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**1 - 5**of**5**### Chapter 5 Conceptual Graphs

"... A conceptual graph (CG) is a graph representation for logic based on the semantic networks of artificial intelligence and the existential graphs of Charles Sanders Peirce. Several versions of CGs have been designed and implemented over the past thirty years. The simplest are the typeless core CGs, w ..."

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A conceptual graph (CG) is a graph representation for logic based on the semantic networks of artificial intelligence and the existential graphs of Charles Sanders Peirce. Several versions of CGs have been designed and implemented over the past thirty years. The simplest are the typeless core CGs, which correspond to Peirce’s original existential graphs. More common are the extended CGs, which are a typed superset of the core. The research CGs have explored novel techniques for reasoning, knowledge representation, and natural language semantics. The semantics of the core and extended CGs is defined by a formal mapping to and from the ISO standard for Common Logic, but the research CGs are defined by a variety of formal and informal extensions. This article surveys the notation, applications, and reasoning methods used with CGs and their mapping to and from other versions of logic. 5.1 From Existential Graphs to Conceptual Graphs During the 1960s, graph-based semantic representations were popular in both theoretical and computational linguistics. At one of the most impressive conferences of the

### FREGE ON AXIOMS, INDIRECT PROOF, AND INDEPENDENCE ARGUMENTS IN GEOMETRY: DID FREGE REJECT INDEPENDENCE ARGUMENTS?

"... Abstract It is widely believed that some puzzling and provocative remarks that Frege makes in his late writings indicate he rejected independence arguments in geometry, particularly arguments for the independence of the parallels axiom. I show that this is mistaken: Frege distinguished two approache ..."

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Abstract It is widely believed that some puzzling and provocative remarks that Frege makes in his late writings indicate he rejected independence arguments in geometry, particularly arguments for the independence of the parallels axiom. I show that this is mistaken: Frege distinguished two approaches to independence arguments and his puzzling remarks apply only to one of them. Not only did Frege not reject independence arguments across the board, but also he had an interesting positive proposal about the logical structure of correct independence arguments, deriving from the geometrical principle of duality and the associated idea of substitution invariance. The discussion also serves as a useful focal point for independently interesting details of Frege’s mathematical environment. This feeds into a currently active scholarly debate because Frege’s supposed attitude to independence arguments has been taken to support a widely accepted thesis (proposed by Ricketts among others) concerning Frege’s attitude toward metatheory in general. I show that this thesis gains no support from Frege’s puzzling remarks about independence arguments. 1.

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"... Language A general and fundamental tension surrounds our concept of what is said. On the one hand, what is said (asserted, claimed, stated, etc.) by utterances of a significant range of sentences is highly context sensitive. More specifically, (Observation 1 (O1)), what these sentences can be used t ..."

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Language A general and fundamental tension surrounds our concept of what is said. On the one hand, what is said (asserted, claimed, stated, etc.) by utterances of a significant range of sentences is highly context sensitive. More specifically, (Observation 1 (O1)), what these sentences can be used to say depends on their contexts of utterance. On the other hand, speakers face no difficulty whatsoever in using many of these sentences to say (or make) the exact same claim, assertion, etc., across a wide array of contexts. More specifically, (Observation 2 (O2)), many of the sentences in support of (O1) can be used to express the same thought, the same proposition, across a wide range of different contexts. The puzzle is that (O1) and (O2) conflict: for many sentences there is evidence that what their utterances say depends on features F1…Fn of their contexts of utterance; while, at the same time, there is also evidence that two utterances of these sentences in contexts C and C ' express agreement, despite C and C ' failing to overlap on F1…Fn. Here’s a simple illustration. What an utterance of (1) says depends in part on the

### Consistency - What's Logic Got to Do with It?

, 1996

"... this paper, I want to explore the origin of the modern conception of the idea of consistency in logic in the work of German mathematician David Hilbert. My interest in the development of the modern idea of consistency arises from my belief that an overriding concern with a strict requirement of cons ..."

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this paper, I want to explore the origin of the modern conception of the idea of consistency in logic in the work of German mathematician David Hilbert. My interest in the development of the modern idea of consistency arises from my belief that an overriding concern with a strict requirement of consistency, borrowed primarily from the rigors of modern developments in logic, has prevented latter day twentieth century philosophers from producing philosophical systems of the type produced in earlier times.