Exam 1 Material Flashcards
What is a tautology?
A formula that outputs true on every truth-assignment (input).
What is a contradictory?
A formula that outputs false on every truth assignment (input).
What is a contingent formula?
A formula that outputs true for some truth assignments (inputs) and false for others.
A satisfiable formula (sat) is…
A formula for which there exists a truth-assignment that makes the formula’s output true.
p -> q is a “guarded” or “triggered” two-step proposition because…
We only concern ourselves about q (second step) if the guard/trigger, p (first step) is true.
The precedence order for the 4 basic logical connectives is (from highest to lowest):
~ (NOT)
^ (AND)
v (OR)
–> (IMPLIES)
The associativity of the AND (^) connector means that its always combines to the…
Left
The associativity of the OR( (v) connector means that it always combines to the…
Left
The associativity of the IMPLIES (–>) connector means that it always combines to the…
Right
Linear temporal logic:
Supports reasoning about event sequencing
Propositional logic:
Supports reasoning about propositions (statements that are true or false) and about valid ways of drawing conclusions from premises
A (valid) argument consists of sentences (claims) chained together in such a way that the truth of each sentence…
- Is assumed (i.e., the sentence is a premise) or…
2. Follows from the truth of the previous sentences (via inference or deduction).
In a valid argument, if all of the premises are true, then…
…the conclusions must be true.
Act of inference:
Attempting to establish the truth of the conclusions from the truth of the premise.
Valid inference:
The “transmission of truth” such that in every situation where all the premises P are true, the conclusion Q is also true.
Syllogism:
Consists of exactly 2 premises and a conclusion, whose validity is determined by the underlying structure of the argument.
Negation (~) can be recognized in an English sentence by…
the presence of the word “not” or morphemes like “un-“ or “ir-“.
Conjunction (^) can be recognized in an English sentence by…
the presence of the words “and” or “both”.
An exclusive OR (disjunction)…
Capture two events that cannot occur simultaneously (either/or). Can be represented as (p V q) ^ ~(p ^ q)
An inclusive OR (disjunction)…
Captures two events that can occur simultaneously or alone (either… or both).
Implication (–>) is used to capture…
Conditionality.
Implication (–>) can be recognized in an English sentence by words such as…
If…then..., … provided that, assuming, only if..., given…
A fact C is said to be “known” by person P if…
- C is true, and…
- P believes C to be true, and…
- P has some sort of justification that C is true (C is not something that P arrived at by a guess or chance.)
- P believes C to be true, and…
Deduction:
The synthesis of new facts (consequences) from known facts via truth-preserving inferences.
^i
AND Introduction Rule
Provided that there are proofs for P and Q, then one can conclude that P^Q is true.
^i : P Q
------------
P ^ Q^e1
AND Elimination Rule 1
A rule to eliminate the RIGHT operand Q, leaving P:
^e1 : P ^ Q
——–
P
^e2
AND Elimination Rule 2
A rule to eliminate the LEFT operand P, leaving Q:
^e2: P ^ Q
——–
Q
