Logic - syntax of propositional logic

connectives (+main), propositional letters, modus ponens/tollens, syntax vs semantics, formal language L1, formalisation, brackets

if … then …

->

… and …

^

… or …

v

it is not the case that

¬

… if and only if …

double arrow

propositional letters

replace english sentences with arbitrary letters, uniformity must be respected

modus ponens

P → Q, P | Q

modus tollens

P → Q, ¬Q | ¬P

Syntax

expressions

Semantics

meaning of expressions

Formal language L1 - Vocabulary

sentence letters and connectives

Formal language L1 - Syntax

all sentences are sentences of L1, if P and Q are sentences then so are ¬P or (P^Q), nothing else is a sentence of L1

Formal language L1 - formalisation

going from metalanguage (Ω) to object language (P^Q)

conventions for dropping brackets

outermost can be dropped, drop in left associated series (for ^ and V), ^ and V binds more than → and ←>

main connective

that which is applied last