LECTURE 4 rules

Theorem

A sentence is a theorem if it is provable with no premises ($\vdash C$)

Logical Equivalence

Two sentences are logically equivalent if they can be proved from each other ($A \vdash B$ and $B \vdash A$)

Inconsistent Set of Sentences

A set of sentences is inconsistent if $\bot$ can be derived from them

Entailment Symbol ($\vdash$)

Read as "proves"; $A_1, A_2, \dots, A_n \vdash C$ means there is a proof of $C$ from those assumptions