endobj 2 + 3 . 2-4 CHAPTER 2. All men are mortal. It will actually take two lectures to get all the way through this. Example of propositions: Example of propositions: John loves CSE 191. Propositional Logic Denition Apropositionis a declarative statement. Propositional Logic • Propositional resolution • Propositional theorem proving •Unification Today we’re going to talk about resolution, which is a proof strategy. stream Stated differently but equivalently, an inference is valid if it has no ‘counter-examples’: First, we’ll look at it in the propositional case, then in the first-order case. �$B���t�k��h�[x����4�B��TR ����E�Q:� �k� ,���[*���h�@��r�w� \*e�TJw��&��2�e�™ݤ�S�+�Av�!��'LdGP /�ez�`ҳq�$ΘK��9���r茒�٧��k��G�Y�&�ʢR.�FY���:��[�T���x��/������5Dra���I�H��Bc�y`4�jwK��rd$X>��cݸ�=�)��fn�����*�] ��d{|��=�3�nH\#Dd���偻���2���T��Q������v�|=l�.����G�S#�U�mN�tUÄ�k=� 48 0 obj NB�e'��4Y�\l�0R~$��[�#�tN�]�/�����n/��v�>�Ԗ��x�r��J��Rav2I�+��(yda׀g�K4�]C����{��D�A���;�gk��u4����:������]��c�2}�;]�͙u��cƨ��&_Kt�\�г������� �����_���m!�o&C�m=e�r�_o߯�:zU,�8��F��F��w H�����]�%���5>p��/�u�b�ڍ;6#� ��r��U�4c��dB�����v~���Z�����\q �K�k|_��k���*���9��`�f��C ګEAW�RW������{�A�7��iOGi3��R�'0��_�5f��v7�us��S�u�W.����)�]��=�C ��s���bЁ}�w�zj7����4����5�����m$� ��ڊ Examples of propositions: The Moon is made of green cheese. ϕ⇒ψ ϕ ψ 14 Rule Instances An instance of a rule of inference is a rule in which all … x��Zݏ۸߿B����X'R$%����} �i��C�Z�^�%�$g����AR��$ ��-P k�C�p8��8J��L�����?5�q�-r� ��dLH��@. 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Predicate logic can express these statements and make inferences on them. Propositional Logic. J��|?��0}��N]Oŗ2ae�ǭ��Â��T��� �i��w$\4���$��ke��mN�h>��*fy���l���NJ�����(MP.��3����0�Y�/�J#e�ʫz��Hw��3ǰ�Q'�p����ƿ'�HY����Sr (��og� ��cc��Nys�������d�%���^�J�ѝ%[ge뻋*�u�W!y�Y��#�0�. We use T to denote TRUE and F to denote FALSE. “Logic” is “the study of the principles of reasoning, especially of the structure of propositions as distinguished The following are propositions: – the reactor is on; – the wing-flaps are up; – John Major is prime minister. It cannot be both TRUE and FALSE. 7 13 Rules of Inference A rule of inference is a rule of reasoning consisting of one set of sentence patterns, called premises, and a second set of sentence patterns, called conclusions. /Length 2680 )��X�� �%��|�Gt�� n�;�A=�/�8\��DB����o�UU��pu�+��� PROPOSITIONAL LOGIC we call an inference valid if there is ‘transmission of truth’: in every situation where all the premises are true, the conclusion is also true. logic can be used to specify precisely the conditions under which a particular diagnosis would apply. Toronto is the capital of Canada. Propositional Logic Denition Apropositionis a declarative statement. Let p be a proposition. c prns nd l ives An ic prn is a t or n t t be e or f. s of ic s e: “5 is a ” d am . Propositional Logic Overview The most basic logical inferences are about combinations of sentences, ex-pressed by such frequent expressions as ‘not’, ‘and’, ‘or’, ‘if, then’. stream The Truth Value of a proposition is True(denoted as T) if it is a true statement, and False(denoted as F) if it is a false statement. Some trees have needles. 2+3=5. ! Propositional Logic Exercise 2.6. x + 1 = 2 x + y = z Five themes: logic and proofs, discrete structures, combinatorial analysis, induction and recursion, algorithmic thinking, and applications and modeling. It is defined as a declarative sentence that is either True or False, but not both. PROPOSITIONAL LOGIC: THE FULL LANGUAGE VL Logic, Lecture 2, WS 20/21 Armin Biere, Martina Seidl Institute for Formal Models and Verification Johannes Kepler University Linz Proposition Truth value %PDF-1.5 Propositional Logic Representing a proposition Representing a proposition Use letters to represent propositional variables Usually, the following letters used: p, q, r, s, ... examples: let p denote the proposition: ”Today is Monday” let q denote the proposition: ”Mary missed class” Propositional Logic September 13, 2020 6 / 52 A proposition is a declarative sentence that is either true or false. A proposition is a statement that is either true or false. Sun rises from West. @��ඃ�xl�, ?o��?�V;�I/�A�Ӎ��R���ؾ �Ϋ��ؑmGK�nr*؉E�]�t�8�>?�k�"�p�VNӞ�R#���kȡṏ�Ǹ�ZQ��\�����}"t��1�� ~���>)}�h�!�G���r� �I����*9=�]w���؎`H���螧�x��k���e�m�O�ĐHP���<�8�~�N�E;�c-�����Z�{��j�g�� �j��]��f������f��+P@�Z�' S:%,^m+ڲ4K��`��3���M�B�^�oM��O]0f���i]�:�� . Trenton is the capital of New Jersey. Definition: A proposition is a statement that can be either true or false; it must be one or the other, and it cannot be both. Propositional logic In logic, the conditional is defined by its truth table, e.g. What is a proposition? - Use the truth tables method to determine whether the formula ’: p^:q!p^q is a logical consequence of the formula : :p. /Length 3645 << /Filter /FlateDecode 1 + 0 = 1 0 + 0 = 2 Examples that are not propositions. Sit down! 2+3=5. X > 3. ! De nition 5. Introduction to Logic using Propositional Calculus and Proof 1.1. 2 + 3 . 2 Propositional Logic The simplest, and most abstract logic we can study is called propositional logic. For Example, Order Logic Propositional Logic First Order Logic Basic Concepts Propositional logic is the simplest logic illustrates basic ideas usingpropositions P 1, Snow is whyte P 2, oTday it is raining P 3, This automated reasoning course is boring P i is an atom or atomic formula Each P i … Example of non-propositions: Does John love CSE 191? It cannot be both TRUE and FALSE. Prl s e d from ic s by g lol s. tives fe e not d or l ) l quivt) A l l la is e th e of a l la can be d from e th vs of e ic s it . p →q where p and q are any statements, this can be translated as: p implies q if p then q p, only if q if p p is necessary for p For example, let p represent “you are 18 or older” and q represents “you can vote” 2.3 Negation Our last basic logical operator is negation, a fancy way to say \not." x��[m��6����ȗ�Y�o������%��A(me[�,m$;�ܯ��[�w�= �dR$g�Ùg���,��W�?�����JB3��\ܮ�a¤�Dr&U��]-~����2����by}��8���)����u�R[V������9��Oewe�^�v��g/҅e�H���ō�,��V�����2��f�7����D��*�e�ϩ��A�۶�u�>��XD��qNc�����B7�~�5N��n���S��ο��j=)k��˛u��jC�YS췻|�b����D��`6��o����u�XT& ,*C,�s�m�%g��y�F�ߚ���ۜ��&/��F�� ��^���m�UK�����b�;J��.�����@��&jN7U*�����IZ,�� Rj$t�t���rhr�v҄��{�J���Q3�-�����}��k��}����y�&�� v�̊G24ǎ���b���g� ʾ�����>/��؏zyhh�N�q���ˬ��:(.�Tj*��|��s�=M�Ϊ�{jq*���ޏ%�f���*�ɱgHqg^�e;�]$L%�h�:G�+'M:� rn&� 0.3. Sun rises from West. understanding of propositional logic. Example of non-propositions: Does John love CSE 191? We use T to denote TRUE and F to denote FALSE. 2+3=8. endstream It must be either TRUE or FALSE. The negation of p, denoted :p, is a proposition that is true when p is false, and false when p is true. %���� ! What time is it? /Filter /FlateDecode Predicate Logic ! Such combinations allow you to describe situations, and what properties these situations have or lack: some-thing is ‘not this, but that’. >> It must be either TRUE or FALSE. >> 65 0 obj �II� 2� @K3`H=�Ч�U��_�bf��DR��n��3�84Lo�ӕ�D�m�)�ֱ�]f�JH��v��=Ł�Y�oQ��b�\����|�v�/"���ۄ��17��d�̫&�F�b2]Qě}/�Y2�����u�A�g�غ�_*�. << !���_' '�aI� ҁ�t �X� �Ҍ�� ���/kF����pq*�nRۏC� �2�n �]� �`_�fR�*���u1��>�[8w�s�熗~�o�*|��*%�[�7;4hO�* P�=K���Ѐ{�a-�9n0 �����d� Some statements cannot be expressed in propositional logic, such as: ! EXAMPLES. 2 The most basic element in logic is a proposition. x�@Xe�@]a��9d�0AD�:�Oc�ؒ�Vf��@/�C��o�U+k� Example of propositions: Example of propositions: John loves CSE 191. 2+3=8. A proposition is the basic building block of logic.
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