Definitions Flashcards
(25 cards)
What is a logically valid argument?
- Iff there is no possible situation in which its premises are all true and its conclusion is false.
- The conclusion of the argument is a logical consequence of its premises.
- Its conclusion is logically entailed by its premises.
What is the different focus of validity compared to truth?
Focuses on the logical relationship between premises and conclusion, not the actual truth or the falsity of the premises/ conclusion itself.
How can an argument be defined as sound?
Iff it is logically valid and all its premises are true.
What are constants?
Lower case letters from the beginning of the alphabet that refer to a particular object.
What are variables?
Lower case letters from the end of the alphabet.
What are predicates?
- That which is said of the subject.
- The part of a sentence/ clause in which something is said about the subject.
- Its role is to express property (of objects) or a relation (between objects).
What is an atomic sentence?
- The syntax rule: A result of combining an n-place predicate (a predicate of arity n) with n occurrences of individual constants.
Define arity.
The number of places.
What is a counterexample?
- A possible situation in which the premises of the argument are all true and its conclusion is false.
An argument is logically invalid iff it has a counterexample.
What is another way of defining a counterexample?
Suggesting an argument is logically invalid (Iff there is a possible situation in which its premises are all true and its conclusion is false.
What are the five sentential connectives?
- ¬ it is not the case that/ negation symbol
- ∧ and
- ∨ or
- → material conditional symbol (if, then)
- ↔ bio-conditional symbol (logically equivalent to)
What do sentence variables stand for?
Any sentence in the formal language.
Define a logical truth.
A sentence is a logical truth iff it is true in every possible situation/ in FOLp, it is when a sentence has no row in its truth table which is F.
What are the three logical properties of a sentence?
- Logical truth
- Contradiction
- Logical Possibility
What is a contradiction?
- Iff a sentence is false in every possible situation.
- An FOLp sentence is a contradiction iff there is no row in its truth table in which it is T.
What is a logical possibility?
- A sentence is a logical possibility iff there is at least one possible situation in which it is T.
- This means that a sentence is a logical possibility iff it is not a contradiction.
What does it mean for sentences to be logically equivalent?
Iff they have the same truth values in every possible situation.
When can it be said hat the scope of a connective is wider?
If the latter occurs within the former but not vice versa.
What is the contradiction symbol?
⊥
What is ⊥?
- The contradiction symbol.
- It is treated as a sentence where F is assigned to every situation.
- Logically equivalent to any contradiction sentence.
What are the two quantifiers?
- Universal quantifier: ∀
- Existential quantifier: ∃
What is ∀?
Universal quantifier (all, every)
What is ∃?
Existential quantifier (one, someone, singular)
How is a sentence defined in FOL?
Iff it has no free/ unbound occurrences of variables.
