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’)
