Chpt. 3 Formalization in Propositional Logic

Question 1

Connectives (in English) are

Answer 1

Expressions that can be used to combine/modify English sentences to form a sentence.

Question 2

Truth Functionality

Answer 2

A connective is truth-functional if and only if the truth value of the compound sentence cannot be changed by replacing a direct subsentence with another sentence having the same truth value.

Question 3

Define truth functionality in terms of truth tables

Answer 3

A connective is truth functional if and only if its truth table does not contain any question marks.

Question 4

What are the steps for bringing an English sentence into a standardized form?

Answer 4

1. Check if the sentences can be reformulated in a natural way as a sentence built up from one or more sentences with a truth-functional connective.
2. If the sentence can be reformulated as such do so, but if not put it in brackets and don’t analyse further.
3. If that truth functional connective is not one of the stand connectives, reformulate the sentence using them.
4. Enclose the whole sentence in brackets, unless it is a negated sentence.
5. Apply this procedure, starting back at 1 to the next subsentence.

Question 5

What is the standard connective for but?

Answer 5

And.

Question 6

What is the standard connective for although?

Answer 6

And.

Question 7

What is the standard connective for unless?

Answer 7

Or.

Question 8

What is the standard connective for “provided that”?

Answer 8

If … then

Question 9

What is the standard connective for “only if”?

Answer 9

If … then

Question 10

What is the standard connective for “exactly if”?

Answer 10

If and only if

Question 11

What is the standard connective for “precisely if”?

Answer 11

If and only if

Question 12

What are the steps for converting a standardized English sentence into logic symbols?

Answer 12

1. Replace standard connectives by their respective symbols.
2. Replace every English sentence by a sentence letter and delete the brackets surrounding the sentence letter. Use different sentence letters for different sentences and the same sentence letter for multiple occurrences of the same sentence.
3. Give a dictionary of all sentence letters in the resulting L1 sentence together with the respective sentences they have replaced.

Question 13

Scope of a connective.

Answer 13

The scope of an occurrence of a connective in a sentence Φ of L1 is the occurrence of the smallest subsentence of Φ that contains this occurrence of the connective.

Question 14

The formalization of a sentence is

Answer 14

the sentence obtained by translating an English sentence into the language of propositional logic.

Question 15

An English sentence is a tautology if and only if

Answer 15

its formalization in propositional logic is logically true (it is a tautology).

Question 16

An English sentence is a propositional contradiction if and only if

Answer 16

its formalization in propositional logic is a contradiction.

Question 17

A set of English sentences is propositionally consistent if and only if

Answer 17

the set of all their formalizations in propositional logic is semantically consistent.

Question 18

The formalization of an argument in English is

Answer 18

the argument in L1 that has as its premisses all the formalization of the premisses of the English argument and has as its conclusion the formalizations of the English conclusion.

Question 19

An argument in English is propositionally valid if and only if

Answer 19

its formalization in L1 is valid.

Question 20

Ex Falso Quodlibet

Answer 20

is used to describe the situation that an argument with a contradiction as its premmiss is always propositionally valid, it means from something false everything follows.

Question 21

A tautology can also be described as

Answer 21

propositionally valid.