Week 7 Flashcards
What is propositional logic?
a notation for logical words that connect propositions such as and, or, if … then, not
What is predicate logic?
an artificial language containing predicates and
arguments - it looks inside propositions e.g. Fido is a dog: f DOG
What is the Principle of Compositionality?
the meaning of a complex expression is determined by the lexical meaning of its components, their grammatical meanings and the syntactic structure of the whole
How is a complex proposition formed?
by joining simple propositions with a sentence connective e.g. and
What can logical & do?
& can only join propositions, not names, i.e. c & g is not well-formed (conjunction)
What does the truth table say about &?
it is only true if P and Q are both true; it is false for ~P and Q, ~Q and P and ~P and ~Q
Give examples of inference patterns with &
- commutativity of conjunction p & q ⇔ q & p
- conjunction introduction p/ q = q & p
- conjunction elimination p & q/ p
What can logical V do?
V can only join propositions, not names, i.e. j V m is not well-formed (disjunction)
What does the truth table say about V?
it is true if P and Q , ~P and Q, ~Q and P are all true; but it is false for ~P and ~Q
Give examples of inference patterns with V
- commutativity of disjunction p V q ⇔ q V p
- disjunction introduction p/ q = q V p
- disjunction elimination does not work!
What is negation(~)?
when one proposition is the opposite of another
What is the inference pattern of ~
~~p/ p
What does the conditional state?
if ….., then ……
What is ‘but’ turth-conditionally similar to?
‘and’
What does ‘&’ and ‘V’ fail to capture?
other aspects of the meaning of the english connectives, such as temporality and causality (‘and’)
What does ‘or’ exclude?
the possibility of both disjuncts being true
