What are the main branches of formal logic?

Formal logic is the abstract study of propositions and deductive arguments, focusing on their structure rather than their specific subject matter. While the field is unified by its concern with validity and inference forms, it is broadly categorized into several distinct branches based on the elements they analyze.123

Primary Divisions

• Propositional calculus: This branch deals with whole, unanalyzed propositions. It treats these as atomic units and uses logical symbols to form and analyze compound propositions and their relationships.43
• Predicate calculus: Unlike propositional logic, this branch analyzes the internal structure of propositions, specifically the attribution of characteristics (predicates) to subjects. It is considered a species of the broader logic of terms, which also encompasses the logic of classes, relations, and identity.3

Nonclassical and Alternative Logics

Beyond classical first-order logic, various alternative systems have been developed to address specific philosophical or mathematical needs:5
* Modal logic: An extension of classical logic that incorporates concepts of necessity and possibility, often applied to the analysis of knowledge, belief, and obligation.56
* Intuitionistic logic: A system that restricts logical truth to what can be constructively established or known, rejecting certain classical principles like the law of excluded middle.5
* Many-valued logics: Systems that move beyond the binary "true" and "false" by assuming additional truth values.5