Propositional Logic 1 Flashcards
Lesson 1 - Introduction to types of language, propositional logic, (including logical connectives/operators) propositional variables, propositional statements etc
natural language
a language used for normal everyday communication
formal language
a set of strings of symbols formed from a finite alphabet and defined by specific rules
4 examples of rules that can be used to define formal languages
regular expressions, regular grammar, context-free grammar, context-sensitive grammar
natural language is inherently…?
ambiguous
premises
a proposition used in an argument to prove the truth of the conclusion
formal languages have no invalid…?
inferences
programming language
a formal constructed language designed to communicate instructions to a machine to control its behaviour
propositional logic is a type of…?
formal system
a formal system is a formal language equipped with a…?
consequence operation/deduction rule/inference rule
inference rules
logical tools used to draw conclusions from premises
inference rules form the foundation of…?
logical reasoning
propositional
a logical statement that can either be true or false but NOT both
atomic proposition
a logical statement that is either true or false (but not both) and cannot be broken down any further
compound propositions state…?
relationships between propositions
compound proposition
a proposition combining multiple propositions using logical connectives
defining languages involves at least…?
two languages
what are the two fundamental languages required for defining languages
the object language and the meta-language
object language
the language being defined
meta-language
the language used to define an object language
an object language has how many aspects?
2
aspects of an object language
its syntax and semantics
syntax
rules for writing an object language
semantics
the meanings of constructions in an object language
defining syntax involves how many steps?
2
step 1 in defining syntax
defining the symbols
step 2 in defining syntax
defining larger constructions (e.g. sentences in NLs and formulae in propositional logic)
propositional variables represent…?
atomic propositions
names for propositional variables are often…?
abbreviations of the proposition
propositional variables tend to be…?
lower case
purpose of propositional connectives
form compound propositions from multiple simpler propositions
each logical connective has its own…?
semantics
p ∧ q
‘p’ and ‘q’ can be referred to as the…?
conjuncts
p ∨ q
‘p’ and ‘q’ can be referred to as the…?
disjuncts
law of excluded middle
for every proposition, either the proposition or its negation is true
why is the ‘law of excluded middle’ named as such?
every truth value is either true of false since there is no middle ground when it comes to the truth of a propositional formula
p ⇒ q is equivalent to…?
¬q ⇒ ¬p
¬q ⇒ ¬p is equivalent to…?
p ⇒ q
the contrapositive of p ⇒ q
¬q ⇒ ¬p
WFF stands for
well-formed formulae
law for equivalence
(p ⇒ q) ∧ (q ⇒ p)
number of steps in the process of logical deduction
3
step 1 in the process of logical deduction
identify the premises (true propositions)
step 2 in the process of logical deduction
construct and inference from the premises
step 3 in the process of logical deduction
give a conclusion
what is a conclusion
the process of giving some new proposition a truth value
if p and (p ⇒ q) are both true, then it can be inferred that…?
q is true as well
what is ‘q if p’ written using propositional logic?
p ⇒ q
what is ‘q whenever p’ written using propositional logic?
p ⇒ q
what is ‘p only if q’ written using propositional logic?
p ⇒ q
describe the equivalence law in words.
the conjuncts are proposition and its converse
p ⇒ ¬q is equivalent to
q ⇒ ¬p
technical term for ¬
negation
the law of the excluded middle is associated with which propositional connective?
disjunction
the process of defining syntax has how many step..?
2
what is the first step in defining syntax?
defining the basic symbols
what is the second step in defining syntax?
defining the rules for writing formulae with these symbols
