Basic Notation (Kartei)

48 Karteikarten

• 1
  argument

  A pair of two things: # A set of sentences, the premises # ...
• 2
  validity

  An argument is valid if and only if it is necessary that if ...
• 3
  entailment

  When an argument is valid we say that its premises entail ...
• 4
  soundness

  An argument is sound if and only if it is valid and all its ...
• 5
  connectives

  The sentential connectives are the members of the following ...
• 6
  "if and only if"

  <->
• 7
  "both ... and ..."

  ambersand &
• 8
  expression

  An expression is any sequence of sentence letters, ...
• 9
  Seven rules for WFFs

  # A sentence letter standing alone (atomic sentence) # If ...
• 10
  Sentence

  A sentence is a wff that is not part of a larger wff.
• 11
  denial

  - For Φ: ¬Φ - For ¬Φ: Φ and ¬¬Φ
• 12
  Parenthesis-dropping: Binding

  In order of most -> least binding: # ¬ # &, v # -> # <->
• 13
  Φ only if Ψ

  (Φ -> Ψ)
• 14
  If Φ, Ψ

  (Φ -> Ψ)
• 15
  Φ is sufficient for Ψ.

  (Φ -> Ψ)
• 16
  Ψ is necessary for Φ

  (Φ -> Ψ)
• 17
  Whenever Φ, Ψ

  (Φ -> Ψ)
• 18
  Φ and Ψ

  (Φ & Ψ)
• 19
  Φ, although Ψ

  (Φ & Ψ)
• 20
  Though Φ Ψ

  (Φ & Ψ)
• 21
  Φ if and only if Ψ

  (Φ <-> Ψ)
• 22
  Φ just in case Ψ

  (Φ <-> Ψ)
• 23
  turnstile

  |-
• 24
  sequent

  premise 1, premise 2, ... |- conclusion
• 25
  a line of a proof

  assumption set (line number) sentence annotation
• 26
  substitution instance

  A substitution instance of a sequent is the result of ...
• 27
  theorem

  A theorem is a sentence that can be proved from the empty ...
• 28
  truth table for conditional

  In order for a conditional to be false, the antecedent must ...
• 29
  truth table for biconditional

  In order for a biconditional to be true, both sentence ...
• 30
  truth tables for sequents

  If there is a line in the truth table where all the ...
• 31
  incompatible premises

  If there is no line on which all the premises are true, the ...
• 32
  tautology

  True independent from the truth values of its ...
• 33
  contradiction (inconsistent)

  False independent from the truth values of part-sentences: ...
• 34
  contingent (logically determined)

  A sentence that is neither a tautology nor a contradiction.
• 35
  assignment

  A mapping that assigns to all sentence letters sentences of ...
• 36
  "satisfies"

  An assignment satisfies a sentence if it is true for the ...
• 37
  literal

  an atomic sentence or the negation of an atomic sentence
• 38
  conjunctive-normal-form (CNF)

  a conjunction of disjunctions of literals (p1 v p2 v ¬p3) ...
• 39
  disjunctive-normal-form (DNF)

  a disjunction of conjunctions of literals (p1 & p2 & ¬p3) ...
• 40
  DNF from truth table

  # Each line of the truth table that is T delivers one of ...
• 41
  CNF from truth table

  # Each line of the truth table that is F delivers one of ...
• 42
  horn-formula

  A sentence in CNF where each disjunction entails at most ...
• 43
  valid vs. logically true

  argument: valid sentence: logically true
• 44
  semantic trees

  - useful to evaulate whether or not an argument is valid or ...
• 45
  axiomatic system

  # p->(q->p) # (p->(q->r)->((p->q)->(p->r)) # ...
• 46
  law of contraposition

  (A->B) == (¬B->¬A)
• 47
  When CNF, when DNF?

  - less Ts: disjunctive normal form - less Fs: conjunctive ...
• 48
  line semantic tree

  line number. sentence (developed from line #)