M3: Propositional Logic: Symbolic Translation Flashcards
study of the symbolic language used in Logic
Symbolic Logic
translation of propositions, operations, and other concepts into symbolic form to manipulate them easily
Symbolic Logic
dummy letters indicate propositions with empty value
Propositional variables
indicate atomic propositions that contain truth-value (has an equivalent proposition)
Propositional Constants
T or F: Propositional Constants, lowercase Roman Alphabet is used
False, capital
3 ways in using propositional constants
- underlining a word or part of a proposition with the first letter indicating what letter to be used in representing the whole proposition.
- whole proposition is underlined and a letter is written above.
3.list of letters with corresponding propositions is provided (marked with the word ‘wherein’).
4 Main Logical Connectives
Conjunction
Disjunction
Conditional
Biconditional
2-way horizontal arrow (sometimes = )
biconditional
Arrow pointing right (sometimes ⊃)
conditional
Either-Or
disjunction
Inverted V (sometimes * is used)
conjunction
the combination of two or more atomic propositions, additional symbols are used which are called
Logical Connectives
are symbols that aid in the truth-value computation of compound/complex propositions
Logical Operations
T or F: All four logical connectives are logical operations.
TRUE
T or F Negation is a logical connective but not a logical operation
False, it is a logical operation but is not a logical connective.
T or F: Note that not all compound/complex propositions containing conjunction are indeed conjunctions
True
some conjunctions become absurd once ____
either the subject or the predicate is distributed to their corresponding predicates and subjects.
Two types of disjunctions
Inclusive/Weak and Exclusive/Strong
Inclusive or Exclusive? Contradictions or contrasts
Exclusive
Example of Exclusive disjunction
asleep or awake
two options can be true at the same time
Inclusive/Weak Disjunctions
Latin word for and/or
ver
Latin Word for exclusive disjunctions
aut
Other ways to indicate conjunctions:
and, but, yet, also, while, meanwhile, furthermore, however, moreover, in addition, at the same time, on the other hand, although.
Other ways to indicate conditionals:
because, in order to, so that, only if, whenever.
Conditionals are sometimes referred to as
Implications
equivalent to two conditionals with the other one reversed
Biconditionals
other names for antecedent
implicans/protasis
other names for consequent
implicate/apodosis
proper arrangement of symbols
syntax
Compound/complex propositions following proper syntax abide by a
Well-Formed Formula
WFF or
String of Symbols (simplified as SOS to rightfully indicate a distress call).
_________ are used to group together symbols related to each other.
Punctuations
