hw3 - predicate symbols, C , T 1, T 2, and M where C ( x,y...

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CISC 404/604 Homework 3 Due on Thursday, April 22, 2010 1. (35 points) For each of the following wfs, give a structure that satisfies the wf and another structure that falsifies it. a. (( x ) P ( x ) ( x ) Q ( x )) ( x )( P ( x ) Q ( x )). b. ( x )( P ( x ) P ( a )). c. ( x )( y )[ P ( x,y ) ( z )( ¬ ( P ( x,z ) P ( z,y )))] d. ( x ) ¬ P ( x,x ) ( x )( y )( z )[( P ( x,y ) P ( y,z )) P ( x,z )] ( x )( y ) P ( x,y ) e. ( x )( y )( z ) P ( x,y,z ) ( x )( y ) P ( x,y,f ( x,y )). 2. (35 points) a. Consider the following sentences. i. Any student who takes CISC301 will also take MATH210. ii. Some instructor of a CISC course has taught a LING course. iii. Some CISC major has taken all CISC courses. iv. No instructor who teaches CISC301 has taught a course taken by a LING student. v. Every LING major has taken a course taught by some instructor who has taught CISC301. Translate the sentences above using the following constants, c 3, m 2, c , and l (for CISC301, MATH210, CISC, and LING respectively); unary predicate symbols, S and I (for is-student, and is-instructor respectively); and binary
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Unformatted text preview: predicate symbols, C , T 1, T 2, and M where C ( x,y ) stands for course x is offered by department y , T 1( x,y ) corresponds to course x is taught by y , T 2( x,y ) corresponds to course x is taken by y , and M ( x,y ) corresponds to x is the major of y Important : Do not use any other function, constant or predicate symbols. Clearly parenthesize your formulae, especially to ensure that there is no am-biguity about the scope of the quantifiers. b. (Exercise 86 from Schoening’s book) Translate the following two sen-tences into wfs: i. Every barber shaves all persons who do not shave themselves. ii. No barber shaves any any person who shaves himself. For this part, use S ( x,y ) to stand for x shaves y and B ( x ) to correspond to x is a barber. 1...
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This document was uploaded on 12/07/2011.

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