E)
16. Robinson, J. Alan. 1965 A Machine-Oriented Logic Based on the Resolution Principle. JACM 12, 23-41. [find](https://scholar.google.com/scholar?q=Robinson%2C+J%2E+Alan%2E+1965+A+Machine%2DOriented+Logic+Based+on+the+Resolution+Principle%2E+JACM+12%2C+23%2D41%2E)
17. Ueda, Kazunori. 1986 Making Exhaustive Search Programs Deterministic. In Shapiro, Ehud, Ed., Procs of the Third International Conference on Logic Programming. Springer Verlag. [find](https://scholar.google.com/scholar?q=Ueda%2C+Kazunori%2E+1986+Making+Exhaustive+Search+Programs+Deterministic%2E+In+Shapiro%2C+Ehud%2C+Ed%2E%2C+Procs+of+the+Third+International+Conference+on+Logic+Programming%2E+Springer+Verlag%2E)
18. Warren, David H. D. 1977 Implementing Prolog: Compiling Predicate Logic Programs: Research Reports 39 and 40, Department of Artificial Intelligence, University of Edinburgh. [find](https://scholar.google.com/scholar?q=Warren%2C+David+H%2E+D%2E+1977+Implementing+Prolog%3A+Compiling+Predicate+Logic+Programs%3A+Research+Reports+39+and+40%2C+Department+of+Artificial+Intelligence%2C+University+of+Edinburgh%2E)
19. Winograd, Terry. 1972 Understanding Natural Language. Academic Press. [find](https://scholar.google.com/scholar?q=Winograd%2C+Terry%2E+1972+Understanding+Natural+Language%2E+Academic+Press%2E)
20. Winograd, Terry. 1983 Language as a Cognitive Process. Volume 1: Syntax. Addison Wesley. [find](https://scholar.google.com/scholar?q=Winograd%2C+Terry%2E+1983+Language+as+a+Cognitive+Process%2E+Volume+1%3A+Syntax%2E+Addison+Wesley%2E)
21. NOTES Author's current address: Department of Artificial Intelligence, University of Edinburgh, 80 South Bridge, EDINBURGH EH1 1HN, Scotland. [find](https://scholar.google.com/scholar?q=NOTES+Author%27s+current+address%3A+Department+of+Artificial+Intelligence%2C+University+of+Edinburgh%2C+80+South+Bridge%2C+EDINBURGH+EH1+1HN%2C+Scotland%2E)

*Updated 30 October 2026*