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Logic

Logic is the branch of philosophy that studies the principles of correct reasoning, seeking to infer the conditions under which certain statements can be declared true or false. It encompasses various types of logical systems and methods used to analyze the structure and validity of arguments.
Sub-categories:

Symbolic logic, also known as formal logic, involves the use of symbols and formulas to represent logical expressions and arguments, facilitating their analysis and solving.

Propositional logic, or sentential logic, focuses on the relationships between whole propositions and the connective operators that form compound statements.

Predicate logic extends propositional logic by dealing with predicates and quantifiers, allowing for a more nuanced understanding of statements involving individuals and their properties.

Modal logic incorporates modalities such as necessity and possibility into classical logic frameworks, examining how truths can vary across possible worlds or contexts.

Inductive logic investigates the process of reasoning from specific instances to general conclusions, assessing the strength and validity of such inferential reasoning.

Deductive logic involves reasoning from general premises to specific, inevitable conclusions, ensuring that the truth of the premises guarantees the truth of the conclusion.

Fuzzy logic deals with reasoning that is approximate rather than fixed and exact, particularly useful for dealing with uncertain or imprecise information.

Mathematical logic applies formal logical techniques to mathematical reasoning and the study of mathematical structures, laying the groundwork for proof theory and other logical systems.

Philosophical logic explores advanced issues such as validity, truth, and inferential correctness, often challenging and extending traditional logical theories.

Computational logic applies logical principles to computational systems, laying the foundation for programming language semantics, verification, and artificial intelligence reasoning.

Informal logic emphasizes logical analysis outside of formal systems, focusing on the aspects of everyday and natural language argumentation.

Non-classical logic examines alternative logical systems that modify or reject certain classical logic principles, often to address specific philosophical questions or practical problems.

Intuitionistic logic rejects the law of the excluded middle found in classical logic, reflecting a mathematical philosophy where the truth of a statement is related to our ability to prove it.

Deontic logic studies the logics of duty, permission, and related modalities, often applied in legal reasoning and ethical considerations.

Epistemic logic investigates the properties and outcomes of knowledge and belief, formalizing the concepts of knowing and believing in logical systems.

Syllogistic logic, also known as term logic, is one of the earliest forms of logic, analyzing and classifying arguments by their structure, based on premises involving terms and their inclusion or exclusion.