The circuit representation in the chapter is more detailed than necessary if we care only about Circuit functionality. A simpler formulation describes any rn-input, n-output gate or circuit using a predicate with m + n arguments, such that the predicate is true exactly when the inputs and outputs are consistent. For example, NOT-gates are described by the binary predicate NOT (i, o), for which NOT (0, 1) and NOT (1, 0) are known. Compositions of gates are defined by conjunctions of gate predicates in which shared variables indicate direct connections. For example, a NAND circuit can be composed from ANDs and NOTs: Using this representation define the one-bit adder in Figure and the four-hit adder in Figure, and explain what queries you would use to verify the designs. What kinds of queries are not supported by this representation that is supported by the representation in Section8.4?
Answer to relevant QuestionsProve from first principles that Universal Instantiation is sound and that Existential Instantiation produces an inferentially equivalent knowledge base.Suppose we put into a logical database a segment of the U.S. census data listing the age, city of residence, date of birth, and mother of every person, using social security numbers as identifying constants for each person. ...The following Prolog code defines a predicate P: P(X, [X | Y]). P (X, [Y| Z]):- P (X, Z).a. Show proof trees and solutions for the queries P (A, [1, 2, 3]) and P (2, [1, A, 3])b. What standard list operation does P represent?We said in this chapter that resolution cannot be used to generate all logical consequences of a set of sentences. Can any algorithm do this?Construct a representation for exchange rates between currencies that allows fluctuations on a daily basis.
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