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# I shall begin by listing predicates and domains. SPEAKS takes two inputs. The first input is a person and the second input is a language. The meaning...

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I shall begin by listing predicates and domains. SPEAKS takes two inputs. The first input is a person and the second input is a language. The meaning of SPEAKS(x, y) is that x speaks y. MESSAGE takes four inputs. The first input and the third input are persons. The fourth input is a point in time or interval of time. The second input is the id number of a message. MESSAGE(x, y, z, t) means that x sent a message with id number y to z at time t or during time interval t. LIKES takes two inputs. Both inputs are persons. LIKES(x, y ) means x likes y. KNOWS takes two inputs. Both inputs are persons. KNOWS (x, y) means x knows y. SAMECONTENT takes two inputs. Both inputs are message id numbers. SAMECONTENT(x, y) means that the messages with id numbers x and y have the same content (but the message might be given different id numbers). Your task is to translate into quantificational logic the English sentences 1 through 9 below. The only quantifiers you may use are the basic quantifiers. The only predicates allowed are those mentioned above. You are free to introduce your own constants. Your quantificational logic formulae should be syntactically correct sentences that do not violate type constraints. (In all these sentences, do not worry about tense. So sent means has sent, will send or is sending now. Never sent means never sent and never will send etc.) 1. Somebody sent a message to Elizabeth TODAY (use TODAY as a constant). 2. Nobody sent a message to Elizabeth TODAY. 3. At least two people like Elizabeth.
4. Everyone who knows Henry likes Henry. 5. Henry never sent a message to Elizabeth. 6. Henry sent exactly one message to Elizabeth TODAY. 7. Today Henry sent a message to Elizabeth and sent a message to Jane and the two messages had the same content. 8. Henry did not send a message to Elizabeth if Elizabeth did not send a message to Henry. 9. Henry knows someone who speaks Japanese. You probably should use constants Japanese, Henry, Elizabeth, Jane but you might abbreviate if you are clear about your abbreviations.

∃x, z (MESSAGE(x, ELIZABETH, z, TODAY)) ¬(∃x, z (MESSAGE(x, ELIZABETH, z, TODAY))) ∃x, y (LIKES(x, ELIZABETH) ∧... View the full answer

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