Language Quiz / Introduction to Formal Logic Final Vocabulary

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Review Chapters 1-26 of Introduction to Formal Logic

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In a set of PL wffs, *this* is when there is no possible valuation of the wffs that makes them all true together.
A wff A is *this* of wff B if A appears anywhere on the construction tree for B.
You can instantiate the E quantifier with any name that is what?
QL trees give *what* proofs of validity?
When something must be true in all possible worlds.
The *blank* of two propositions A and B is true when A and B are both true, and is false otherwise.
In a tree (A^B) yields:
What states that an inference with actually true premises and an actually false conclusion can't be deductively valid?
If ~Ax appears on a path, it can be written as what (if c is a variable already on the path)?
A set of propositions is *this* if it is logically impossible for the propositions to be true together.
The *blank* of two propositions A and B is true when exactly one of A and B is true, and is false otherwise.
What is the name of the schema 'If A then C; A; Therefore C'?
A set of PL wffs is *this* if there is at least one possible valuation of the relevant atoms which makes the wffs all true together.
The *blank* of a quantifier in a QL wff is the subformula that starts with that quantifier.
A wff of PL is a *blank* if it takes the value true on every valuation of its atoms.
A wff that isn't closed is called?
In a tree (A --> B) yields:
You can instantiate the A quantifier with any name that is what?
True or false? Any constant can be replaced with a variable and a quantifier to form a new wff.
If Ex appears on an open path, then we can write it as what (for any a not on the path)?
When a chain of argument leads from initial premises to a final conclusion via intermediate inferential steps, which are clearly valid, we will say that the argument is *this*.
When the object language expresses various claims, this is called *this*.
In a tree ~(A^B) yields:
Some A is/are B translates in QL to:
If Ax appears on a path, we can add what (if variable c is already on the path)?
What is the name of the logical fallacy of the form 'If A then C; C; then A'?
What does wff stand for?
If a tree has all closed paths, it is called what?
The *blank* of a non-atomic wff is the connective that is introduce at the final stage of its construction tree.
When the object language is discussed, this is called *this*.
HintAnswer
In a tree ~~A yields:
This describes something that is known without previous experience.
What is the object of logical studies called?
The *blank* of two propositions A and B is true when at least one of A and B is true, and is false otherwise.
A set of propositions is *this* if it is logically possible for the propositions all to be true together.
If ~Ex appears on an open path, then we can add this (with any a not already on the path).
What is the language in which we conduct the investigation of and discuss what is going on in the object-language?
*These* are arguments containing a premise that isn't used in getting to the conclusion.
When using a rule to strip off a quantifier, the resulting wff is called a *blank* of that quantified sentence.
If ~Ex appears on an open path, then we can exchange it with what (using a, a new variable)?
This describes when a claim is true no matter the meanings of the English words.
The *blank* of a proposition A is is true when A is false and is false exactly when A is true.
An occurrence of a variable x in a wff A is *this* iff it is not bound.
Pronouns in QL are called what?
In Propositional Logic (PL), what do the letters P, Q, R, and S stand for?
A tree in which all of the wffs have explicit truth values is called what?
In a tree (AvB) yields:
An occurrence of a variable x in a wff A is *this* iff it is in the scope of some matching quantifier that occurs in A.
A wff is a *blank* if it takes the value false on every valuation of its atoms.
This describes knowing something from prior knowledge
*This* is an individual constant or individual variable.
A *blank* of QL is a wff with no free occurrences of variables.
An inference step from given premises to a particular conclusion is *this* iff there is no possible situation in which the premises would be true and the conclusion false.
The *blank* of a connective in A is the wff on A's construction tree where the connective is introduced.
If a path does not contain a pair of wffs of the form W, ~W then the path is *blank*.
This describes when a claim is true in the meaning of the words.
An atomic wff of QL is formed from a n-place *blank* followed by n *blank*
If a tree has an open path it is called what?
What is the term for the logical fallacy when you change the quantifier of the derived premise?
~(A=B)
HintAnswer
What is the term for an argument with the same form of an argument with questionable validity, but is itself invalid?
An argument is *this* just if it has all true premises and the inference from those premises to the conclusion is valid.
The PL wffs A and B are *this* just if, on each valuation of all the atoms occurring in them, A and B take the same value.
A kind of extrapolation from the past to the future, or more generally from old cases to new cases, is called *this*.
In a tree ~(A --> B) yields:
In a tree ~(AvB) yields:
In a conditional of the form 'If A then C' A is the what?
What means roughly someone/something x is such that ...?
The scope of a *blank* is likewise the wff on the construction tree where the connective is introduced.
If a path contains a pair of wffs of the form W, ~W, then the path is *blank*.
What means roughly everyone/everything x is such that ...?
A tree in which all of the wffs do not have truth values assigned because they are all assumed to be true is called what?
When can two quantifiers be switched around?
No A is B translates in QL to:
In a tree (A=B) yields:
When something is true in this world.
A way of forming a complex sentence is *this* if fixing the truth-values of the constituent sentences of the complex sentence is always enough to determine the truth-value.
All A are B translates in QL to:
The *blank* of A is the operator introduced at the final step in the construction tree. (In QL)
Nodes in a tree are occupied by what?
Positions on a tree are conventionally called what?
In a conditional of the form 'If A then C' C is the what?
Arguments with missing premises left to be understood are called *this*.
What is the name of the schema 'If A then C; not C; Therefore not A'?
Premise wffs do *this* to the conclusion iff there is no valuation of the atoms involved in the premises and the conclusion that makes the premises true and the conclusion false.
When an inference is deductively valid, we'll say that the premises do *this* to the conclusion.
When premise wffs tautologically entail the conclusion, they also do *this* to the conclusion.
An inference step is *this* just if, given that its premises are true, then its conclusion is absolutely guaranteed to be true as well.
Symbols followed by a variable are called what?
A skeletal pattern of an argument is *this*.

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