By Robert S. Boyer

ISBN-10: 0121229505

ISBN-13: 9780121229504

Not like such a lot texts on common sense and arithmetic, this e-book is ready the way to turn out theorems instead of evidence of particular effects. We supply our solutions to such questions as: - while may still induction be used? - How does one invent a suitable induction argument? - while may still a definition be multiplied?

Show description

Read or Download A Computational Logic PDF

Similar applied books

Download e-book for iPad: Applied Mathematics Entering the 21st Century: Invited Talks by James M. Hill, Ross Moore

Papers showing during this quantity are the Invited Talks given at ICIAM 2003, the fifth overseas Congress of business and utilized arithmetic, held in Sydney over the interval July 7 to eleven, 2003. The Congress celebrates and describes the contributions of utilized arithmetic -- as an highbrow production in its personal correct, as a beginning stone of technological improvement, and as an vital collaborative associate for different medical disciplines.

Get Developments in Surface Contamination and Cleaning - PDF

Floor infection is of cardinal value in a bunch of applied sciences and industries, starting from microelectronics to optics to automobile to biomedical. hence, the necessity to comprehend the motives of floor illness and their elimination is especially patent. as a rule conversing, there are wide different types of floor contaminants: film-type and particulates.

Joseph B. Keller, David W. McLaughlin, George C.'s Surveys in Applied Mathematics PDF

Partial differential equations play a primary position in lots of branches of technology and engineering. for this reason you will need to remedy difficulties related to them. One point of fixing a partial differential equation challenge is to teach that it truly is well-posed, i. e. , that it has one and just one resolution, and that the answer relies continually at the information of the matter.

Download e-book for kindle: Recent Developments in Anisotropic Heterogeneous Shell by Alexander Ya. Grigorenko, Wolfgang H. Müller, Yaroslav M.

This short e-book offers ideas of stress-strain difficulties for a large classification of anisotropic inhomogeneous shells bought by way of the subtle version. learning those difficulties ends up in serious computational problems because of partial differential equations with variable coefficients as a result of the constitutive kin of the unique version.

Additional info for A Computational Logic

Example text

Among the theorems that can be derived from the above axioms is the theorem that if X and Y are numeric, then (ADDI X) is equal to (ADDI Y) if and only if X is equal to Y. See Appendix B. We will abbreviate (ZERO) as 0 , and any well-formed nest of ADDl's around a 0 as the decimal numeral expressing the number of ADDI terms in the nest. Thus, 1 is an abbreviation for ( ADDI 0 ) , 2 is an abbreviation for (ADDI (ADDI 0) ) , etc. G. LITERAL ATOMS We want to be able to prove theorems about functions that manipu­ late symbols.

I. DEFINITIONS We have already defined certain simple functions, such as AND, OR, NOT, and IMPLIES. For example, Definition (AND P Q) ( I F P ( I F Q T F) F). Another simple function we define is ZEROP; it returns T if its argu­ ment is virtually 0 (in the sense that ADDI and SUBI treat it as 0) and F otherwise: Definition (ZEROP X) (OR (EQUAL X 0) (NOT (NUMBERP X ) ) ) . In general, if the function symbol f is new, if Xi, . . , x n are dis­ tinct variables, if the term body mentions no symbol as a variable other than these Xi, and if body does not mention f as a function sym­ bol, then adding the axiom ( f xi .

Xn) ) ) , means to add as an axiom the defining equation: ( f Xi . . xn) = body. We now illustrate an application of the principle of definition. Imagine that LESSP is well founded and that the axioms CAR. LESSP and CDR. LESSP have been added as in Chapter II. The defining equa­ tion for MC. FLATTEN is added to our theory by the following instantia­ tion of our principle of definition, f is the function symbol MC . FLATTEN (CDR X) ANS)) (CONS X ANS)); r is LESSP ; m is the function symbol COUNT 1, where ( COUNT 1 X Y ) is 46 / III.

Download PDF sample

A Computational Logic by Robert S. Boyer

by George

Read e-book online A Computational Logic PDF
Rated 4.86 of 5 – based on 26 votes