Logic

Download A Computational Logic Handbook by Robert S. Boyer PDF

By Robert S. Boyer

This e-book is a user's consultant to a computational good judgment. A "computational common sense"
is a mathematical common sense that's either orientated in the direction of dialogue of computation
and mechanized in order that proofs might be checked by way of computation. The
computational common sense mentioned during this guide is that built through Boyer and Moore.
This guide includes a particular and entire description of our good judgment and a
detailed reference consultant to the linked mechanical theorem proving method.
In addition, the instruction manual features a primer for the common sense as a useful
programming language, an advent to proofs within the good judgment, a primer for the
mechanical theorem prover, stylistic suggestion on how one can use the good judgment and theorem
prover successfully, and plenty of examples.
The good judgment used to be final defined thoroughly in our booklet A Computational
Logic, [4], released in 1979. the most function of the e-book was once to explain in
detail how the concept prover labored, its association, facts innovations,
heuristics, and so forth. One degree of the luck of the publication is that we all know of 3
independent winning efforts to build the theory prover from the ebook.

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Example text

That is, if you know that (EQUAL (APPEND (APPEND X Y) Z) (APPEND X (APPEND Y Z))) always evaluates to T. The situation just described is a simple example of a very deep problem: formalization. 10 Almost invariably, when confronted with the challenge to formalize a problem, new users of our logic are baffled. How can anything as complicated or as abstract as your problem be couched in the simple, nearly constructive system described here? It is hard enough to formalize concepts in a truly powerful mathematical system such as set theory.

LEN L) (EVAL$ T '(IF (NULL L) (QUOTE 0) (ADD1 (LEN (CDR L)) ) ) (LIST (CONS 'L L)))). We are the first to admit the hackish nature of this mechanism of defining FORMALS and BODY when the body used in the definition is such an EVAL$ expression. The rationale behind our choice of this mechanism follows. First, note that unlike the mere assumptions that the FORMALS and BODY of ' LEN are as desired, this mechanism actually introduces the function symbol LEN into the logic. Not only can we talk about the result of interpreting expressions such as ' (LEN X) with EVAL$ or V&C$, but we can talk about such terms as (LEN X).

We explain the fourth restriction later. In general the restrictions on definitional equations are present to insure that there exists one and only one function satisfying the equation. " For example, defining a function named CAR will almost certainly lead to inconsistent statements about its properties. One subtle consequence of this restriction is that it prohibits mutually recursive definitions: if F1 is defined in terms of F l and F2, then a subsequent attempt to define F2 will fail because F2 is already mentioned in an axiom.

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