Truth functional logic (relevant)

Question 1

Three kinds of symbols in TFL

Answer 1

Atomic sentences, connectives, brackets

Question 2

Formal definition of a sentence of TFL

Answer 2

1. Every atomic sentence is a sentence
2. If A is a sentence, then ¬A is a sentence
3. If A and B are sentences, then (A ˄ B) is a sentence
4. If A and B are sentences, then (A v B) is a sentence
5. If A and B are sentences, then (A → B) is a sentence
6. If A and B are sentences, then (A ↔ B) is a sentence
7. Nothing else is a sentence

Question 3

Every sentence is constructed out of…

Answer 3

An atomic sentence

Question 4

The connective that was introduced most recently =

Answer 4

Main logical operator (main connective) of the sentence

Question 5

What is the scope of a negation?

Answer 5

The subsentence for which that connective is the main logical operator

Question 6

A connective is truth functional if the truth value of the sentence…

Answer 6

Is uniquely determined by the truth value of the constituent sentence

Question 7

The truth value of a negation is uniquely determined by…

Answer 7

The truth value of the unnegated sentence

Question 8

The truth value of a conjunction is uniquely determined by…

Answer 8

The truth value of both conjuncts

Question 9

The truth value of a disjunction is uniquely determined by…

Answer 9

The truth value of both disjuncts

Question 10

How can we assign truth values?

Answer 10

Valuations- find out if atomic sentences are to be true or false

Question 11

Valuation

Answer 11

Is any assignment of truth values to particular atomic sentences of TFL

Question 12

What does a truth table represent?

Answer 12

All possible valuations

Question 13

What is a gap in a truth table represented by?

Answer 13

-

Question 14

What can a truth table be used for?

Answer 14

Calculating the truth value of complex sentences, each line represents a variation, can use to determine if a sentence is a tautology

Question 15

When is a sentence a tautology?

Answer 15

If it is true on every valuation

Question 16

Necessary truth =

Answer 16

Tautology symbolized

Question 17

Necessary falsity =

Answer 17

Sentence is a contradiction if it is false on every valuation

Question 18

When are sentences jointly tautologically consistent?

Answer 18

If there is some valuation which makes them all true

Question 19

Jointly tautologically inconsistent

Answer 19

There is no valuation which makes them all true

Question 20

If they tautologically entail…

Answer 20

Then they are valid

Question 21

We can demonstrate the validity of arguments by?

Answer 21

1. Symbolising the arguments in TFL

2. Checking for tautological entailment using truth tables

Question 22

Can we demonstrate the validity of every argument through TFL and tautological entailment?

Answer 22

No

Question 23

Why might TFL not demonstrate the validity of an argument?

Answer 23

It is formally valid but our formal language is not strong enough to capture its formal validity

Question 24

Tautological equivalence

Answer 24

Sentences are tautologically equivalent iff they have the same truth value on every valuation.

Question 25

Jointly tautologically consistent

Answer 25

Sentences are jointly tautologically consistent iff there is some valuation which makes them all true.