diff --git a/Logic/Proofs/Conditional_Introduction.md b/Logic/Proofs/Conditional_Introduction.md index 5b552be..947234a 100644 --- a/Logic/Proofs/Conditional_Introduction.md +++ b/Logic/Proofs/Conditional_Introduction.md @@ -1,6 +1,6 @@ --- categories: - - + - Logic tags: [derivation-rules] --- diff --git a/Logic/Propositional_logic/Syntax_of_propositional_logic.md b/Logic/Propositional_logic/Syntax_of_propositional_logic.md index 44f46b4..c68faa4 100644 --- a/Logic/Propositional_logic/Syntax_of_propositional_logic.md +++ b/Logic/Propositional_logic/Syntax_of_propositional_logic.md @@ -18,30 +18,30 @@ Syntax is talking about the order and placement of propositions relative to conn Propositions in SL are capitalised Roman letters (non-bold) with or without natural number subscripts. We may call these proposition letters. For example: -```plain -P, Q, R...P1, Q1, R1... -``` +$$ + P, Q, R,... P_{1}, Q_{1}, R_{1}, ... +$$ The connectives of SL are the five truth-functional connectives: -``` -~, &, v, ⊃, ≡ -``` +$$ + \lnot, \land, \lor, \rightarrow, \leftrightarrow +$$ The punctuation marks of SL consist in the left and right parentheses: -``` -( ) -``` +$$ + ( ) +$$ ### Grammar -1. Every proposition letter is a proposition. -1. If **P** is a proposition then **~P** is a proposition. -1. If **P** and **Q** are propositions, then **(P & Q)** is a proposition -1. If **P** and **Q** are propositions, then **(P v Q)** is a proposition -1. If **P** and **Q** are propositions, then **(P ⊃ Q)** is a proposition -1. If **P** and **Q** are propositions, then **(P ≡ Q)** is a proposition +1. Every letter in a statement is a proposition. +1. If $P$ is a proposition then $\lnot P$ is a proposition. +1. If $P$ and $Q$ are propositions, then $P \land Q$ is a proposition +1. If $P$ and $Q$ are propositions, then $P \lor Q$ is a proposition +1. If $P$ and $Q$ are propositions, then $P \rightarrow Q$ is a proposition +1. If $P$ and $Q$ are propositions, then $P \leftri **(P ≡ Q)** is a proposition 1. Nothing is a proposition unless it can be formed by repeated application of clauses 1-6 ### Additional syntactic concepts