Solvable Cases of the Decision Problem

Name: Solvable Cases of the Decision Problem
Brand: Elsevier
Price: 215.0 EUR
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Lev D. Beklemishev(Autor*in)

Elsevier (Verlag)

Erschienen am 14. Mai 2014

123 Seiten

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Front Cover
Solvable Cases of the Decision Problem
Copyright Page
CONTENTS
CHAPTER I. VALIDITY AND SATISFIABILITY IN FINITE DOMAINS
1. Well-formed formulas
2. Valuation of well-formed formulas in a finite domain. Validity and satisfiability
CHAPTER II. THE DECISION PROBLEM
1. Valuation in arbitrary domains. Universal validity
2. Equivalences
3. S-formulas. Elimination of the propositional variables
4. Normal forms
5. Three forms of the decision problem
CHAPTER III. SOLUTION OF THE DECISION PROBLEM FOR EQUALITY FORMULAS
1. Solution of the form II of the decision problem
2. Another criterion for the universal validity of equality formulas
CHAPTER IV. SOLUTION OF THE DECISION PROBLEX FOR WELL- FORMED FORMULAS CONTAINING ONLY MONADIC PREDICATE VARIABLES
1. Solution of the form II of the decision problem for wffs which do not contain bound predicate variables and the sign of equality
2. Elimination theorems
3. General solution of the decision problem for wffs with only monadic predicate variables
CHAPTER V. SOME GENERAL THEOREMS ABOUT THE VALIDITY OF FORMULAS OF THE PREDICATE CALCULUS OF FIRST ORDER INCLUDING EQUALITY
1. Skolem's normal form
2. Theorems about the validity of wffs not containing the sign of equality
3. Theorems about the validity of wffs which may contain the sign of equality
CHAPTER VI. SOLUTION OF THE DECISION PROBLEM FOR WFFS WITH SPECIAL PREFIXES
1. Remarks on the selection of special cases of the decision problem
2. Solution for wffs having prefixes consisting solely of universal quantifiers
3. Solution for wffs having prefixes consisting solely of existential quantifiers
4. Reduction of the decision problem for wffs with certain prefixes to that for wffs with simpler prefixes
5. Solution for wffs having prefixes such that all the universal quantifiers precede all the existential ones
CHAPTER VII. FURTHER CLASSES OF PREFIXES FOR WHICH THE DECISION PROBLEM CAN BE SOLVED
1. Solution for wffs having prefixes containing only one existential quantifier
2. Solution for wffs having prefixes containing only two existential quantifiers which are not separated by universal quantifiers
CHAPTER VIII. GENERAL REMARKS ABOUT FURTHER INVESTIGATIONS
1. Limitation of the range of the method hitherto used
2. Some other cases for which the decision problem has been solved
3. A general theorem about the validity of wffs
CHAPTER IX. THE DECISION PROBLEM FOR WFFS WITH FUNCTIONAL VARIABLES
1. Introduction of wffs with functional variables
2. Special cases for which the decision problem is solved for wffs with functional variables
BIBLIOGRAPHY
INDEX

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