Because you presumably speak English, you should know why and also why "not both" is not the same as "both not," (these examples are also covered extensively in the Chapter), but to get the right answers on a test, at first all you have to do is mimic the dictionary. 2. HINT: What kinds of truth conditions would you get if you translated (6) literally? The domain that you are working over is X, the set of people. then you could simply look in the dictionary for the key words "not both" and mimic that example. In the present section, we examine the latter in a little more detail. Translate the following sentences from English to predicate logic. So, for communicating the rest of the semester we need to make a few substitutions. So the answer is ~(S • T), but not ~ S • ~ T.". 10.1 Solutions to predicate translation exercises; 10.2 Proofs in Predicate Logic. Also, keep in mind that most people are not proficient in a language right away. �:�F�$VK�P�!�}�b���Ǝ�������rB��Gm�i�}��5�e7��R��r� ͭ���Xڡd�T�Z�k$���r��쐝2�{�Jk��(��r�[x;ڄ�)r��*8b�b[�-����i�>v�TnZ�x^��)n�5]��M���9� ��XoL���wKL�G�F`Εl�8�B�z)�����N���1_r�� �@�Z�[���ӊ� ��2��%^] ?��s�HRj��h��w( ��f���[_�J8��eue�6�! stream As the chapter shows, we will be using: Pua and Kanoe are Native Hawaiians. Instead they try to think the sentence through and then translate. If you don't understand what you read, then you will have a difficult time representing what you read in a new language. We saw that we could represent the patterns of common fallacies and simplify them in symbols. See number 18 in the dictionary. (P, F). What we will be learning in chapters 7-11 is basically the software foundation -- the most basic logical operations -- of our thinking that we put into computers. ", Often I find some students don't use the dictionary. It takes lots of practice. x���o��Q%���C$��Ҧrn���^1��x-З"/)�A�S�(� q��$�����[�t�v�9\�^`Dh���M�w�����_�7����_��5b�?_�?�+�vm��P��,���1���N This chapter is our first on symbolic logic. The notes for #s 19, 20, and 21 are a reminder that "if only" and "provided that" are the same as "if." 226 Hardegree, Symbolic Logic 4. Although the basic symbols for the logical connectives are supported by Microsoft Word and Microsoft's Outlook Express e-mail program, they are usually not supported by most other e-mail programs and by the Laulima program we are using for our discussion forums (unless you know how to program in HTML). But he or she might make the second statement to students to remind them that there is more than just the final exam in the course. Students will often also miss ones like this in the exercises, "Keoni will make the Dean's List this year, if he receives at least a 3.5 GPA for the semester.". G vC ⊃--> 'if, then' If George attends the meeting tomorrow, then Chelsea will attend. #s 20 & 21 "provided that" = "if" = antecedent. Both 17 and 21 are telling us that "if" and "provided that" are translated as regular "if, then" statements and that what follows "if" or "provided that" will be an antecedent. In the above languages, students must learn hundreds of words each semester. G > (H > C) Also, learning languages is difficult for most people. In the present section, we examine the latter in a little more detail. (H & E) > ~C Remember learning a new language takes time and practice, but also keep in mind that symbolic logic was invented to help us keep track of English statements that can easily lead to confusion and logical mistakes. P •K v= 'or' George or Chelsea will be at the meeting tomorrow. (Translations) Translate an English sentence into a predicate formula. Translate a predicate formula into an English sentence. The most important pages in Chapter 7 cover what we call The Dictionary. Chapter 7 focuses on simply translating regular English statements into a new symbolic language. From the viewpoint of sentential logic, there are five standard connectives – ‘and’, ‘or’, ‘if...then’, ‘if and only if’, and ‘not’. As the chapter shows, we will be using: ~--> 'not' Obama will notbe president in 2016, ~O •--> 'and' Pua and Kanoe are Native Hawaiians. Practice, practice, practice. 1 Response to Solutions to predicate translation exercises. The textbook compares the translation process to a child learning a language. Number 11 in the dictionary shows that our answer should be ~(S • T). B ⊃ (H • E)     / ∴ ~B, 1. As an exercise, figure out whether you could get essentially the same results by using a more direct translation (i.e., one that literally translates the English into predicate logic), and taking pragmatic information into account. G ⊃C ≡--> 'if and only if' Democracy will be possible in Iraq if and only if the ethnicities cooperate. 2. P • K, George or Chelsea will be at the meeting tomorrow. (S, M). 226 Hardegree, Symbolic Logic 4. Obviously, predicate logic can be very expressive. The note for #16 is a reminder that the easiest way to translate "unless" is to interpret it as an "or" statement. At this stage of the semester, the videos usually become very useful for most students, as a lot of what we will be doing now involves visual learning and recognizing patterns. That would be correct, but understanding the dictionary examples and then just looking a similar statement up in the dictionary is easier. ~G > ~(A v B) But if the "not" comes before the "if," then the entire statement is being negated and you should translate as in 2. B > (H & E)        / ~B. For many students translating is one of the hardest parts of learning how to do symbolic logic. And, the note for #23 is a reminder that a sufficient condition will be translated as an antecedent. D = "Keoni will make the Dean's List this year", G = "Keoni receives at least a 3.5 GPA for the semester,". In mathematical logic, predicate logic is the generic term for symbolic formal systems like first-order logic, second-order logic, many-sorted logic, or infinitary logic. Students will often comment that their heads are spinning after reading C7. At this stage of the semester, the videos usually become very useful for most students, as a lot of what we will be doing now involves visual learning and recognizing patterns. So, notice that the answer for #20, Ex III: 1. This was an important step in the eventual development of our modern technological society and our use of digital computers. which connective is the major connective? CS 245 Logic and Computation Fall 2019 3 / 37 III in the textbook (C7). Obviously these statements are very different. The Chapter 7 exercises (I, II, III) are only the first ones. The note for #22 is a reminder that whatever a necessary condition is in a statement, it will be translated as a consequent. (Introduction to Predicate Logic) Give examples of English sentences that can be modeled using predicate logic but cannot be modeled using propositional logic. T = "Lena can play tennis this year" [Reminder]. III of (A • B) ⊃ ~ C -- it would become: When we start doing arguments we have to use ( / ) without the three dots for the conclusion. This makes the expressions compact and precise. The process is very similar. Two common quantifiers are the existential ∃ ("there exists") and universal ∀ ("for all") quantifiers. See why? Do Ex. Below also. It thus eliminates possibilities of misinterpretation of sentences. G v C, If George attends the meeting tomorrow, then Chelsea will attend. If you don't want to cut and paste the symbols from the Laulima announcements, you can substitute & for ( • ), > for ( ⊃ ), and = for ( ≡ ) . When we use 'only if' we are saying something is necessary. G ⊃ (H ⊃ C) For instance, suppose I asked you on the final exam to translate the sentence, "Lisa can not play both soccer and tennis this year.". 2. Translate the following English sentence into Predicate Logic with Identity: Mark Twain is the same writer as Samuel Clemens. 1. For all the basics listed in the dictionary, all the thinking has already been done. The note for #18 is a reminder that an "only if" statement is special and what follows an "only if" in a statement will be translated as a consequent. ����f)��y��������h��y!5��ж�����%i4���H����NZu?&Ie�D-�Y��N�M��� f��凫+��dҨ� (�@����) �婿P2�i�A[�Ԗ��IS���5Ӎ$�5��Nږ�������3��������ǿj�8u�7�3+�bM�#�k�=��� ��ڈ"��뎶����q�o�ag�z���-�;�uI����4)�}I�� This example shows that "provided that" is translated the same as #17 when "if" is in the middle of a sentence. Before a child can communicate, he or she must know how to use the words 'and ,' 'or ,' and 'not .' The sentence is really saying if he does G, then he gets D. "Harold can be a STEM major only if he gets better in math." 4. It is not true that if you pass the final exam, you will automatically pass the course. You may use the functions S(x), meaning that “x has been a student of 6.042,” A(x), meaning that “x has gotten an ‘A’ in 6.042,” T(x), meaning that “x is … i;8��GRgpRcMAQa�aYX�x���JPm���ڪ��F����"�6D�L�{��� J4Ҽ��a~�͍��+�8��h{� They tell me they "just go for it." Centuries ago philosophers discovered that we could put our thoughts into symbols and more easily follow and judge the reasoning trails we create. SINGULAR TERMS Predicate logic analyzes every atomic sentence into a predicate and one or more subjects. So, for the rest of the semester, unless you want to cut and paste, submit answers for feedback via either e-mail or our discussion forums as follows: So, if you had an answer for Ex. Transcribing English to Predicate Logic wffs Subjects to be Learned. Today we create programming languages to accomplish this process. Translating from English to predicate Logic with Identity: Mark Twain is the writer. Tell me they `` just go for it. the word `` if '' = Lena! 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