Propositional and Predicate Calculus A Model of Argument 1st edition by Derek Goldrei – Ebook PDF Instant Download/Delivery: 1852339217, 9781852339210
Full download Propositional and Predicate Calculus A Model of Argument 1st edition after payment
Product details:
ISBN 10: 1852339217
ISBN 13: 9781852339210
Author: Derek Goldrei
At the heart of the justification for the reasoning used in modern mathematics lies the completeness theorem for predicate calculus. This unique textbook covers two entirely different ways of looking at such reasoning. Topics include:
- the representation of mathematical statements by formulas in a formal language;
- the interpretation of formulas as true or false in a mathematical structure;
- logical consequence of one formula from others;
- formal proof;
- the soundness and completeness theorems connecting logical consequence and formal proof;
- the axiomatization of some mathematical theories using a formal language;
- the compactness theorem and an introduction to model theory.
This book is designed for self-study by students, as well as for taught courses, using principles successfully developed by the Open University and used across the world. It includes exercises embedded within the text with full solutions to many of these. In addition there are a number of exercises without answers so that students studying under the guidance of a tutor may be assessed on the basis of what has been taught.
Some experience of axiom-based mathematics is required but no previous experience of logic. Propositional and Predicate Calculus gives students the basis for further study of mathematical logic and the use of formal languages in other subjects.
Derek Goldrei is Senior Lecturer and Staff Tutor at the Open University and part-time Lecturer in Mathematics at Mansfield College, Oxford, UK.
Propositional and Predicate Calculus A Model of Argument 1st Table of contents:
Chp1 f a card has a vowel on one side, then it has an even number on the other side.
Chp2 Soriteses ; h = understood by me. 47. (1) Every idea of mine, that cannot be expressed as a Syllogism, is really ridiculous ; (2) None of my ideas about Bath-buns are worth writing down ; (3) No idea of mine, that fails to come true, can be expressed as a Syllogism ; (4) I never have any really ridiculous idea, that I do not at once refer (5) My dreams are all about Bath-buns ; [to my solicitor ; (0) I never refer any idea of mine to my solicitor, unless it is worth writing down. Univ. “my ideas…
Cp3 – X* the set of all functions with domain Y and values in X, and by X x Y the Cartesian product of X and y (that is, the set of all ordered pairs such that xeX and ye Y).
Chp4 Kuratowski has shown that a graph is planar if and only if it contains no subgraph homeomorphic to either of the graphs #33 or K5 shown in Fig.
Cp5 It states that every even number greater than 2 is the sum of two primes in at least one way.
Cp6 Q for the set of rational numbers, R for the set of real numbers and C for the set of complex numbers.
Cp7 Two sets are equal if, and only if, they contain the same elements.
Cp8 Y are equal if and only if they contain the same elements or, equivalently. if and only if every element of X is an element of Y and vice versa.
Cp9 The proof of this theorem is left as an exercise for the student.
Cp10 A subgroup of a group (G, •) is a subset of G which is a group under the operation • . Here we are misusing the terms ‘operation’ and ‘group’ according to the conventions of the preceding section.
People also search for Propositional and Predicate Calculus A Model of Argument 1st:
propositional vs non-propositional
propositional logic vs predicate calculus
propositional calculus examples
propositional calculus axioms
predicate calculus examples
Tags:
Derek Goldrei,Predicate Calculus,A Model