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We have to consider the … [j��������^�r/��ߋ��;�����vb�� Axiomatizability. %�쏢 e�p6?�i����?g_�ɔ}�2M&¨�;���� Gm�V�*W��!�r�^:z3:��(�P���r�^(K/�h�x��? Truth Values An interpretation I is a function which assigns to any atomic formula p i a truth value I(p i) 2f0;1g: If I(p i) = 1, then p i is called true under the interpretation I. K�$�`9���PB�����{.q9"����m���7�ۉ]o����r�Ė4?&� ��X��k0��"{�0�%� ! propositional logic if and only if there is a signature of size n and a set of sentences from the corresponding language such that the vectors in the set correspond to the set of interpretations satisfying the sentences. PROPOSITIONAL FORMULAS: SYNTAX VL Logic Part I: Propositional Logic. x��ً��0�������>�%�3%�$�}�� �C��ݑ� �t��j3 �� h#h&��� �n��j3 �� h#h&ё� ��5Th��R �̈́���7��^L�B�� ��Z ��h&�x�= ��\zZm��� mD3�7#�e ��T��f�ZH- �F�Lr#�q p%]IZm��� m�$7�� '҉T��f�ZH- �F�L�#� pGZm��� m�$7� propositional logic, such as: ! A predicate P describes a relation or property. G�i�7ه ȗI�,�5$b��“�Y��2UE�EK�L(/P�����G��c�$���To)�~=�X��ߜČ�@ǖ:�6�=u���R��ti�.#�J|���9�Z&�n����04-S1^$��7�ً�������*�|�i ����h2�xW�ԙwW����O��R�)��09�M:� ��&�o� ���h���ƁS$y�*k����j�U�)���Ԫi7MY���?v�q�$U2��U�K��6��G For example, Chapter 13 shows how propositional logic can be used in computer circuit design. 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Logic in Computer Science 4. stream 1 0 obj <<>> endobj M[�4J� �;Bi+|��7fV8�-C? Variables (x,y) can take arbitrary values from some domain. X > 3. ! ]"��N!��^V'�r+�LN�]���i,�ʯg�_�``�d��c�6��%vܡ��~���Y�X��͂�Q��y+(g�j .��yںr�Ε�1[���RA�U�O�V�y�@�c� Predicate logic can express these statements and make inferences on them. 12 0 obj <> /XObject <> /ProcSet [/PDF /Text /ImageC ] >> /Group 14 0 R /Trans <> /Parent 22 0 R /MediaBox [0 0 453.543 255.118 ] /TrimBox [0 0 453.543 255.118 ] /Rotate 0 >> endobj Unfortunately, the selection of the guests is not straight forward. The fundamentals of proofs are based in an understanding of logic. ! x��\[��4��S��S���qt�`!,,�����d&$�$�K��~-YV˖s2���$. �,�9%�S��Y�7�Ew�8��a�jg�+{�⩒j�v6�E'�����Ӽ�6 n�P ò��F������4���^� '��3�]�,[3�RI��&C��!�\��$��T�tv�z��55m�j1���nݺԋ�y^�Y�O�-�Oe�n�"Z��Y�v9�4���W�vyR��e�Se߮l�c���D�Fs All men are mortal. 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