Download Conceptual Graphs and Fuzzy Logic: A Fusion for Representing by Tru Hoang Cao PDF

By Tru Hoang Cao

The capability for people to speak utilizing language permits us to offer, obtain, and comprehend info expressed inside a wealthy and versatile representational framework. additionally, we will be able to cause in response to common language expressions, and make judgements in line with the knowledge they communicate, notwithstanding this knowledge often includes vague phrases and unsure proof. particularly, conceptual graphs invented through John Sowa and fuzzy common sense based by way of Lofti Zadeh have the typical goal of representing and reasoning with linguistic details. At this juncture, conceptual graphs supply a syntactic constitution for a soft mapping to and from ordinary language, whereas fuzzy good judgment presents a semantic processor for approximate reasoning with phrases hav-ing imprecise meanings. This quantity is the mixed results of an interdisciplinary examine programme involved in the mixing of conceptual graphs and fuzzy good judgment for numerous wisdom and knowledge processing initiatives that includes ordinary language. First, it really is approximately fuzzy conceptual graphs and their common sense programming foundations, as a graph-based order-sorted fuzzy set common sense programming language for automatic reasoning with fuzzy item attributes and kinds. moment, it extends conceptual graphs with normal quantifiers and develops direct reasoning operations on those prolonged conceptual graphs, which may be mapped to and from in most cases quantified typical language statements. 3rd, it defines similarity and subsumption measures among item forms, names, and attributes and makes use of them for approximate retrieval of data represented in graphs. eventually, it proposes a strong ontology-based approach for figuring out average language queries utilizing nested conceptual graphs.

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A basic inference rule in logic is one of modus ponens. In fuzzy logic, given a fuzzy rule “y is H ← x is B” and a fuzzy fact “x is B*”, where x is a variable and B and B* are fuzzy sets on a domain U, and y is a variable and H is a fuzzy set on a domain V, the question is how H* in a conclusion “y is H*” is derived from B, B*, and H. It depends on the meaning of a fuzzy rule for which there are two different views. One is that the rule implies a relation between the possibility of x taking a value u∈U and that of y taking a value v∈V and, thus, defines a joint possibility distribution of (x, y) on U × V (cf.

1 illustrates some typical fuzzy truth-values. For a TRUE-characteristic value like true, the closer to 1 a truth degree is, the higher its possibility degree is. Whereas, for a FALSEcharacteristic value like false, the closer to 0 a truth degree is, the higher its possibility degree is. The membership functions of true and false as in the figure are defined as follows: ∀u∈[0, 1]: μtrue(u) = u ∀u∈[0, 1]: μfalse(u) = 1 − u The four extreme values absolutely true, absolutely false, absolutely inconsistent and absolutely unknown correspond to the four-valued truth-values in Belnap (1977), where absolutely true and absolutely false are equivalent to the binary truth-values true and false in classical logic.

Those of Pavelka (1979), Novák (1987) and Hájek (1995). The other trend is a development of fuzzy logic as a logic to deal with possibility in contrast to probability. Possibilistic logic, developed by Dubois and Prade (1988), also has formulas associated with values in [0, 1], but their meaning is possibility or necessity degrees instead of truth degrees. , ones that involve vague linguistic terms represented by fuzzy sets (Zadeh 1975a). We call a fuzzy logic whose formulas involve fuzzy sets fuzzy set logic.

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