Woods, William A. (1991). Understanding Subsumption and Taxonomy: A Framework for Progress. In: Sowa, John (ed.). Principles of Semantic Networks: Explorations in the Representation of Knowledge. M. Kaufmann, California, pp. 45 - 94.  @ NUS  Home/Search   Document Not in Database   Summary   Related Articles   Check

....subsumes a clause B if there is a substitution s such that the literals in As are a subset of the literals in B. Clauses 10 and 11 are descendents of the question clauses and are not syntactically subsumed by other clauses in Table 4.5. Subsumption is often considered a taxonomic phenomenon [Woods, 1991] , but in our discussions it is important to separate syntactic from taxonomic subsumption. Note that clause 10 taxonomically subsumes clause 11. We do not consider taxonomic subsumption when determining what counts as an answer, though it may be considered in selecting from among 74 answers. The ....

W. A. Woods. Understanding Subsumption and Taxonomy: A Framework for Progress. In John Sowa, editor, Principles of Semantic Networks, pages 45--94. Morgan Kaufmann, 1991.

....for organizing many aspects of knowledge, much of which can be expressed mathematically with partial orders. Taxonomies are used for representing information at appropriate levels of generality and automatically making it available to more specific concepts by means of a mechanism of inheritance [18]. As components of ontologies, taxonomies can provide an organizational model of a domain (domain ontologies) or a model suitable for specific tasks (application ontologies) The principles used to produce taxonomies are either intrinsic (properties of the partial ordering relation) or added to ....

Woods, W.A. Understanding subsumption and taxonomy: A framework for progress. in Sowa, J.F. ed. Principles of Semantic Networks, Morgan Kaufmann, San Mateo, CA, 1991, 45-94.

....of using descriptions: a person and a blue pen that has not run out of ink . The descriptions are enclosed in curly braces. an object of class pen, the speaker may want a blue pen that has not run out of ink. To support this kind of description, we use a representational approach based on [79]. The basic idea is that there are descriptions of objects and then there are actual grounded objects. A description specifies the sorts of objects that satisfy it. There may be hundreds of descriptions that fit a given object, and a given description may be satisfied by hundreds of di#erent ....

William A. Woods, Understanding subsumption and taxonomy: A framework for progress, Principles of Semantic Networks: Explorations in the Representation of Knowledge, Morgan Kaufmann, 1991.

....[25] the IS A relation is treated in the same way as all other relations. In [18] Levinson presents the principle of pattern associativity by indexing objects into multi levels. This approach allows one to organize conceptual graphs into a multi level partial order by subgraph isomorphism. In [30], Woods describes the taxonomies of structured conceptual descriptions following work of the KL ONE family [5] Such taxonomies were generated by the subsumption relationship that relates each pair of concepts [13] Our formula provides an approach to break the IS A hierarchy in a reasonable way ....

Woods, W. A.: Understanding subsumption and taxonomy: A framework for progress. In Sowa, J. F. (ed.): Principles of Semantic Networks. Morgan Kaufmann Publishers, Inc., San Mateo, CA (1991) 45--94 This article was processed using the L A T E X macro package with LLNCS style

....module above. a. For is a relationships: i. If the hypernym is the focus, then classify the NP under the focus. For example, software products, including Microsoft Oce = Microsoft Oce is a software product. 1 This classi cation procedure is based on the subsumption procedures described in (W.A.Woods, 1991) and (Moldovan, 2000) ii. If in the hypernym position there is an NP that has the focus as head, then classify the new NP under the focus: operating systems software product, such as OS 2. OS 2 is a operating systems software product which is a software product. iii. Classify all ....

W.A.Woods. 1991. Understanding subsumption and taxonomy: A framework for progress. Principles of Semantic Networks: Explorations in the Representation of Knowledge, 1991.

....these optimizations have on the classi cation process are evaluated on three di erent sets of test data, which are described below. It should be noted that we do not claim that all the presented optimizations are novel. Similar optimizations can probably be found in many of the existing systems [27, 28, 38, 44]. Further, the optimizations on the rst level described below are very similar to methods that can be found in the conceptual graphs literature [25, 14, 26] and which have been used in the implementation of the peirce system [15] However, until now it was not possible to nd a coherent ....

W. A. Woods. Understanding subsumption and taxonomy: A framework for progress. In J. F. Sowa, editor, Principles of Semantic Networks, pages 45-94. Morgan Kaufmann, San Mateo, CA, 1991.

....as the ontology, according to their levels of generality. How a taxonomy accounts for knowledge and can be used by a knowledge based system is a knowledge acquisition issue. Understanding the very nature of the subsumption represented in a taxonomy is fundamental when using the taxonomy [ Woods, 1991 ] 2.2 Ontology Acquisition The goal of the knowledge acquisition task is to obtain a formal representation of human knowledge that a computer can use at the symbol level in conformance with its meaning at the so called knowledge level [ Newell, 1982 ] A same symbolic expression is given a ....

W. A. Woods. Understanding subsumption and taxonomy: A framework for progress. In Sowa [ 1991 ] , chapter 1, pages 45--94.

....Subsumption test algorithms. Classification depends primarily on a subsumption test a test which determines when one concept definition is a generalization of another. The current implementation of the concept module uses a normalize and compare or structural style of subsumption algorithm [35]. Such algorithms have been shown to have problems with incompleteness the classifier may not spot all subsumption relationships that hold. The algorithms are sound however, in that any subsumption relationships determined by the classifier will hold and research is ongoing in the ....

W. Woods. Understanding Subsumption and Taxonomy: A Framework for Progress. In J. Sowa, editor, Principles of Semantic Networks: Explorations in the representation of knowledge, pages 45--94. Morgan Kaufmann, San Mateo, CA, 1991.

....translation would remove the uncomfortable dependence on conventions and weak heuristics during translation. For example, it would be useful to extend the input language to enable the user to explicitly indicate: 1. the intended quantification over elements of referenced collections (e.g. see [Woo91] 2. whether or not a reference is figurative 3. whether or not the interpretation of the inverse tuples should be asserted However, such an extension would also force the user to be much more adept with the target language (e.g. the internal representation language of the knowledge base) and ....

W.A. Woods. Understanding subsumption and taxonomy: A framework for progress. In J.F. Sowa, editor, Principles of Semantic Networks: Explorations in the Representation of Knowledge, pages 45--94. San Mateo, CA: Morgan Kaufmann, 1991. 330

....For any there is some subset containing the world histories that satisfy the description. An abstraction will generally describe some properties of the world history, while leaving many others unspecified. Of 1. For a reference on the use of description taxonomies for knowledge representation, see [Woods 90]. W A A S A W 143 course, to make this definition concrete we must have some well defined language in which we express our abstractions. It is useful to associate with the abstraction proposition that asserts that the actual world history will turn out to satisfy . An agent s belief or ....

William A. Woods. Understanding subsumption and taxonomy: A framework for progress. Technical report 19-90, Center for Research in Computing Technology, Harvard University, 1990. Also appears in Principles of Semantic Networks, edited by John F. Sowa.

....3.2 illustrates the tableaux method by describing a simple tableaux satisfiability testing algorithm; and finally, Section 3.3 shows how the algorithm can be extended to deal with general terminologies. 3. 1 Tableaux Subsumption Testing Most early DL systems used structural subsumption algorithms [Woo91] based on rules such as: 45 46 CHAPTER 3. TABLEAUX ALGORITHMS (C 1 u : u C n ) v T (D 1 u : u Dm ) if for every D in D 1 ; D n there is some C in C 1 ; C n such that C v T D 9R:C v T 9S:D if R v T S and C v T D The rules are used to recursively decompose the problem ....

W. A. Woods. Understanding subsumption and taxonomy: a framework for progress. In Sowa [Sow91], chapter 1, pages 45-- 94.

....many concept names are compound (multi word) terms. In Boeing s Thesaurus, 32,000 (85 ) of the concept names are compound nouns or phrases. This allows some automated analysis of the concepts to be performed, based on the constituent words in these terms, using subsumption computation techniques (Woods 1991). For example, the concept space shuttle main engine is an orphan in the Thesaurus, but by comparing its constituents with other concept names, an algorithm can infer that it is related to the concept space shuttle (as space shuttle is a concept in the Thesaurus) and generalizes to ....

Woods, W. A. 1991. Understanding subsumption and taxonomy: A framework for progress. In Sowa, J. F., ed., Principles of Semantic Networks. CA: Kaufmann. 45--94.

....with taxonomies that can be used to classify categories or concept types in a knowledge base [22] A taxonomy contains a stronger concept of structure and organisation than the word ontology as the word is derived from the Greek taxis and nomos, which respectively mean arrangement and law. Woods [24] notes that: conceptual taxonomies which allow probabilistic and default rules and abstract and partial definitions may be useful for indexing and organising information and for managing the resolution of conflicting defaults [24,p.45] Taxonomies include a classification system which provides ....

....which means isa when traversing the graph from bottom to top for extensions. Nets also provide clustering of properties around concepts and the incorporation of inheritance hierarchies [17,p.102] and inference propagation. Each of these features are supported by the FCA line diagram. Woods [24] sees semantic networks as different to other knowledge representation because of the use of links to record facts and store associations which can be used for reasoning. Schubert, however, points out that many, if not most, knowledge representation are able to provide many of these features and ....

Woods, W.A. (1991) Understanding Subsumption and Taxonomy: A Framework for Progress In John Sowa (ed) Principles of Semantic Networks: Explorations in the Representation of Knowledge Morgan Kaufmann Publishers, Inc. California, 45-94.

....both simultaneously [9] A slot on a concept s frame is used to represent either an attribute of the concept or a relationship between that concept and others. In this paper, these attribute and relationship features of a concept, either class or individual, are referred to as properties. Woods [10] notes that an atomic concept, such as Person, can be augmented by relational modifiers to produce composite conceptual 5 descriptions. Golfer could be defined as Person (Play : Golf) where the relational modifier (Play : Golf) might be said to be a property of Person. In a frame based ....

....class as a whole, but not for an instance of Person. The member own slot distinction can be useful in organizing slots that are used on class concepts. This distinction depends on the representation language and can be used as a means for organizing slots at the symbol level (Section 3. 2) Woods [10, 11] emphasizes the distinction between structural and assertional links. Structural links are used (1) to form composite description of concepts, such as a person who takes every math course, and (2) to determine whether one concept subsumes (is more general than) another. Assertional links state ....

[Article contains additional citation context not shown here]

W. A. Woods, "Understanding Subsumption and Taxonomy: A Framework for Progress," in Principles of Semantic Networks, J. F. Sowa, ed., Morgan Kaufmann, San Mateo, CA, pp. 45-94, 1991.

....World Assumption for the Rule reasoner. This architecture generalizes all existing hybrids of descriptions and rules. 1 Introduction Description Logic (DL) is a collective name for knowledge representation formalisms that concentrate on the management of essential descriptive vocabulary ([2, 12, 15, 4]) The combination of a DL reasoner with reasoners in di erent paradigms is studied and implemented within several research e orts. The CLASSIC ( 2] and BACK ( 10, 11] systems include an operational rule component, and have features for reasoning under the Closed World Assumption (CWA) AL log ....

W. Woods. Understanding subsumption and taxonomy: A framework for progress. In J. Sowa, editor, Principles of Semantic Networks: Explorations in the Representation of Knowledge, pages 45-94. Morgan Kaufmann, 1991.

.... LinearOrdering Mereology Integers Sequences Sets VNGB Sets ZF Sets Prehension SpatialForm Arrangement Continuant Occurrent T Firstness Physical Secondness T T Abstract Thirdness 28 Subsumption of Logical Formulae CS433 Lecture 12 Consider the following sentences describing concepts taken from [Woo91] where we consider intension or deduced subsumption the more general concept is deduced to subsume the more specific concept by deductive inference operations applied to knowledge of the domain. 1. A person who takes every math course subsumes A person who takes every course. We can see that ....

William A. Woods. Understanding subsumption and taxonomy: A framework for progress. In John F. Sowa, editor, Principles of Semantic Networks: Explorations in the Representation of Knowledge, pages 45--94. Morgan Kaufmann, San Mateo, CA, 1991. 33

....about logistics. 1 A concept A is said to subsume a concept B if all the possible entities that could be described by B are also necessarily described by A. For example, a man who only drinks beer subsumes a man who only drinks imported beer. More details about subsumption can be found in (Woods, 1991). Grammar Some of the knowledge about objectives in air campaign plans is used to produce case grammars that enable a syntax oriented editor to define these objectives in a structured manner. This ontology contains the concepts and relations necessary to map the representation of objectives in ....

Woods, W. A. (1991). Understanding subsumptionand taxonomy: A framework for progress. In Sowa, J. F., (Ed.), Principles of Semantic Networks: Explorations in the Representation of Knowledge, pages 45--94. San Mateo, CA, Morgan Kaufmann.

....of the properties of the class objects; the second part, which is delineated after the key word properties of the concept allows to state the properties of the concept. The syntax used to formalize the properties corresponds to the linear syntax proposed by Woods for a semantic network [Woo91]: the links between concepts, or pairs of relations, have a quantificational import, moreover assertional links are distinguished from structural links. The assertional links comprise double quantifiers such as: 4 , whereas the structural links comprise quantifiers such as: M ....

W.A. Woods. Understanding Subsumption and Taxonomy: A Framework for Progress. In: JF. Sowa, ed., Principles of Semantic Networks; Explorations in the Representation of Knowledge, Morgan Kaufmann, 45-94.

....is always also the former: C D if and only if for every model M, D M C M . In logic, a model is a particular mapping from symbols to a universe of objects) There is debate in the description logic community as to whether an extensional or intensional semantics is more desirable [23]. For ontologies, a Fregean semantics is appropriate [7] The intensional meaning of a concept is a function that maps from models to the concept s extension, W C : M C M . Thus, ontologies can be understood as nets of constraints that restrict the set of possible models. 2 ....

W. A. Woods, "Understanding Subsumption and Taxonomy: A Framework for Progress," in Principles of Semantic Networks, J. F. Sowa, Ed. San Mateo, California: Morgan Kaufmann Publishers, 1991, pp. 45-94.

....usefulness of classification based reasoning [DP91] they suggest that the correct classification of some concepts is dependant on assertional knowledge. Woods has also shown that the rejection of assertional knowledge restricts the kinds of facts that can be represented by a terminological system [Woo91]. It has also been pointed out by Doyle and Patil [DP91] and by MacGregor [Mac91a] that the extreme stance taken by KRYPTON has been softened in almost all subsequent systems so as to allow some assertional knowledge to be represented in the T box. Subsumption relations between primitive ....

.... the current implementation does not support multiple semi disjoint definitions which are required in order to represent concepts such as triangle which can be defined in more than one way: as a 3 sided polygon which necessarily has 3 angles or as a 3 angled polygon which necessarily has 3 sides [Woo91]. 7.5.1 The GRAIL classifier It has been demonstrated in sections 6.4.1 (inferred non primitive conjunctions) and 6.4.2 (cardinality restrictions and the relation hierarchy) that there are some serious problems with GRAIL s classification algorithm. In certain circumstances the classifier ....

W. A. Woods. Understanding subsumption and taxonomy: a framework for progress. In J. F. Sowa, editor, Principals of semantic networks: Explorations in the representation of knowledge, pages 45--94. Morgan Kaufmann, San Mateo, California, 1991.

....we also create a system for an explicit representation of Kauppi s theory. 2 1. Introduction Concepts are usually considered as results of generalisation from sets of individuals or from other concepts [see Smith and Smith, 1977] In this way it is natural to take the subsumption relation [Woods, 1991] to be the main relation for presenting containment among concepts. According to this approach, the containment among concepts are based on inclusion of individuals sets, and the conception of concepts is extensional. This conception is limited, because if there exists no extension of a concept, ....

W. A. Woods, Understanding subsumption and taxonomy: A framework for progress, in J. F. Sowa (ed.), Principles of Semantic Networks. Morgan Kaufman Publishers, San Mateo, California, 1991. pp. 45-94

....by using a clever order in which to make the subsumption calls, and by appropriately propagating the results of each call in the already computed part of the hierarchy, most of the n 2 calls can be avoided. 2 Such techniques are employed in many of the implemented terminological KR systems [15, 16, 19, 28], and similar methods have independently been developed in the conceptual graphs community [12, 8, 13, 9] The subsumption hierarchy provides only a limited amount of information about the interaction between defined concepts. For example, assume that we have appropriately defined concepts ....

W.A. Woods. Understanding subsumption and taxonomy: A framework for progress. In J.F. Sowa, editor, Principles of Semantic Networks, pages 45--94. Morgan Kaufmann, San Mateo, CA, 1991. This article was processed using the L a T E X macro package with LLNCS style

....a unique decoration. Partial set theory ZFAP is the set of all these axioms. ZFAP is a conservative extension of ZFA. 5.4. Dionne et al. s work Dionne, Mays, and Oles (1992) propose a new approach to intensional semantics of term subsumption languages. Their work is inspired by the research of Woods (1991) who suggested that a more intensional view of concept descriptions should be taken. In general, most of the work in semantics of term subsumption languages adopts an extensional view. Thus, concepts are interpreted as sets of objects from some universe. Roles of concepts are interpreted as binary ....

Woods, W. A. (1991). Understanding Subsumption and Taxonomy: A Framework for Progress.

....j n 2 M [ R: However, we will continue to use the metapredicates, as they are more perspicuous. 5.1.6 Reduction We follow [ Shapiro, 1986; Shapiro, 1991 ] in arguing for a form of reduction inference as being useful and natural, relative to language. This is a form of structural subsumption [ Woods, 1991 ] peculiar to semantic network formalisms, which allows a proposition (say n 1 ) to reduce to (logically imply) a proposition (say n 2 ) whose wires are a subset of the wires of the original proposition. This is written Reduce(n 2 , n 1 ) Figure 5.2 gives an example of a proposition ....

....we specify subsumption as a binary relation between arbitrary nodes in the network. We define subsumption between two nodes x and y in Figure 5.3. This definition of subsumption includes subsumption mechanisms that Woods classifies as structural, recorded, axiomatic, and deduced subsumption [ Woods, 1991 ] In Figure 5.3, case (1) corresponds to identical nodes (a node, obviously, subsumes itself) Case (2) is the reduction inference case discussed in section 5.1.6. Case (3) applies when a universal structured vari72 Subsume(x; y) in a model (A; B; M; R; U; E; Gamma) if any one of: 1. x = y. 2. ....

William A. Woods. Understanding Subsumption and Taxonomy: A Framework for Progress. In John F. Sowa, editor, Principles of Semantic Networks, pages 45--94. Morgan Kaufmann, 1991.

.... Gamma to: human u 9(has Gamma parent:human) and New structural properties can be defined as the conjunction of simpler structural properties. This constructor corresponds to the conjunction FLE Gamma constructor (u) unify The previous constructs permit us to express a subset of what [ Woods, 1991 ] has called type I descriptions. But this does not allow to express coordination among nodes. The :unify particle permits us to state that a node appearing in a structural property should be the same one that appears in another place of the structural property. This corresponds to a ....

W. A. Woods. Understanding subsumption and taxonomy: A framework for progress. In Sowa [ 1991 ] , chapter 1, pages 45--94.

....to subsume HIGHSCHOOL INFO FINDER because every role in the former corresponds to a role in the definition of the latter, with a filler value that subsumes the corresponding filler value. Therefore, automatic classification depends on a precise meaning for every relation in the ontology. See Woods (Woods 1991) for a thorough discussion of automatic classification. 6 This technology should not be confused with automatic classification based on keywords, or other non logical approaches) Figure 2: Intensional check for subsumption Description logic is also amenable to inference by modus ponens , ....

.... subsumption algorithms, and thus classification, are NPcomplete are not quite to the point, since concept definitions generally do not grow arbitrarily large; rather, the biggest problem is that classification of very general concepts can take time proportionate to the size of the concept taxonomy (Woods 1991). Loom, for example, is a very expressive system with a huge array of capabilities, including truth maintenance, default reasoning, a full first order query language, and disjunction and negation in concept definitions. Loom can be surprisingly fast, but in some situations is very slow. The ....

Woods, W. A. (1991). Understanding Subsumption and Taxonomy: A Framework for Progress. Principles of Semantic Networks. J. F. Sowa. San Mateo, California, Morgan Kaufmann Publishers: 45-94.

....existing hierarchy is an essential part of partial order classification and of preorder classification. Partial orders [6] are often referred to as ordered sets (or just orders) and as hierarchies. There are a number of classification systems [3, 4, 19, 10, 18] based usually on logical subsumption [23], which is a preorder relation: different object representations (or logical formulae) may be logically equivalent. The existing systems build a hierarchy of formulae with a strict ordering and are not able to retain multiple logically equivalent formulae. In some domains this retention is a ....

William A. Woods. Understanding subsumption and taxonomy: A framework for progress. In John F. Sowa, editor, Principles of Semantic Networks: Explorations in the Representation of Knowledge, pages 45--94. Morgan Kaufmann, San Mateo, CA, 1991. This article was processed using the L A T E X macro package with LLNCS style

.... reflects partial order relation that may be either weak partial order relation (reflexive, transitive, antisymmetric) or strict partial order relation (irreflexive, transitive, antisymmetric) Now we assume that C rel covers weak partial order containment relations, for example concept subsumption [Woods, 1991], IS A relation [Brachman, 1983] and intensional containment [Kauppi, 1967; Palom ki, 1994] There are also part whole relations [Winston et al., 1987; Padgham and Lambrix, 1994; Sattler, 1995; Artale et al. 1996] that are either weak partial order relations or strict partial order relations. We ....

W. A. Woods, Understanding subsumption and taxonomy: A framework for progress, in J. F. Sowa (ed.), Principles of Semantic Networks. Morgan Kaufman Publishers, San Mateo, California, 1991. Pp. 45-94. 20

....a system constructs an explicit collection of concept nodes . the result is a subgraph of the virtual taxonomy . Woods motivation for viewing a collection of descriptions this way is that although its structure is important, one never wants to make it explicit in the memory of a computer [3]. For database navigational purposes, we introduce a shift towards a dynamic database virtual hierarchy ; providing users the provision to virtually organise the database as a hierarchical structure based on user specific priorities [4] Each level of the database virtual hierarchy corresponds ....

Woods, W.A. (1991). "Understanding Subsumption and Taxonomy: A Framework for Progress". in John. W. Sowa (eds) Principles of Semantic Networks. Morgan Kaufmann Publishers, California, 1991.

....(we use font to identify concept and relation names in a real or hypothetical ontology) The concept chair denotes the set of objects that are chairs; the instance chair001 denotes a particular chair object. The logic must, like description logic, support computational inference of subsumption (Woods 1991). Concept A subsumes B if and only if every instance of B is always an instance of A. Highchair, for example, might be defined as a kind of furniture that a toddler can sit upon; by comparing the definitions for chair and highchair and person and toddler, respectively, description logic can ....

Woods, W. A. (1991). Understanding Subsumption and Taxonomy: A Framework for Progress. Principles of Semantic Networks. J. F. Sowa. San Mateo, California, Morgan Kaufmann Publishers: 45-94.

....Center P.O. Box 218, Route 134 Yorktown Heights, NY 10598 weida watson.ibm.com Computer Science Department Columbia University New York, NY 10027 weida cs.columbia.edu Introduction My background is in knowledge representation, especially description logic [ Brachman and Schmolze, 1985; Woods, 1991; Woods and Schmolze, 1992 ] In particular, my work with the k rep system has focused on practical applications such as expert systems and computer system configuration, as well as issues of persistence, scalability and collaboration [ Mays et al. 1991a; 1991b; Weida, 1995 ] For context, this ....

W. A. Woods. Understanding subsumption and taxonomy: A framework for progress. In J. Sowa, editor, Principles of Semantic Networks: Explorations in the Representation of Knowledge, pages 45--94. Morgan Kaufmann, Los Altos, CA, 1991.

.... Thus, generic knowledge classification has to be distinguished from specific knowledge classification, unlike classification performed by terminological languages [BMPS 91] which joins classes (concepts) and instances (individuals) for the same algorithm based on the subsumption relation [Woo91] Assuming that the categorization is a process which constructs a class definition from a set of instances, it is not related to class classification process which is applied to a given class description in order to find its position into a hierarchy. 2 Object based knowledge representation ....

W.A. Woods. Understanding subsumption and taxonomy: a framework for progress, chapter 1, pages 45--94. Principles of semantic networks. Morgan Kaufmann, 1991.

....that the metapredicates Believe and Conceive are, by definition: Believe(n) n 2 Gamma. Conceive(n) n 2 M [ R 5.1.6 Reduction We follow [ 38, 39 ] in arguing for a form of reduction inference (defined in axioms 2 and 3 below) as being useful. This is a form of structural subsumption [ 44 ] , peculiar to semantic network formalisms,s which allows a proposition to reduce to (logically imply) propositions whose wires are a subset of the wires of the original proposition. Figure 7 gives an example of a proposition expressing a brotherhood relation among a group of men. Node M1 ....

....ANALOG, we specify subsumption as a binary relation between arbitrary nodes in the network. We define subsumption between two nodes x and y in Figure 8. This definition of subsumption includes subsumption mechanisms that Woods classifies as structural, recorded, axiomatic, and deduced subsumption [ 44 ] . In Figure 8, case (1) corresponds to identical nodes (a node, obviously, subsumes itself) Case (2) is the reduction inference case discussed in section 5.1.6. Case (3) Subsume(x; y) in a model (A; B; M; R; U; E; Gamma) if any one of: 1. x = y. 2. Reduce(x; y) 3. For x 2 U and y 2 B [ M [ ....

William A. Woods. Understanding subsumption and taxonomy: A framework for progress. In John F. Sowa, editor, Principles of Semantic Networks, pages 45 -- 94. Morgan Kaufmann, 1991.

....the system knew enough about the meanings of such phrases to do more with them than simply look for exact matches. Specifically, the hypothesis was that by organizing recognized phrases by the relationship of generality, using subsumption technology derived from knowledge representation research (Woods 91) one could automatically relate more general words and phrases to more specific words and phrases that they subsume and that this would be useful for dealing with paraphrase relationships between query terms and index terms. 2 Conceptual Indexing As suggested above, we attempt to go beyond ....

William A. Woods; "Understanding Subsumption and Taxonomy: A Framework for Progress," in John Sowa

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Woods, William A. (1991). Understanding Subsumption and Taxonomy: A Framework for Progress. In: Sowa, John (ed.). Principles of Semantic Networks: Explorations in the Representation of Knowledge. M. Kaufmann, California, pp. 45 - 94.

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Woods, W. 1991. Understanding subsumption and taxonomy: A framework for progress. In Sowa, J. F., editor, Principles of Semantic Networks. Morgan--Kaufmann. 45--94.

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Woods, William A. (1991). Understanding Subsumption and Taxonomy: A Framework for Progress. In: Sowa, John (ed.). Principles of Semantic Networks: Explorations in the Representation of Knowledge, M. Kaufmann, San Mateo, California.

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Woods, William A. (1990). Understanding Subsumption and Taxonomy: A Framework for Progress. In: Sowa, John (ed.). Principles of Semantic Networks: Explorations in the Representation of Knowledge, M. Kaufmann, California.

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W.A. Woods. Understanding subsumption and taxonomy: A framework for progress. In J.F. Sowa, editor, Principles of Semantic Networks. Morgan Kaufman Publishers, 1991.

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William A. Woods. Understanding Subsumption and Taxonomy: A Framework for Progress. In John F. Sowa, editor, Principles of Semantic Networks --- Explorations in the Representation of Knowledge, pages 45--94. Morgan Kaufmann Publishers, Inc., 1991.

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W.A. Woods. Understanding subsumption and taxonomy: A framework for progress. In J.F. Sowa, editor, Principles of Semantic Networks: Explorations in the Representation of Knowledge, pages 45--94. Morgan Kaufmann, San Mateo, CA, 1991. 69

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W. A. Woods, Understanding Subsumption and Taxonomy: A Framework for Progress, Principles of Semantic Networks: Explorations in the Representation of Knowledge, Morgan Kaufmann, San Mateo, California 1991, pp. 45-94.

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W.A. Woods. Understanding Subsumption and Taxonomy: A Framework for Progress. In Principles of Semantic Networks: Explorations in the Representation of Knowledge, Morgan Kaufmann, San Mateo, Calif. 1991, pag. 45-94.

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William A. Woods. Understanding subsumption and taxonomy: A framework for progress. In John F. Sowa, editor, Principles of Semantic Networks: Explorations in the Representation of Knowledge, pages 45--94. Morgan Kaufmann, San Mateo, CA, 1991. 7

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Woods, W. A. 1991. Understanding Subsumption and Taxonomy: A Framework for Progress. pp. 45-94 in Sowa, John. F. (ed.), Principles of Semantic Networks, Morgan Kaufmann Publishers, San Mateo, California.

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W. A. Woods. Understanding subsumption and taxonomy: A framework for progress. In J. F. Sowa, editor, Principles of Semantic Networks, pages 45--94. Morgan Kaufmann, San Mateo, CA, 1991.

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W.A. Woods. Understanding subsumption and taxonomy: A framework for progress. In J. Sowa, editor, Principles of semantic networks, pages 45--94. Morgan Kaufmann Publishers, 1991.

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William A. Woods (1991). Understanding subsumption and taxonomy: A framework for progress. In John F. Sowa, editor, Principles of Semantic Networks, pages 45--94. Morgan Kaufmann, San Mateo, CA.

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