Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language. The scope of logic can therefore be very large, ranging from core topics such as the study of fallacies and paradoxes, to specialized analyses of reasoning such as probability, correct reasoning, and arguments involving causality. One of the aims of logic is to identify the correct (or valid) and incorrect (or fallacious) inferences. Logicians study the criteria for the evaluation of arguments.

Foundations of logic

Philosophy of logic

• Analytic-synthetic distinction
• Antinomy
• A priori and a posteriori
• Definition
• Description
• Entailment
• Identity (philosophy)
• Inference
• Logical form
• Logical implication
• Logical truth
• Logical consequence
• Name
• Necessity
• Material conditional
• Meaning (linguistic)
• Meaning (non-linguistic)
• Paradox  (list)
• Possible world
• Presupposition
• Probability
• Quantification
• Reason
• Reasoning
• Reference
• Semantics
• Strict conditional
• Syntax (logic)
• Truth
• Truth value
• Validity

Branches of logic

• Affine logic
• Alethic logic
• Aristotelian logic
• Boolean logic
• Buddhist logic
• Bunched logic
• Categorical logic
• Classical logic
• Computability logic
• Deontic logic
• Dependence logic
• Description logic
• Deviant logic
• Doxastic logic
• Epistemic logic
• First-order logic
• Formal logic
• Free logic
• Fuzzy logic
• Higher-order logic
• Infinitary logic
• Informal logic
• Intensional logic
• Intermediate logic
• Interpretability logic
• Intuitionistic logic
• Linear logic
• Many-valued logic
• Mathematical logic
• Metalogic
• Minimal logic
• Modal logic
• Non-Aristotelian logic
• Non-classical logic
• Noncommutative logic
• Non-monotonic logic
• Ordered logic
• Paraconsistent logic
• Philosophical logic
• Predicate logic
• Propositional logic
• Provability logic
• Quantum logic
• Relevance logic
• Sequential logic
• Strict logic
• Substructural logic
• Syllogistic logic
• Symbolic logic
• Temporal logic
• Term logic
• Topical logic
• Traditional logic
• Zeroth-order logic

Philosophical logic

Informal logic and critical thinking

Informal logic Critical thinking Argumentation theory

• Argument
• Argument map
• Accuracy and precision
• Ad hoc hypothesis
• Ambiguity
• Analysis
• Attacking Faulty Reasoning
• Belief
• Belief bias
• Bias
• Cognitive bias
• Confirmation bias
• Credibility
• Critical pedagogy
• Critical reading
• Decidophobia
• Decision making
• Dispositional and occurrent belief
• Emotional reasoning
• Evidence
• Expert
• Explanation
• Explanatory power
• Fact
• Fallacy
• Higher-order thinking
• Inquiry
• Interpretive discussion
• Occam's razor
• Opinion
• Practical syllogism
• Precision questioning
• Propaganda
• Propaganda techniques
• Problem Solving
• Prudence
• Pseudophilosophy
• Reasoning
• Relevance
• Rhetoric
• Rigour
• Socratic questioning
• Source credibility
• Source criticism
• Theory of justification
• Topical logic
• Vagueness

Deductive reasoning

Theories of deduction

• Anti-psychologism
• Conceptualism
• Constructivism
• Conventionalism
• Counterpart theory
• Deflationary theory of truth
• Dialetheism
• Fictionalism
• Formalism (philosophy)
• Game theory
• Illuminationist philosophy
• Logical atomism
• Logical holism
• Logicism
• Modal fictionalism
• Nominalism
• Polylogism
• Pragmatism
• Preintuitionism
• Proof theory
• Psychologism
• Ramism
• Semantic theory of truth
• Sophism
• Trivialism
• Ultrafinitism

Fallacies

• Fallacy  (list) – incorrect argumentation in reasoning resulting in a misconception or presumption. By accident or design, fallacies may exploit emotional triggers in the listener or interlocutor (appeal to emotion), or take advantage of social relationships between people (e.g. argument from authority). Fallacious arguments are often structured using rhetorical patterns that obscure any logical argument. Fallacies can be used to win arguments regardless of the merits. There are dozens of types of fallacies.

Formal logic

• Formal logic – Mathematical logic, symbolic logic and formal logic are largely, if not completely synonymous. The essential feature of this field is the use of formal languages to express the ideas whose logical validity is being studied.
  • List of mathematical logic topics

Symbols and strings of symbols

Logical symbols

• Logical variables
  • Propositional variable
  • Predicate variable
  • Literal
  • Metavariable
• Logical constants
  • Logical connective
  • Quantifier
  • Identity
  • Brackets

Logical connectives

Logical connective

• Converse implication
• Converse nonimplication
• Exclusive or
• Logical NOR
• Logical biconditional
• Logical conjunction
• Logical disjunction
• Material implication
• Material nonimplication
• Negation
• Sheffer stroke

Strings of symbols

• Atomic formula
• Open sentence

Types of propositions

Proposition

• Analytic proposition
• Axiom
• Atomic sentence
• Clause (logic)
• Contingent proposition
• Contradiction
• Logical truth
• Propositional formula
• Rule of inference
• Sentence (mathematical logic)
• Sequent
• Statement (logic)
• Subalternation
• Tautology
• Theorem

Rules of inference

Rule of inference  (list)

• Biconditional elimination
• Biconditional introduction
• Case analysis
• Commutativity of conjunction
• Conjunction introduction
• Constructive dilemma
• Contraposition (traditional logic)
• Conversion (logic)
• De Morgan's laws
• Destructive dilemma
• Disjunction elimination
• Disjunction introduction
• Disjunctive syllogism
• Double negation elimination
• Generalization (logic)
• Hypothetical syllogism
• Law of excluded middle
• Law of identity
• Modus ponendo tollens
• Modus ponens
• Modus tollens
• Obversion
• Principle of contradiction
• Resolution (logic)
• Simplification
• Transposition (logic)

Formal theories

• Formal proof
• List of first-order theories

Expressions in a metalanguage

Metalanguage

• Metalinguistic variable
• Deductive system
• Metatheorem
• Metatheory
• Interpretation

Propositional and boolean logic

Propositional logic

Propositional logic

• Absorption law
• Clause (logic)
• Deductive closure
• Distributive property
• Entailment
• Formation rule
• Functional completeness
• Intermediate logic
• Literal (mathematical logic)
• Logical connective
• Logical consequence
• Negation normal form
• Open sentence
• Propositional calculus
• Propositional formula
• Propositional variable
• Rule of inference
• Strict conditional
• Substitution instance
• Truth table
• Zeroth-order logic

Boolean logic

• Boolean algebra   (list)
• Boolean logic
• Boolean algebra (structure)
• Boolean algebras canonically defined
• Introduction to Boolean algebra
• Complete Boolean algebra
• Free Boolean algebra
• Monadic Boolean algebra
• Residuated Boolean algebra
• Two-element Boolean algebra
• Modal algebra
• Derivative algebra (abstract algebra)
• Relation algebra
• Absorption law
• Laws of Form
• De Morgan's laws
• Algebraic normal form
• Canonical form (Boolean algebra)
• Boolean conjunctive query
• Boolean-valued model
• Boolean domain
• Boolean expression
• Boolean ring
• Boolean function
• Boolean-valued function
• Parity function
• Symmetric Boolean function
• Conditioned disjunction
• Field of sets
• Functional completeness
• Implicant
• Logic alphabet
• Logic redundancy
• Logical connective
• Logical matrix
• Product term
• True quantified Boolean formula
• Truth table

Predicate logic and relations

Predicate logic

Predicate logic Zdroj:https://en.wikipedia.org?pojem=Outline_of_logic
Text je dostupný za podmienok Creative Commons Attribution/Share-Alike License 3.0 Unported; prípadne za ďalších podmienok. Podrobnejšie informácie nájdete na stránke Podmienky použitia.