Question 1

True or False
-Truth table analysis constitutes a decision procedure for sentential logic.

Accepted Answer

A) True 
 B)False  True

Question 2

True or False
-There is a complete and consistent axiom system for arithmetic.

Accepted Answer

A) True 
 B)False  False

Question 3

True or False
-It is possible to construct an inconsistent axiom system for arithmetic in which all truths of arithmetic would be derivable.

Accepted Answer

A) True 
 B)False  True

Question 4

True or False
-An axiom system for arithmetic is complete if either every well-formed formula or its negation is derivable as a theorem.

Accepted Answer

A) True 
 B)False

Question 5

True or False
-An axiom system for predicate logic is complete if either every well-formed formula or its negation is derivable as a theorem.

Accepted Answer

A) True 
 B)False

Question 6

True or False
-There can be no decision procedure for any consistent formulation of arithmetic.

Accepted Answer

A) True 
 B)False

Question 7

Theory
-a. Roughly, how does one prove that a given consistent axiom system is consistent? 
 b. Roughly, how does one prove that a given inconsistent axiom system is inconsistent?

Accepted Answer

a. One proves that there is so

Question 8

Theory
-Can we say that an axiom system for predicate logic is complete if every formula or its negation is derivable as a theorem? If so, why? If not, why not?

Accepted Answer

This would be too strong since

Question 9

True or False
-There are complete and consistent axiom systems for both sentential and predicate logic.

Accepted Answer

A) True 
 B)False

Question 10

True or False
-There are decision procedures both for sentential and predicate logic.

Accepted Answer

A) True 
 B)False

Question 11

Theory
-If an axiom system is not complete, can we say whether it is consistent? (Defend your answer.)

Accepted Answer

If an axiom system is not complete then

True or False -Truth table analysis constitutes a decision procedure for sentential logic.

True or False -There is a complete and consistent axiom system for arithmetic.

True or False -It is possible to construct an inconsistent axiom system for arithmetic in which all truths of arithmetic would be derivable.

True or False -An axiom system for arithmetic is complete if either every well-formed formula or its negation is derivable as a theorem.

True or False -An axiom system for predicate logic is complete if either every well-formed formula or its negation is derivable as a theorem.

True or False -There can be no decision procedure for any consistent formulation of arithmetic.

Theory -a. Roughly, how does one prove that a given consistent axiom system is consistent? b. Roughly, how does one prove that a given inconsistent axiom system is inconsistent?

Theory -Can we say that an axiom system for predicate logic is complete if every formula or its negation is derivable as a theorem? If so, why? If not, why not?

True or False -There are complete and consistent axiom systems for both sentential and predicate logic.

True or False -There are decision procedures both for sentential and predicate logic.

Theory -If an axiom system is not complete, can we say whether it is consistent? (Defend your answer.)

Introduction

Symbolizing in Sentential Logic

Truth Tables

Proofs Without CP or IP

Proofs With CP or IP

Sentential Logic Truth Trees

Predicate Logic Symbolization

Predicate Logic Semantics

Predicate Logic Proofs

Relational Predicate Logic

Quantifier Rules Theory

Predicate Logic Truth Trees

Identity

Syllogistic Logic

Informal Fallacies

Inductive Logic

Filters

Exam 17: Axiom Systems

True or False -Truth table analysis constitutes a decision procedure for sentential logic.

True or False -There is a complete and consistent axiom system for arithmetic.

True or False -It is possible to construct an inconsistent axiom system for arithmetic in which all truths of arithmetic would be derivable.

True or False -An axiom system for arithmetic is complete if either every well-formed formula or its negation is derivable as a theorem.

True or False -An axiom system for predicate logic is complete if either every well-formed formula or its negation is derivable as a theorem.

True or False -There can be no decision procedure for any consistent formulation of arithmetic.

Theory -a. Roughly, how does one prove that a given consistent axiom system is consistent? b. Roughly, how does one prove that a given inconsistent axiom system is inconsistent?

Theory -Can we say that an axiom system for predicate logic is complete if every formula or its negation is derivable as a theorem? If so, why? If not, why not?

True or False -There are complete and consistent axiom systems for both sentential and predicate logic.

True or False -There are decision procedures both for sentential and predicate logic.

Theory -If an axiom system is not complete, can we say whether it is consistent? (Defend your answer.)

Introduction

Symbolizing in Sentential Logic

Truth Tables

Proofs Without CP or IP

Proofs With CP or IP

Sentential Logic Truth Trees

Predicate Logic Symbolization

Predicate Logic Semantics

Predicate Logic Proofs

Relational Predicate Logic

Quantifier Rules Theory

Predicate Logic Truth Trees

Identity

Syllogistic Logic

Informal Fallacies

Inductive Logic

Filters