Proceedings ArticleDOI
A new look at fuzzy-logic inference
K.K. Thornber
- pp 271-278
TLDR
The author constructs a fuzzy modus ponens and other rules of inference which include modus tollens and reductio ad absurdum, and suggests that the implicit processes of inference can be affected in fuzzy logic if one ventures outside the scope of (fuzzy) logic operations.Abstract:
The modus ponens, the inference primitive, and many more complex inferences, are not, as logic operations, reducible to expressions involving logic functions exclusively. Some of the consequences of this observation are considered for inference in fuzzy logic. The author constructs a fuzzy modus ponens and other rules of inference which include modus tollens and reductio ad absurdum. These in turn are based on a choice for the operation of implication which preserves the symmetry implicit in its definition. Extensions including conditional quantification, cut rules, and fuzzy mathematical induction are sketched. As an example, a fuzzy-logic treatment of the Yale shooting problem is discussed. The results suggest that the implicit processes of inference can be affected in fuzzy logic if, as in classical logic, one ventures outside the scope of (fuzzy) logic operations. >read more
Citations
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Journal ArticleDOI
The fidelity of fuzzy-logic inference
TL;DR: The concept of fidelity of inference is introduced in order to quantify the degree to which the inferred value of a consequent can be regarded as valid, and provides a natural measure of noise immunity.
Proceedings ArticleDOI
The role of fidelity in fuzzy-logic inference
TL;DR: The concept of fidelity of inference is introduced to quantify the degree to which the inferred value of a consequent can be regarded as valid and enables many of the results derived earlier for element-by-element implication and derived implication to be taken over to inclusion and derived inclusion.
Journal ArticleDOI
A connectionist production system which can perform both modus ponens and modus tollens simultaneously
TL;DR: A connectionist production system called ConnPS that can perform both modus ponens and modus tollens simultaneously is described and its implementations of implications, conjunctions, disjunctions and negation are intuitively consistent with Boolean logic.
Proceedings ArticleDOI
Transitive fuzzy logic inference for the nearest pattern search
K. Takahashi,K.K. Thornber +1 more
TL;DR: The fidelity based transitive fuzzy-logic inference is utilized to accelerate the nearest neighbour pattern search in the hierarchically categorized filed patterns.
Proceedings ArticleDOI
Inference beyond logic: protologic
TL;DR: A countably infinite class of inferences with no counterpart in logic is presented and can serve as a protologic with relatively low fidelity in the absence of the stronger relations of logic, and/or fuzzy-logic inference.
References
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Book
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
TL;DR: Probabilistic Reasoning in Intelligent Systems as mentioned in this paper is a complete and accessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty, and provides a coherent explication of probability as a language for reasoning with partial belief.
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TL;DR: Whiteheadek et al. as mentioned in this paper proposed a proposizio axiomatzat hartuz, eta horietatik, zehatz azaldutako inferentzia printzipioetan oinarrituz, logikako eta matematikako teoremak guztiz modu formalean ondorioztatu dituztela (hau da, sinboloen esanahiaren erabilpen gehigarririk egin gabe).
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Nonmonotonic logic and temporal projection
Steve Hanks,Drew McDermott +1 more
TL;DR: This paper provides axioms for a simple problem in temporal reasoning which has long been identified as a case of default reasoning, thus presumably amenable to representation in nonmonotonic logic, and finds that the logics considered are inherently incapable of representing this kind ofdefault reasoning.
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Everything That Linguists Have Always Wanted to Know About Logic But Were Ashamed to Ask
TL;DR: McCawley supplements his earlier book with new material on the logic of conditional sentences, linguistic applications of type theory, Anil Gupta's work on principles of identity, and the generalized quantifier approach to the logical properties of determiners.
Journal ArticleDOI
Implication in fuzzy logic
Philippe Smets,P. Magrez +1 more
TL;DR: In this article, a canonical scale for the truth value of a fuzzy proposition is selected such that the → operator is the Lukasiewicz operator and the negation is the classical 1− operator.