Logic

Logic is the study of valid reasoning and formal systems of inference. It investigates how conclusions follow from premises and how those relations can be represented and tested.

Proposition: A declarative statement that can be assigned a truth value. Propositions serve as the truth-bearing units in many formal systems.
Propositional calculus: A formal system for reasoning about propositions using truth-functional connectives. It is the simplest standard setting for studying formal inference.
Aristotelian logic: The system of syllogistic reasoning developed in Aristotle's logical works. Aristotle's syllogisms provided a systematic account of categorical deduction.
Intuitionistic logic: A logic that treats proofs as evidence and rejects some unrestricted classical principles. It does not accept the law of excluded middle for every proposition.
Mathematical logic: The mathematical study of formal languages, proof, models, and computability. It applies logical methods to the structure and foundations of mathematics.
Logical consequence: A relation in which a conclusion must be true whenever specified premises are true. It captures the central question of whether premises support a conclusion necessarily.
First-order logic: A formal system with quantifiers over individuals and predicates describing them. It expresses quantified claims while keeping quantification restricted to individuals.
Stoic logic: An ancient Greek tradition that analyzed propositions and their combinations. Stoic logicians developed influential forms of propositional reasoning.
Paraconsistent logic: A logic in which contradictions do not entail every proposition. It blocks classical explosion, allowing inconsistent information to be reasoned with.
Automated theorem proving: The use of computer programs to search for formal proofs of specified statements. It turns inference rules into procedures for discovering and checking proofs.

Linked from 10 pages