Academia.eduAcademia.edu

Figure 13 – uploaded by John Sowa

See full PDFdownloadDownload figure
Figure 17. Nested situations with indexicals resolved

Figure 17 Nested situations with indexicals resolved

Related Figures (14)

Metalanguage consists of signs that signify something about other signs, but what they signify depends on what relationships those signs have to each other, to the entities they represent, and to the agents who use those signs to communicate with other agents. Figure 1 shows the basic relationships in a meaning triangle (Ogden and Richards 1923). On the lower left is an icon that resembles a cat named Yojo. On the right is a printed symbol that represents his name. The cloud on the top gives an impression of the neural excitation induced by light rays bouncing off Yojo and his surroundings. That excitation, called a concept, is the mediator that relates the symbol to its object. Figure 1. The meaning triangle The triangle in Figure 1 has a long history. Aristotle distinguished objects, the words that refer to them, and the corresponding experiences in the psyché. Frege and Peirce adopted that three-way distinction from Aristotle and used it as the semantic foundation for their systems of logic. Frege's terms for the three vertices of the triangle were Zeichen (sign) for the symbol, Sinn (sense) for the concept, and Bedeutung (reference) for the object. As an example, Frege cited the terms morning star and evening star. Both terms refer to same object, the planet Venus, but their senses are very different: one means a star seen in the morning, and the other means a star seen in the evening. Following is Peirce's definition of sign:
Metalanguage consists of signs that signify something about other signs, but what they signify depends on what relationships those signs have to each other, to the entities they represent, and to the agents who use those signs to communicate with other agents. Figure 1 shows the basic relationships in a meaning triangle (Ogden and Richards 1923). On the lower left is an icon that resembles a cat named Yojo. On the right is a printed symbol that represents his name. The cloud on the top gives an impression of the neural excitation induced by light rays bouncing off Yojo and his surroundings. That excitation, called a concept, is the mediator that relates the symbol to its object. Figure 1. The meaning triangle The triangle in Figure 1 has a long history. Aristotle distinguished objects, the words that refer to them, and the corresponding experiences in the psyché. Frege and Peirce adopted that three-way distinction from Aristotle and used it as the semantic foundation for their systems of logic. Frege's terms for the three vertices of the triangle were Zeichen (sign) for the symbol, Sinn (sense) for the concept, and Bedeutung (reference) for the object. As an example, Frege cited the terms morning star and evening star. Both terms refer to same object, the planet Venus, but their senses are very different: one means a star seen in the morning, and the other means a star seen in the evening. Following is Peirce's definition of sign:
Aristotle observed that symbols could symbolize other symbols, as "written words are symbols of the spoken." Frege said that his logic could be used as a language to talk about the logic itself. But Peirce went further than either of hem in recognizing tha multiple triangles could be linked together in different ways by attaching a vertex of one to a vertex of another. By stacking another triangle on top, Figure 2 represents the conce the cloud that suggests the concept of Yojo to the symbol for the more elusive neural excita when some person recognizes tha ion. At the very top is a pt of representing an obj Yojo is being represen ect by a concept. The upper triangle relates [Cat: Yojo], which is a printable symbol cloud for the neural excitation that occurs ed by a printed symbol. Figure 2. Concept of representing an object by a concept
Aristotle observed that symbols could symbolize other symbols, as "written words are symbols of the spoken." Frege said that his logic could be used as a language to talk about the logic itself. But Peirce went further than either of hem in recognizing tha multiple triangles could be linked together in different ways by attaching a vertex of one to a vertex of another. By stacking another triangle on top, Figure 2 represents the conce the cloud that suggests the concept of Yojo to the symbol for the more elusive neural excita when some person recognizes tha ion. At the very top is a pt of representing an obj Yojo is being represen ect by a concept. The upper triangle relates [Cat: Yojo], which is a printable symbol cloud for the neural excitation that occurs ed by a printed symbol. Figure 2. Concept of representing an object by a concept
Figure 3. Object, name of object, symbol of name, and character string
Figure 3. Object, name of object, symbol of name, and character string
Table 1. Five semantic primitives The five primitives in Table | are available in every natural language and in every version of first- order logic. They are called semantic primitives because they go beyond syntactic relations between signs to semantic relations between signs and the world. Any notation that is capable of expressing these five primitives in all possible combinations must include all of FOL as a subset. As an example, the WHERE clause of the SQL query language can express each of these primitives and combine them in all possible ways; therefore, first-order logic is a subset of SQL. Different languages may use different notations for representing the five primitives:
Table 1. Five semantic primitives The five primitives in Table | are available in every natural language and in every version of first- order logic. They are called semantic primitives because they go beyond syntactic relations between signs to semantic relations between signs and the world. Any notation that is capable of expressing these five primitives in all possible combinations must include all of FOL as a subset. As an example, the WHERE clause of the SQL query language can express each of these primitives and combine them in all possible ways; therefore, first-order logic is a subset of SQL. Different languages may use different notations for representing the five primitives:
Figure 5. EG for Some human has two distinct human parents. The bar that represents (3x) in Figure 4 is connected to both copies of the HasParent relation in Figure 5. Two bars represent each of the human parents. If they were connected, they would represent the same individual; but to represent distinct individuals, the connection must be negated. In existential graphs, Peirce used an oval to indicate negation; in Figure 5, the oval negates part of the connecting bar. In the algebraic notation, Figure 5 would be represented by the following formula: EG and RDF notations. The symbol ~ in the formula represents conjunction, which is implicit in the | Figure 4 could be represented by a triple in RDF: the first human could be treated as an RDF resource, the HasParent relation as an RDF property type, and the second human as an RDF value. The existence of the human on the left would be indicated by the proposed RI var="x">, and the one on the right by <exists var="y">. DF quantifier <exists
Figure 5. EG for Some human has two distinct human parents. The bar that represents (3x) in Figure 4 is connected to both copies of the HasParent relation in Figure 5. Two bars represent each of the human parents. If they were connected, they would represent the same individual; but to represent distinct individuals, the connection must be negated. In existential graphs, Peirce used an oval to indicate negation; in Figure 5, the oval negates part of the connecting bar. In the algebraic notation, Figure 5 would be represented by the following formula: EG and RDF notations. The symbol ~ in the formula represents conjunction, which is implicit in the | Figure 4 could be represented by a triple in RDF: the first human could be treated as an RDF resource, the HasParent relation as an RDF property type, and the second human as an RDF value. The existence of the human on the left would be indicated by the proposed RI var="x">, and the one on the right by <exists var="y">. DF quantifier <exists
Figure 6. EG for Every human has two distinct human parents. As Table 2 illustrates, a pair of negations can represent either a universal quantifier or an implication. The EG in Figure 6 may be read in either way. If the two ovals are considered an implication, Figure 6 could be read /f there exists a human, then that human has a parent who is human and another parent who is human and the two parents are distinct. Another option is to read an existential quantifier nested between two ovals as the universal quantifier V, which is expressed by the English word every. Then Figure 6 could be read Every human has a parent who is human and another parent who is human and the two parents are distinct. By using the defined operators of Table 2, the formula could be rewritten in a form that shows the universal quantifier V and the implication D explicitly: Ontology, Metadata, and Semiotics
Figure 6. EG for Every human has two distinct human parents. As Table 2 illustrates, a pair of negations can represent either a universal quantifier or an implication. The EG in Figure 6 may be read in either way. If the two ovals are considered an implication, Figure 6 could be read /f there exists a human, then that human has a parent who is human and another parent who is human and the two parents are distinct. Another option is to read an existential quantifier nested between two ovals as the universal quantifier V, which is expressed by the English word every. Then Figure 6 could be read Every human has a parent who is human and another parent who is human and the two parents are distinct. By using the defined operators of Table 2, the formula could be rewritten in a form that shows the universal quantifier V and the implication D explicitly: Ontology, Metadata, and Semiotics
Figure 7. CG for If there is a human, then he or she has two distinct human parents.
Figure 7. CG for If there is a human, then he or she has two distinct human parents.
Figure 8. CG for Every human has two distinct human parents. Figure 8 could be represented in RDF with the proposed <foral1> quantifier, but CGs also support other generalized quantifiers that have not yet been considered for RDF. As an example, Figure 9 simplifies Figure 8 by introducing the generic plural symbol {*} to represent a set and the number 2 to represent its count or cardinality. The resulting CG can be mapped to the following formula:
Figure 8. CG for Every human has two distinct human parents. Figure 8 could be represented in RDF with the proposed <foral1> quantifier, but CGs also support other generalized quantifiers that have not yet been considered for RDF. As an example, Figure 9 simplifies Figure 8 by introducing the generic plural symbol {*} to represent a set and the number 2 to represent its count or cardinality. The resulting CG can be mapped to the following formula:
Figure 11. Definition of the HasParent relation. form dyadic relations by combining with concept types that represent roles. Figure 11 shows how the HasParent relation is defined in terms of the relation Has and the role type Parent.
Figure 11. Definition of the HasParent relation. form dyadic relations by combining with concept types that represent roles. Figure 11 shows how the HasParent relation is defined in terms of the relation Has and the role type Parent.
Although the Chases relation allows shorter graphs and formulas than the concept [Chase], it introduces other complexities into the ontology. A general representation for tenses and modality, fo: example, would require a proliferation of relation types, such as HasChased, Wil1Chase, and MustHaveBeenChasing., Furthermore, the dyadic relation chases (x, y) makes no provision for attaching adverbs and other modifiers to the verb. Figure 13 takes advantage of the more general representation to define the concept type Chase in terms of a graph for an animate agent (parameter #1) that is following a mobile entity (parameter #2) in a rapid manner. Figure 13. Definition of the concept type Chase Figure 13 is only a partial definition because it represents a necessary, but not a sufficient condition. Runners in a race, for example, might be following one another rapidly, but only because they are pursuing a common goal. A more complete definition must include the purpose, which might be different for different senses of the word chase. Figure 14 defines one sense, called ChaseHunt, in which the purpose of the agent is to catch the mobile entity that is being chased.
Although the Chases relation allows shorter graphs and formulas than the concept [Chase], it introduces other complexities into the ontology. A general representation for tenses and modality, fo: example, would require a proliferation of relation types, such as HasChased, Wil1Chase, and MustHaveBeenChasing., Furthermore, the dyadic relation chases (x, y) makes no provision for attaching adverbs and other modifiers to the verb. Figure 13 takes advantage of the more general representation to define the concept type Chase in terms of a graph for an animate agent (parameter #1) that is following a mobile entity (parameter #2) in a rapid manner. Figure 13. Definition of the concept type Chase Figure 13 is only a partial definition because it represents a necessary, but not a sufficient condition. Runners in a race, for example, might be following one another rapidly, but only because they are pursuing a common goal. A more complete definition must include the purpose, which might be different for different senses of the word chase. Figure 14 defines one sense, called ChaseHunt, in which the purpose of the agent is to catch the mobile entity that is being chased.
Figure 14. Definition of the concept type ChaseHunt
Figure 14. Definition of the concept type ChaseHunt
In Figure 14, the purpose relation (Purp) links the action to a situation that would occur upon the successful completion of the chase. According to Peirce, purpose is a triadic relation, of which two arguments are shown explicitly in Figure 14. The implicit third argument is the agent of Chase, whose intention is to bring about the desired situation. That situation is nested inside a context box because its intentional status is different from the context of the act of chasing. If the chase is unsuccessful, the act of catching might never occur. Figure 15 defines another concept type ChaseAway, in which the agent's purpose is not to catch the mobile entity, but to cause it to leave its current location. Figure 15. Definition of the concept type ChaseAway
In Figure 14, the purpose relation (Purp) links the action to a situation that would occur upon the successful completion of the chase. According to Peirce, purpose is a triadic relation, of which two arguments are shown explicitly in Figure 14. The implicit third argument is the agent of Chase, whose intention is to bring about the desired situation. That situation is nested inside a context box because its intentional status is different from the context of the act of chasing. If the chase is unsuccessful, the act of catching might never occur. Figure 15 defines another concept type ChaseAway, in which the agent's purpose is not to catch the mobile entity, but to cause it to leave its current location. Figure 15. Definition of the concept type ChaseAway
These sentences show how indexicals are used to make context-dependent references. When new en ities are first mentioned, they are introduced with the indefinite article, as in the phrases a situation, a cat named Yojo, and a mouse. The two middle sentences refer to the mouse with the de of finite article the and to the cat with the name Yojo or the pronoun he. In the last sentence, the head the mouse, which had not been mentioned explicitly, is marked with the definite article because the introduction of the mouse implicitly introduces all of its expected parts. In Figure 16, the indexicals are marked with the # symbol: the pronoun he is represented as #he, and the definite article the is represented with the # symbol by itself. Figure 16. Nested situations with unresolved indexicals
These sentences show how indexicals are used to make context-dependent references. When new en ities are first mentioned, they are introduced with the indefinite article, as in the phrases a situation, a cat named Yojo, and a mouse. The two middle sentences refer to the mouse with the de of finite article the and to the cat with the name Yojo or the pronoun he. In the last sentence, the head the mouse, which had not been mentioned explicitly, is marked with the definite article because the introduction of the mouse implicitly introduces all of its expected parts. In Figure 16, the indexicals are marked with the # symbol: the pronoun he is represented as #he, and the definite article the is represented with the # symbol by itself. Figure 16. Nested situations with unresolved indexicals
No single system discussed in this paper incorporates all the features desired in a KE system, but the critical research has been done, and the remaining work requires more development effort than pure research. Figure 18 shows the flow of information from documents to logic and then to documents or to various computational representations. The dotted arrow from documents to controlled languages requires human assistance. The solid arrows represent fully automated translations that have been implemented in one or more systems. Figure 18. Flow of information from documents to computer representations
No single system discussed in this paper incorporates all the features desired in a KE system, but the critical research has been done, and the remaining work requires more development effort than pure research. Figure 18 shows the flow of information from documents to logic and then to documents or to various computational representations. The dotted arrow from documents to controlled languages requires human assistance. The solid arrows represent fully automated translations that have been implemented in one or more systems. Figure 18. Flow of information from documents to computer representations
Related topics:
SemioticsComputer ScienceInformation RetrievalComputational LinguisticsHuman AnimationControlled Natural Language
580 California St., Suite 400
San Francisco, CA, 94104
© 2025 Academia. All rights reserved