Based on the direct product of Boolean algebra and Lukasiewicz algebra, six lattice-valued logic is put forward in this paper. The algebraic structure and properties of the lattice are analyzed profoundly and the taut...Based on the direct product of Boolean algebra and Lukasiewicz algebra, six lattice-valued logic is put forward in this paper. The algebraic structure and properties of the lattice are analyzed profoundly and the tautologies of six-valued logic system L6P(X) are discussed deeply. The researches of this paper can be used in lattice-valued logic systems and can be helpful to automated reasoning systems.展开更多
First, the numerous claims that the theory of natural selection would be a tautology, just empty circular reasoning, are shown to be erroneous, and that they follow from an essentialistic and deterministic way of thin...First, the numerous claims that the theory of natural selection would be a tautology, just empty circular reasoning, are shown to be erroneous, and that they follow from an essentialistic and deterministic way of thinking, which is not consistent with the dynamic theory of evolution. Secondly, it is proposed that a careful analysis applying Fisher’s Fundamental Theorem of Natural Selection of the seemingly tautologous sentence in question: “those who reproduce most, reproduce most” shows that in actual fact it is a predictive statement. Consequently, the analysis presented reduces the essence of the theory of natural selection to that one single statement.展开更多
That there are only three different kinds of α_ tautologies in revised Kleene systems is proved first; then in finite case the diversity theorem of α_ tautologies with α’ s larger than the mid_value is established...That there are only three different kinds of α_ tautologies in revised Kleene systems is proved first; then in finite case the diversity theorem of α_ tautologies with α’ s larger than the mid_value is established. Lastly, also in finite case, a representation theorem of α_ tautologies by means of tautologies is given.展开更多
文摘Based on the direct product of Boolean algebra and Lukasiewicz algebra, six lattice-valued logic is put forward in this paper. The algebraic structure and properties of the lattice are analyzed profoundly and the tautologies of six-valued logic system L6P(X) are discussed deeply. The researches of this paper can be used in lattice-valued logic systems and can be helpful to automated reasoning systems.
文摘First, the numerous claims that the theory of natural selection would be a tautology, just empty circular reasoning, are shown to be erroneous, and that they follow from an essentialistic and deterministic way of thinking, which is not consistent with the dynamic theory of evolution. Secondly, it is proposed that a careful analysis applying Fisher’s Fundamental Theorem of Natural Selection of the seemingly tautologous sentence in question: “those who reproduce most, reproduce most” shows that in actual fact it is a predictive statement. Consequently, the analysis presented reduces the essence of the theory of natural selection to that one single statement.
文摘That there are only three different kinds of α_ tautologies in revised Kleene systems is proved first; then in finite case the diversity theorem of α_ tautologies with α’ s larger than the mid_value is established. Lastly, also in finite case, a representation theorem of α_ tautologies by means of tautologies is given.
