Syllogistic fuzzy reasoning is introduced into fuzzy system, and the new Cascaded Fuzzy System(CFS) is presented. The thoroughly theoretical analysis and experimental results show that syllogistic fuzzy reasoning is m...Syllogistic fuzzy reasoning is introduced into fuzzy system, and the new Cascaded Fuzzy System(CFS) is presented. The thoroughly theoretical analysis and experimental results show that syllogistic fuzzy reasoning is more robust than all other implication inferences for noise data and that CFS has better robustness than conventional fuzzy systems, which provide the solid foundation for CFS's potential application in fuzzy control and modeling and so on.展开更多
Jan Lukasiewicz acknowledged that Aristotle＇s syllogistic does not admit singular terms and presents syllogism as an implication. But he failed to recognize syllogistic necessity, reducing this necessity to ＂formal ...Jan Lukasiewicz acknowledged that Aristotle＇s syllogistic does not admit singular terms and presents syllogism as an implication. But he failed to recognize syllogistic necessity, reducing this necessity to ＂formal implication＂ as introduced by Russell, when Aristotle shows it as binding relations between three terms. On the contrary, Paul Lorenzen directly recognized syllogistic necessity as the typical example of his own logical implication. His reconstruction of syllogistic differs from the original by his interpretation of particular propositions as the determination of classes which are specified by predicates. The result is the representation of valid moods as the board of all multiplications of relations which are permitted. These relations are not only the Aristotelian ,4, E,I, O, but also the new converse asymmetrical relations of A and O： （a） and （o）.展开更多
Vladimir Markin proposes a certain construction---a generalisation of syllogistic--in which he uses the constant @ with indef＇mite arity. The atomic formulae are of the following sort： S1S2 ...Sm@P1P2...Pn, where re...Vladimir Markin proposes a certain construction---a generalisation of syllogistic--in which he uses the constant @ with indef＇mite arity. The atomic formulae are of the following sort： S1S2 ...Sm@P1P2...Pn, where re＋n〉0. The standard syllogistic functors are here interpreted as follows： SAP=： S@P SeP=： SP@ SIP=： -SP@ SOP=： ~S@P Markin constructs a system of Fundamental Syllogistic （FS） with constant @ in an axiomatic way. Based on Markin＇s idea, we propose two constructions, which are formulations of the system of sequential predication built upon the quantifier-less calculus of names. The first one includes the FS system. The second one is enriched with individual variables and, among other things, allows including sequences of individual names in which one has to do with enumerative functors. The counterpart of Hao Wang＇s algorithm holds in the first system extended with negative terms.展开更多
文摘Syllogistic fuzzy reasoning is introduced into fuzzy system, and the new Cascaded Fuzzy System(CFS) is presented. The thoroughly theoretical analysis and experimental results show that syllogistic fuzzy reasoning is more robust than all other implication inferences for noise data and that CFS has better robustness than conventional fuzzy systems, which provide the solid foundation for CFS's potential application in fuzzy control and modeling and so on.
文摘Jan Lukasiewicz acknowledged that Aristotle＇s syllogistic does not admit singular terms and presents syllogism as an implication. But he failed to recognize syllogistic necessity, reducing this necessity to ＂formal implication＂ as introduced by Russell, when Aristotle shows it as binding relations between three terms. On the contrary, Paul Lorenzen directly recognized syllogistic necessity as the typical example of his own logical implication. His reconstruction of syllogistic differs from the original by his interpretation of particular propositions as the determination of classes which are specified by predicates. The result is the representation of valid moods as the board of all multiplications of relations which are permitted. These relations are not only the Aristotelian ,4, E,I, O, but also the new converse asymmetrical relations of A and O： （a） and （o）.
文摘Vladimir Markin proposes a certain construction---a generalisation of syllogistic--in which he uses the constant @ with indef＇mite arity. The atomic formulae are of the following sort： S1S2 ...Sm@P1P2...Pn, where re＋n〉0. The standard syllogistic functors are here interpreted as follows： SAP=： S@P SeP=： SP@ SIP=： -SP@ SOP=： ~S@P Markin constructs a system of Fundamental Syllogistic （FS） with constant @ in an axiomatic way. Based on Markin＇s idea, we propose two constructions, which are formulations of the system of sequential predication built upon the quantifier-less calculus of names. The first one includes the FS system. The second one is enriched with individual variables and, among other things, allows including sequences of individual names in which one has to do with enumerative functors. The counterpart of Hao Wang＇s algorithm holds in the first system extended with negative terms.
