Formal concept analysis （FCA） is a discipline that studied the hierarchical structures induced by a binary relation between a pair of sets, and applies in data analysis, information retrieval, knowledge discovery, e...Formal concept analysis （FCA） is a discipline that studied the hierarchical structures induced by a binary relation between a pair of sets, and applies in data analysis, information retrieval, knowledge discovery, etc. In this paper, it is shown that a formal context T is equivalent to a set-valued mapping S ： G → P（М）, and formal concepts could be defined in the set-valued mapping S. It is known that the topology and set-valued mapping are linked. Hence, the advantage of this paper is that the conclusion make us to construct formal concept lattice based on the topology.展开更多
Our ability to arrive at knowledge by chains of judgment is constitutive of our rationality, likewise our ability to discern the self-evidence of logical and arithmetical laws. To count an activity as ＂thinking about...Our ability to arrive at knowledge by chains of judgment is constitutive of our rationality, likewise our ability to discern the self-evidence of logical and arithmetical laws. To count an activity as ＂thinking about the physical world＂ is to hold it assessable in the light of the laws of physics; whereas to count an activity as ＂thinking at all＂ is to hold it assessable in the light of the laws of logic. Thus, the kind of generality that distinguishes logic from the special sciences is a generality in the applicability of the norms it provides. Logical laws are more general than laws of the special sciences because they prescribe universally the way in which one ought to think, if one is to think all. Logicism is usually understood to be the thesis that all, or at least large parts of, mathematics can be reduced to logic. This thesis has two sides： （1） all mathematical concepts can be defined in terms of basic logical concepts; （2） all mathematical theorems can be deduced from basic logical truths. According to logicism all terms, including all mathematical terms, are to be given a definite meaning within the basic system. This paper aims at a comparative analysis of the contributions of Frege and Russell to the development of modem logic by reviewing in some detail their essential features and derivations. Without making any pretensions to proffering a definitive resolution of any puzzles, the discussion will, however, raise some fundamental questions, and offer a critical evaluation of the putative success or failure of the logicist programmes of Frege and Russell.展开更多
基金the Young Foundation of Sichuan Province(06ZQ026-037) the Education Department Foundation of Sichuan Province(2005A1212006A084)
文摘Formal concept analysis （FCA） is a discipline that studied the hierarchical structures induced by a binary relation between a pair of sets, and applies in data analysis, information retrieval, knowledge discovery, etc. In this paper, it is shown that a formal context T is equivalent to a set-valued mapping S ： G → P（М）, and formal concepts could be defined in the set-valued mapping S. It is known that the topology and set-valued mapping are linked. Hence, the advantage of this paper is that the conclusion make us to construct formal concept lattice based on the topology.
文摘Our ability to arrive at knowledge by chains of judgment is constitutive of our rationality, likewise our ability to discern the self-evidence of logical and arithmetical laws. To count an activity as ＂thinking about the physical world＂ is to hold it assessable in the light of the laws of physics; whereas to count an activity as ＂thinking at all＂ is to hold it assessable in the light of the laws of logic. Thus, the kind of generality that distinguishes logic from the special sciences is a generality in the applicability of the norms it provides. Logical laws are more general than laws of the special sciences because they prescribe universally the way in which one ought to think, if one is to think all. Logicism is usually understood to be the thesis that all, or at least large parts of, mathematics can be reduced to logic. This thesis has two sides： （1） all mathematical concepts can be defined in terms of basic logical concepts; （2） all mathematical theorems can be deduced from basic logical truths. According to logicism all terms, including all mathematical terms, are to be given a definite meaning within the basic system. This paper aims at a comparative analysis of the contributions of Frege and Russell to the development of modem logic by reviewing in some detail their essential features and derivations. Without making any pretensions to proffering a definitive resolution of any puzzles, the discussion will, however, raise some fundamental questions, and offer a critical evaluation of the putative success or failure of the logicist programmes of Frege and Russell.
