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. This concept also enhances our understanding of other aspects of fuzzy-logic inference including transitivity, intuitive leap, rada, and coupled implicative equations. It also enables many of the results derived earlier for element-by-element implication and derived implication to be taken over to inclusion and derived inclusion. Finally, it permits this inference to be carried out in hardware using simple circuitry, and provides a natural measure of noise immunity. >

The fidelity of fuzzy-logic inference

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. This concept also enhances the understanding of other aspects of fuzzy-logic inference including transitivity, intuitive leap, rada, and coupled implicative equations. It also enables many of the results derived earlier for element-by-element implication and derived implication to be taken over to inclusion and derived inclusion. >

http://ieeexplore.ieee.org/iel2/1022/7759/00327388.pdf

The role of fidelity in fuzzy-logic inference

Modus ponens is used in forward inference and backward inference, where the truth of the conclusion is inferred from the truth of the premise. In modus tollens, the falseness of the premise is inferred from the falseness of the conclusion. Although modus ponens is used in general connectionist production systems, modus tollens is rarely used, except in Quinlan’s proposed INFERNO system and in the system proposed by Thornber. A connectionist production system called ConnPS that can perform both modus ponens and modus tollens simultaneously is described. Compared to the INFERNO system, one of the advantages of ConnPS is its supervised learning ability. The rules and examples given as external knowledge are often erroneous and incomplete. In ConnPS, these rules can be refined by using the supervised learning. Both positive and negative examples are presented to ConnPS, onto which the external rules and observations are mapped. Moreover, ConnPS’s implementations of implications, conjunctions, disjunctions and negation are intuitively consistent with Boolean logic.

A connectionist production system which can perform both modus ponens and modus tollens simultaneously

The fidelity based transitive fuzzy-logic inference is utilized to accelerate the nearest neighbour pattern search in the hierarchically categorized filed patterns. The extraction method of inference rules and the transitive inference method of categories are discussed. Inference hardware configuration is shown and performance is estimated. The effect of an intuitive leap on flexible selecting and filtering of categories by the transitive fuzzy-logic inference are cleared. >

Transitive fuzzy logic inference for the nearest pattern search

A countably infinite class of inferences with no counterpart in logic is presented These comprise an autonomous subclass of inferential equations previously introduced by the author (1992, 1993) They can serve as a protologic with relatively low fidelity in the absence of the stronger relations of logic, and/or fuzzy-logic inference >

http://ieeexplore.ieee.org/iel2/3225/9177/00409837.pdf

Inference beyond logic: protologic

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. >

K.K. Thornber

Papers

A new look at fuzzy-logic inference

The role of fidelity in fuzzy-logic inference

Transitive fuzzy logic inference for the nearest pattern search

Inference beyond logic: protologic