Minds and Computers : An Introduction to the Philosophy of Artificial Intelligence
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- Exercise 13.2
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Exercise 13.1
(a) If something is a woman, then that thing is human. If something is human, then that thing is mortal. Represent this symbolically. (b) Sue is a woman. Give a symbolic representation of the deduction you can make from this, given the conditionals you represented in (a). The predicates we have seen so far have been one-place or monadic predicates. We will also want to use, in our example expert system, predicates which attribute relations between two names. Consider the relation expressed in the statement ‘Mia is older than Linus’. The relation ‘older than’ is asserted to hold between two things which we can name m and l, allowing the following symbolic representation: older_than (m , l) Note that the order of names in two-place predicates is important. The following statement is interpreted as saying that Linus is older than Mia. older_than (l , m) We can use the symbolism we have developed so far to encode some- thing that we know – as a matter of common-sense knowledge – about the relation ‘older than’, as follows: older_than (x , y) & older_than (y , z) → older_than (x , z) The ampersand (&) in the above simply stands, as you might expect, for ‘and’, the logical operation of conjunction. We say that the condi- tional represented above has a conjunctive antecedent. The symbols x, y and z are variables, not names. The above conditional tells us that if x is older than y and y is older than z, then x is older than z. This is something that anyone who understands the meaning of ‘older than’ implicitly understands. In logical terms, it tells us that the symbol ‘older_than’ represents a transitive relation. 136 Exercise 13.2 (a) What other relations can you think of which are transitive? (b) A symmetrical relation is one such that if x bears the relation to y then y also bears the relation to x. What symmetrical relations can you think of ? (c) Use the symbolism we have developed to represent that a Download 1.05 Mb. Do'stlaringiz bilan baham: 
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