Based on the theory of the quasi-truth degrees in two-valued predicate logic, some researches on approximate reasoning are studied in this paper. The relation of the pseudo-metric between first-order formulae and the ...Based on the theory of the quasi-truth degrees in two-valued predicate logic, some researches on approximate reasoning are studied in this paper. The relation of the pseudo-metric between first-order formulae and the quasi-truth degrees of first-order formulae is discussed, and it is proved that there is no isolated point in the logic metric space (F, ρ ). Thus the pseudo-metric between first-order formulae is well defined to develop the study about approximate reasoning in the logic metric space (F, ρ ). Then, three different types of approximate reasoning patterns are proposed, and their equivalence under some condition is proved. This work aims at filling in the blanks of approximate reasoning in quantitative predicate logic.展开更多
Fuzzy logic is a logical calculus which operates with many truth values (while classical logic works with the two values of true and false). Since fuzzy logic considers the truth of scientific statements like somethin...Fuzzy logic is a logical calculus which operates with many truth values (while classical logic works with the two values of true and false). Since fuzzy logic considers the truth of scientific statements like something softened, it is fruitfully applied to the study of biological phenomena, biology is indeed considered the field of complexity, uncertainty and vagueness. In this paper fuzzy logic is successfully applied to the clinical diagnosis of a patient who suffers from different diseases bound by a complex causal chain. In this work it is presented a mathematical foundation of fuzzy logic (with connectives and inference rules) and then the application of fuzzy reasoning to the study of a clinical case. Probabilistic logic is widely considered the unique logical calculus useful in clinical diagnosis, thus the usefulness of fuzzy logic and its relation with probabilistic logic is here explored. The presentation of the case is supplied with all the features necessary to affect a clinical diagnosis: physical exam, anamnesis and tests.展开更多
基金National Natural Science Foundation of China (No. 60875034)Spanish Ministry of Education and Science Fund,Spain (No.TIN-2009-0828)Spanish Regional Government (Junta de Andalucia) Fund,Spain (No. P08-TIC-3548)
文摘Based on the theory of the quasi-truth degrees in two-valued predicate logic, some researches on approximate reasoning are studied in this paper. The relation of the pseudo-metric between first-order formulae and the quasi-truth degrees of first-order formulae is discussed, and it is proved that there is no isolated point in the logic metric space (F, ρ ). Thus the pseudo-metric between first-order formulae is well defined to develop the study about approximate reasoning in the logic metric space (F, ρ ). Then, three different types of approximate reasoning patterns are proposed, and their equivalence under some condition is proved. This work aims at filling in the blanks of approximate reasoning in quantitative predicate logic.
文摘Fuzzy logic is a logical calculus which operates with many truth values (while classical logic works with the two values of true and false). Since fuzzy logic considers the truth of scientific statements like something softened, it is fruitfully applied to the study of biological phenomena, biology is indeed considered the field of complexity, uncertainty and vagueness. In this paper fuzzy logic is successfully applied to the clinical diagnosis of a patient who suffers from different diseases bound by a complex causal chain. In this work it is presented a mathematical foundation of fuzzy logic (with connectives and inference rules) and then the application of fuzzy reasoning to the study of a clinical case. Probabilistic logic is widely considered the unique logical calculus useful in clinical diagnosis, thus the usefulness of fuzzy logic and its relation with probabilistic logic is here explored. The presentation of the case is supplied with all the features necessary to affect a clinical diagnosis: physical exam, anamnesis and tests.
