Related Work in Concept Definition

Scholars of different disciplines have their concept definitions to apply in their work. For philosophers, concept has intension and extension that represent knowledge of concept in human mind. For logicians (Jurafsky & Martin, 2009a, 2009b), a concept can be a symbol to denote an object in a logic model, can be a category to denote a group of objects, and can be a first order logic sentence(s) which specifies its relations with other concepts. In Formal Concept Analysis (Priss, 2006), concepts are objects that have attributes. The objects and attributes are defined by human’s commonsense, in which its meaning is interpreted by human in the context. For linguists, concept may be represented by words. Therefore, they use words to denote a lexicalized concept. The distinguished WordNet (Fellbaum, 1998) database adopt this viewpoint, and no formal definition of concept is given. In WordNet, concept is represented by a synset which contains words for a concept. For ontology builders and users, concept may play different roles in ontology. It may be an object, predicate, quantifier, function, and relation. These terminologies gain their meaning in the ontology. Its connection to real world is also interpreted by human. For researchers in artificial intelligence, concept may be represented by words or an object in a logic model.

In summary, concept definition in these disciplines is an object to be operated, while in our concept definition, a concept itself is a computational process that uses a continuation to represent it. Moreover, the continuation exists in the environment it lives like a continuation in programming language. This viewpoint adopts pragmatism concept theories. Its connection to real world is defined by its ability of understanding language and is modeled inside the definition. A continuation do not contain all information because some information is stored in its environment. A continuation is similar to a device that stores links to its environment and links to machine's internal states. Therefore, a continuation may has its internal structures

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to store different types of information. We discuss this issue in next chapter.

In the viewpoint of continuation, human do not interpret a concept in machine. Human just provides proofs to test the comprehension of concept in language understanding of a machine.

Computer scientist John Sowa (Sowa, 1984) gives a concept definition in pragmatism viewpoint, and we quote it below.

The core insight of his definition is similar to our definition which captures the computational aspect of concept, but we further formulate concept definition in evolutionary language game and add mechanism for verifying language understanding. Marvin Minsky proposes a similar viewpoint of concept definition but uses different terminologies. In his book The society of Mind (Minsky, 1986), mind is a society which is composed of a group of agents. These agents represent various processes in human’s brain, and these processes can be any concepts interested by researchers such as free well, the sense of self, belief, memory, and consciousness. In our definition, we denote all processes in human mind as concepts and do not put any assumption on the structure and implementation of concept in order to gain the ability to analyze system theoretically in modern machine learning perspectives. Our concept definition is also similar to intelligent agent (Russell & Norvig, 2003) in artificial intelligence literatures, but we connect agent’s output to language understanding.

Barker (2004) emphasizes the similarities between formal languages and natural languages and uses continuation to analyze linguistic phenomena in natural language. He

“Concepts are inventions of the human mind used to construct a model of the world. They package reality into discrete units for further processing, they support powerful mechanisms for doing logic, and they are indispensable for precise, extended chains of reasoning. But concepts and percepts cannot form a perfect model of the world,—they are abstractions that select features that are important for one purpose, but they ignore details and complexities that may be just as important for some other purpose.” (Sowa, 1984, p.p. 344)

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treats quantification words like everyone, no one, and someone as a continuation, and defines these words in formal language context. He uses control operators like control, prompt, shift, and reset in delimited continuation (Felleisen, 1988) to demonstrates computation of quantification words in syntax tree. Barker also studies a phenomenon called focus, which is denoted by focus particles such as only. His approach use first order logic to represent the semantic of sentences like the approaches in computational semantics (Jurafsky & Martin, 2009a). Because continuation is a flexible mechanism to handle execution flow of formal language, he uses continuation as a mechanism to handle complex relations and phenomena in natural language, such as coordination, ambiguity, and quantification. In Baker’s formulation, a concept actually is a predefined continuation that has specific effects in parse tree. Although this definition is similar to our definition, the meaning of a concept is interpreted in FOL context, and hence, is interpreted by human.

When considering the relations between concept and language, researchers usually regard concepts as states of mind and study the procedure of translating mind states to languages. For Noam Chomsky (1986), the translation procedure is the knowledge of languages, and languages are internalized language (I-language) that translating the structure of concepts (mind states) to externalized language (E-language), which is independent of mind. In this viewpoint, language understanding is the problem to understand the correspondences between I-language grammars and E-language grammars. In our concept definition, the grammars are one type of concepts, and the E-language is just one type of proofs that can be adopted to measure system’s understanding level.

When considering a concept to be a program that has the ability to do something in an environment, researchers usually regard concepts as a computer program. They follow the approaches of reductionism, which reduces complex thing to many simpler and smaller things and combines these smaller results to solve the complex thing. For example, when studying

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machine understanding, researchers in natural language frame the understanding problem to many smaller problems such as named entity recognition (NER), co-reference resolution, template element, template relation, and scenario template in the Message Understanding Conference. In this case, a program that archives good results in sub-problem is regarded as understanding language well. This approach is similar to our concept definition, which define concept to be a program represented by continuation, and we further link this approach to evolutionary language game to form a more general framework to integrate sub-problems. In other words, we provide a general framework to integrate many sub-systems, and this integration is still within language understanding framework.

In the next section, we will mention some considerations of the proposed definition in implementation.