M3_Predicate Logic and Proof Techniques Flashcards

1
Q

Important in proving if arguments are valid or not and it is being used to represent knowledge

A

Propositional Logic

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2
Q
  • Evaluates to true or false
    • Takes one or more arguments
    • Expresses a predicate involving argument(s)
    • Becomes a PROPOSITION when values are assigned to the arguments
A

Propositional function

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3
Q
  • An extension of Propositional Logic
    • Adds the concept of predicates and quantifiers to better capture the meaning of statements that cannot adequately expressed by propositional logic
A

Predicate logic

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4
Q

Using quantifiers to create such propositions

A

QUANTIFICATION

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5
Q

Two types of quantifier

A

Universal Quantifier
Existential Quantifier

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6
Q

A set of unvirse

A

domain of discourse

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7
Q

Symbol for universal quantifier

A

Inverted A

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8
Q

Symbol for Existential Quantifier

A

Horizontally inverted E

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9
Q

important for conducting proofs and program verification but also for artificial intelligence

A

mathematical reasoning

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10
Q
  • Sequence of statements that form an argument
A

Proof

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11
Q

sets of statements

A

Rules of interference

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12
Q

incorrect reasoning

A

fallacies

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13
Q
  • A basic assumption about mathematical structure that needs no proof because it is accepted as true and correct
A

Axiom

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14
Q
  • used to create new concepts in terms of existing ones
A

Definition

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15
Q
  • Proposition that has been proved to be true
  • proved by logical arguments based on axioms
A

Theorem

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16
Q
  • A minor auxiliary result which aids in the proof of a theorem/proposition
A

LEMMA

17
Q
  • a result whose proof follows immediately from a theorem or proposition
A

Corollary

18
Q
  • is a statement that is suspected to be true by experts but not yet proven
A

Conjecture

19
Q

Every even integer greater than 2 can be expressed as the sum of two prime numbers.

A

Goldbach’s Conjecture

20
Q

if p is true then q must follow

A

Proof by construction or Direct Proof

21
Q

prove p->q by proving ~q->~p

A

Proof by Contraposition

22
Q

prove that the negation of the theorem yields a contradiction

A

proof by contradiction