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Applied Mathematics for Database Professionals phần 10

Lưu ý ukasiewicz cũng giới thiệu các ký hiệu Ba Lan, cho phép các biểu thức để được viết rõ ràng mà không cần sử dụng dấu ngoặc. Đây là cơ sở của các ký hiệu Ba Lan ngược (RPN), nhiều máy tính bỏ túi và các trình biên dịch biểu hiện sử dụng.Điều này là khá trơn, vì nó có nghĩa rằng trong 3VL UNKNOWN giá trị dường như là hơi đặc biệt. | APPENDIX D NULLS AND THREE OR MORE VALUED LOGIC 341 Note tukasiewicz also introduced the Polish notation which allows expressions to be written unambiguously without the use of brackets. This is the basis of the Reverse Polish Notation RPN which many pocket calculators and expression compilers use. In 3VL predicates can change their truth values in time but only from UNKNOWN to TRUE or from UNKNOWN to FALSE. This is rather slippery because it means that in 3VL the value UNKNOWN seems to be somewhat special. This description is too vague anyway we need formal rules definitions and truth tables. We ll look at those details in a minute. 3VL is counterintuitive as opposed to the classical 2-valued logic 2VL . The main reason is that you lose the tertium non datur the principle of the excluded middle . That is if P is unknown then -1P is unknown as well which in turn means that P Ú -1P is unknown. Consider the following famous Aristotelian example. Tomorrow a sea battle will take place is neither TRUE nor FALSE it is unknown yet the sentence Either tomorrow there will be a sea battle or tomorrow there won t be a sea battle is certainly true in reality . However it is unknown in 3VL hence the counterintuitive nature. Another problem arises from the fact that if two predicates are possible that is their truth value could possibly be TRUE then their conjunction is also possible. However this is obviously wrong if one of them is a negation of the second. Ludwik Stefan Borkowski 1914-1993 proposed to fix this problem by introducing a 4-valued logic 4VL this indeed makes the preceding problem disappear but the solution is unsatisfactory and ad hoc. Furthermore 3VL does not solve the problem of handling missing information it does not allow you to represent the reason why information is missing. At the end of this section you ll see that Ted Codd proposed a 4VL in 1990 to distinguish between applicable and inapplicable values. However a 4VL doesn t tell you what to do if you .