In a propositional logic formula, names ( city names, state names) cannot be substituted for letters (A, B, C, etc). Letters represent propositions ( declarative sentences).
Propositional logic (also called sentential logic) is logic that includes sentence letters (A,B,C) and logical connectives, but not quantifiers. The semantics of propositional logic uses truth assignments to the letters to determine whether a compound propositional sentence is true. Predicate logic is usually used as a synonym for first-order logic, but sometimes it is used to refer to other ...
A propositional logic is said to be satisfiable if its either a tautology or contingency. Hence if a logic is a contradiction then it is said to be unsatisfiable.
For details and proof of soundness/completeness, see e.g. Mordechai Ben-Ari, Mathematical Logic for Computer Science (Springer, 3rd ed 2012), Chapter 4 Propositional Logic: Resolution, page 82.
The most misunderstood element of standard propositional logic is the $\to$ symbol. It is often read as "implies," but that has human meaning that one statement follows from the other in some direct way.
Is my translation of unless into propositional logic correct? Ask Question Asked 9 years, 10 months ago Modified 7 years, 11 months ago
Proof of the Compactness Theorem for Propositional Logic Ask Question Asked 13 years, 3 months ago Modified 11 years, 2 months ago
Simon Fraser University: Notes on Chapter 7: Logical Agents and Propositional Satisfiability¶
The suggestions given are fine, but there is not always a direct read over from natural language to formal logic: when could mean "whenever" but there could, in natural language, be an implied "only" as "I only buy food when I get paid" and that is just one of the slippery ambiguities which formal language is explicitly designed to avoid.