An Introduction to Logic Programming Through Prolog by J. M. Spivey

By J. M. Spivey

This is often one of many few texts that mixes 3 crucial theses within the examine of good judgment programming: the good judgment that provides good judgment courses their certain personality: the perform of programming successfully utilizing the good judgment; and the effective implementation of common sense programming on desktops. The e-book starts off with a gradual advent to good judgment programming utilizing a couple of basic examples, by way of a concise and self-contained account of the common sense in the back of Prolog programming. This results in a dialogue of tools of writing courses in order that the method of deriving anwers from them is as effective as attainable. The innovations are illustrated by means of sensible examples and the ultimate a part of the ebook explains how common sense programming could be implented successfully. It comprises resource code for a small yet whole Prolog implementation written in Pascal. The implementation is able to working the entire courses awarded within the ebook, and is obtainable through the net

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Again the body of C3 contains Ri , so C3 is true in M . 1 Substitution and ground resolution 49 in M . In the latter case, either i = j (case 2), or Q = Qj is false in M . In that case, the truth of C2 implies that one of the Ri is also false in M (case 3). Combining the rule of substitution (using a ground substitution) with the rule of ground resolution allows us to derive new ground clauses from a program. Both rules say that if certain clauses are entailed by a program, then so is another clause.

Qn . is true in M exactly if either P ∈ M , or Qi ∈ / M for some i. This agrees with the rule we used earlier with truth tables: a clause is considered true unless all the literals in the body are true, but the head of the clause is false. We translate ‘P is true’ by P ∈ M , because M contains exactly the ground literals that are considered true under the interpretation. 42 The meaning of logic programs Now for clauses that contain variables: we say a clause C is true in an interpretation M exactly if every ground instance of C is true in M .

For parts (3) and (4), we are required to prove the equality of various substitutions. For this, we use the fact that two substitutions are equal if they agree on every variable. If x is any variable, then x [(r ⊲ s) ⊲ w] = x [r ⊲ s][w] = x [r][s][w] = x [r][s ⊲ w] = x [r ⊲ (s ⊲ w)]. Also, x [I ⊲ s] = x [I][s] = x [s] = x [s][I] = x [I ⊲ s]. 4 Substitutions 45 in defining what it means for C to be true in a certain interpretation; they are simply the instances C[g] where g is a ground substitution.

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