St ructure amp dle Consider this sentence bobby' s father can beat up the father of any other kid on the block Solution Let O K(x): x is a child on the block and b means Bobby o f(x):xs father, O B(,): x can beat up y
Structure . Example . . Consider this sentence ”Bobby’s father can beat up the father of any other kid on the block”. . Solution . . Let 1. K(x): x is a child on the block and b means Bobby. 2. f (x): x’s father, 3. B(x, y): x can beat up y, 4. Finally, ∀x(K(x) → (¬(x = b) → B(f (b), f (x)))). Yi Li (Fudan University) Discrete Mathematics May 28, 2013 7 / 27
St ructure amp dle Consider this sentence bobby' s father can beat up the father of any other kid on the block Solution Let O K(x): x is a child on the block and b means Bobby o f(x):xs father, O B(,y): x can beat up y o Finally;x(K(x)→(-(X=b)→B(f(b),f(x)
Structure . Example . . Consider this sentence ”Bobby’s father can beat up the father of any other kid on the block”. . Solution . . Let 1. K(x): x is a child on the block and b means Bobby. 2. f (x): x’s father, 3. B(x, y): x can beat up y, 4. Finally, ∀x(K(x) → (¬(x = b) → B(f (b), f (x)))). Yi Li (Fudan University) Discrete Mathematics May 28, 2013 7 / 27
Structure( Cont Definition a structure A for a language l consists of
Structure(Cont.) . Definition . . A structure A for a language L consists of 1. a nonempty domain A, 2. an assignment, to each n-ary predicate symbol R of L, of an actual predicate R A on the n-tuples (a1, a2, . . . , an) from A, 3. an assignment, to each constant symbol c of L, of an element c A of A and, to each n-ary function symbol f of L, 4. an n-ary function f A from A n to A. Yi Li (Fudan University) Discrete Mathematics May 28, 2013 8 / 27
Structure( Cont Definition A structure A for a language l consists of o a nonempty domain A
Structure(Cont.) . Definition . . A structure A for a language L consists of 1. a nonempty domain A, 2. an assignment, to each n-ary predicate symbol R of L, of an actual predicate R A on the n-tuples (a1, a2, . . . , an) from A, 3. an assignment, to each constant symbol c of L, of an element c A of A and, to each n-ary function symbol f of L, 4. an n-ary function f A from A n to A. Yi Li (Fudan University) Discrete Mathematics May 28, 2013 8 / 27
Structure( Cont Definition A structure A for a language l consists of nonempty domain A o an assignment to each n-ary predicate symbol r of C,of an actual predicate R a on the n-tuples , from A
Structure(Cont.) . Definition . . A structure A for a language L consists of 1. a nonempty domain A, 2. an assignment, to each n-ary predicate symbol R of L, of an actual predicate R A on the n-tuples (a1, a2, . . . , an) from A, 3. an assignment, to each constant symbol c of L, of an element c A of A and, to each n-ary function symbol f of L, 4. an n-ary function f A from A n to A. Yi Li (Fudan University) Discrete Mathematics May 28, 2013 8 / 27