No sloths are energetic (x) (Sx ⊃ ~Ex) There is no free lunch. 39 0 obj 1’. • Theoretically, first-order predicate logic is • Undecidable. If a thing is worth doing, it is worth doing badly. PREDICATES Every predicate has a degree, which is a number. All bears are dangerous (x) (Bx ⊃ Dx) 2. Mark Twain is a writer and Samuel Clemens is a writer and Mark Twain is Samuel Clemens. If a predicate has degree one, we call it a one-place predicate; if it has degree two, we call it a two-place predicate; and so forth. In predicate logic, every atomic sentence consists of one predicate and one or more subjects. Translate the following English sentence into Predicate Logic with Identity: Desdemona loves Othello, but only Desdemona does. }�� �'`� <> Exercises: Translation practice in propositional logic (with answers) Pick a capital letter to represent each simple statement, and represent the following statements symbolically, using the tilde, dot, wedge, horseshoe and triple bar. �ߞYǬ9W����ZKհw����|�ƓE�`��"Z� Ύ������\p����9�ܘqa�q�j>���)lଃ���W��j1��l~�����4�x��F_h��xo �Ѡ$����$�GWi�t�i@���1i/��p�D� �9^ ��G;T�"! Ax[S(x) --> L(x)] S(x) = x is a sin L(x) = x is a form of lying. ~Ex[F(x) & L(x)] F(x) = x is free L(x) = x is lunch. <> stream <> If the goal is true, guaranteed to halt • Together, it is called semidecidable • It is a uniform framework, and a general problem solving method. The first and major task in predicate logic is getting accustomed to representing these predications in this new way that combines the machinery of propositional logic with the focus of categorical logic. %���� x��V=o1��+�N�H�0n(�Ȗ�[ѡ�s�:$�(���%M�! Redo the translations of sentences 1, 4, 6, and 7, making use of the predicate person, as we would have to do if the domain D contains not only humans but cats, robots, and other entities. Translate a predicate formula into an English sentence. xڵVMo�0��W�X�H}X@�À��nrvh�&���I���tM�m�D4E>>>�6/�Go2p�zH���wt͋��Ƥw0��1� ��'s0������!��_��qwaz=��Ӭ_�\�O,'�Ю\ǒ��l��o`|����L m(�Dgf����8�sH�����#۞.���[&����EϞtg&OX~m����HR���/)����MBR�Ή�"r�B�B-�R�A-������.��;aW=Ҿ#��zQ^�-b+pD������ ��"s �I���V��|��*�1���u :'�5.jZ�΅Eq>��tF�eTB� %7�v�+���&ے]m&�LM
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�Z0� parleft[0]+props[2]+cons[0]+bs[0]+props[2]+cons[1]+parright[0]+bs[0]+cons[0]+eq[0]+cons[1], props[1]+cons[0]+cons[1]+bs[0]+all[0]+props[0]+parleft[0]+os[0]+props[0]+eq[0]+cons[0]+bs[2]+os[0]+props[1]+props[0]+cons[1]+parright[0], exists[0]+props[0]+parleft[0]+props[3]+props[0]+bs[0]+exists[0]+props[1]+exists[0]+props[2]+parleft[0]+os[0]+props[1]+eq[0]+props[2]+bs[0]+parleft[0]+parleft[0]+props[4]+props[1]+bs[0]+props[5]+props[0]+props[1]+parright[0]+bs[0]parleft[0]+props[4]+props[2]+bs[0]+props[5]+props[0]+props[2]+parright[0]+parright[0]+parright[0]+parright[0], all[0]+props[0]+all[0]+props[1]+parleft[0]+parleft[0]+parleft[0]+parleft[0]+props[4]+props[0]+bs[0]+props[3]+props[0]+parright[0]+bs[0]+props[5]+props[0]+parright[0]+bs[0]+parleft[0]+parleft[0]+props[4]+props[1]+bs[0]+props[3]+props[1]+parright[0]+bs[0]props[5]+props[1]+parright[0]+parright[0]+bs[2]+props[0]+eq[0]+props[1]+parright[0], exists[0]+props[0]+parleft[0]+parleft[0]+props[3]+props[0]+bs[0]+props[4]+props[0]+parright[0]+bs[0]+all[0]+props[1]+parleft[0]+parleft[0]+props[3]+props[1]+bs[0]+props[4]+props[1]+parright[0]+bs[2]+props[1]+eq[0]+props[0]+parright[0]+bs[0]+props[5]+props[0]+parright[0]. Everyone loves Mary. 31 0 obj All sin is a form of lying. In this course we are concerned with the transcription using given predicate symbols and the universe. ∀x (person(x) → love (x, Mary)) 4’. stream Desdemona loves Othello, but only Desdemona does. x�mR�n1��+�RH��0�P 1����=�v�S��BJ+�A Everyone loves Mary. (Introduction to Predicate Logic) Give examples of English sentences that can be modeled using predicate logic but cannot be modeled using propositional logic. Translation practice Key to symbols ~ = negation & = conjunction--> = conditional implication E = existential quantifier A = universal quantifier. x��V=o�0��+��J$�a��@�[�ۊq.��!��CII�Ή�&H��-����#)�;��7 8g=Ds����n͝xb��`3 J���,��_p�5l�/@0�. • But logic is weak for representing certain kinds of knowledge endobj You are going to love it! (Translations) Translate an English sentence into a predicate formula. 1’. More Answers for Practice in Logic and HW 1.doc Ling 310 Feb 27, 2006 5 15. %PDF-1.5 26 0 obj The Republican candidate can win the election. <> CS 245 Logic and Computation Fall 2019 3 / 37 Translate the following English sentence into Predicate Logic with Identity: Mark Twain is the same writer as Samuel Clemens. stream stream endstream endobj Here are examples to practice with: 1. ��� ���\Ͽw��3"&��D���NVo^_B�ŐRMV9�Q|Z�����3�Fu#��y��JF��qJ>�yo:�v��ˬ�4�:����6+����彮�y���#a ���I�-�PR�6#�� �&{������̋S?�$ �
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^�BL�Xu��^7��-���t��C�>�y�,p��H{�R!�B=�s��WV,�$�UͮU͘S�;>��/��`m-T�W)*q�${퉘�3���]&L7�V�*s�~n�:�o���'G�N�k;/��,3����R>�f�E*�2[mK��{d�n�S�g�:������y��%D�.�=�4�����͓}���w���K�L�cJq���'�1�Z$� �xX�B�!��N�m3��+#p�s&P��{�+�Y�W��K9N�]D* ��J�A�o��`9���q^���F��F��_?a� Everyone loves someone. Desdemona loves Othello and anyone other than Desdemona does not love Othello. cw��p43\x�Aa`�H������v]��5��̱&.��?�����u�)+��+}\й�[�������X�� Desdemona loves Othello and no one other than Desdemona loves Othello. To transcribe a proposition stated in English using a given set of predicate symbols, first restate in English the proposition using the predicates, connectives, and quantifiers. O/T"� 13 0 obj Some one is such that she is a student and she owns two computers. At most one Republican candidate can win the election. )2��N��Y�=�6܃+�5����^��a����P@��F,�;X�F��e�A@�_. Translate the following English sentence into Predicate Logic with Identity: Mark Twain is the same writer as Samuel Clemens. ... 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