In mathematical logic, a tautology (from Ancient Greek: ταυτολογία) is a formula that is true regardless of the interpretation of its component terms,...

literature and rhetoric Tautology (logic), in formal logic, a statement that is true in every possible interpretation Tautology (rule of inference), a...

Paraconsistent logic – Type of formal logic without explosion principle Paradox – Logically self-contradictory statement Tautology – In logic, a statement...

truth. Contradiction False (logic) Logical truth table, a mathematical table used in logic Satisfiability Tautology (logic) (for symbolism of logical truth)...

Logical truth Tautology (logic) (for symbolism of logical truth) Truth table Its noun form is falsity. Jennifer Fisher, On the Philosophy of Logic, Thomson...

considered a tautology. For example, A → A and A ↔ A are tautologies in Ł3 and also in classical logic. Not all tautologies of classical logic lift to Ł3...

theorem. Any tautology of classical logic which contains no negations is also a tautology of paraconsistent logic (by merging b into t). This logic is sometimes...

In the philosophy of logic and logic, specifically in deductive reasoning, a rule of inference, inference rule or transformation rule is a logical form...

contains logic symbols. Without proper rendering support, you may see question marks, boxes, or other symbols instead of logic symbols. In logic, a set...

inference Sentence (mathematical logic) Sequent Statement (logic) Subalternation Tautology Theorem Rule of inference (list) Biconditional elimination...

modal logics, known collectively as normal modal logics, include the following rule and axiom: N, Necessitation Rule: If p is a theorem/tautology (of any...

branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. Sometimes...

were supposed to be logical tautologies, and their program was to show this by means of a reduction of mathematics to logic. Many attempts to realize this...

deductions, based on the following axiom schema: A where A is a tautology of first-order logic G(A→B)→(GA→GB) H(A→B)→(HA→HB) A→GPA A→HFA with the following...

In propositional logic, tautology is either of two commonly used rules of replacement. The rules are used to eliminate redundancy in disjunctions and conjunctions...

fallacy Ipse dixit Ringschluss Paradox Polysyllogism Self-reference Tautology (logic) Chisholm, Hugh, ed. (1911). "Circulus in Probando" . Encyclopædia...

then Θ is again a tautology. This fact implies the soundness of the deduction rule described in the previous section. In first-order logic, a substitution...

classical logic. Each theorem of intuitionistic logic is a theorem in classical logic, but not conversely. Many tautologies in classical logic are not theorems...

logic I can be interpreted as being "overdetermined", being both true and false. K3 does not have any tautologies, while P3 has the same tautologies as...

translation between tautologies of propositional logic and equational theorems of Boolean algebra. Every tautology Φ of propositional logic can be expressed...

Argumentation theory Buddhist logic Enthymeme Formal fallacy Logical fallacy The False Subtlety of the Four Syllogistic Figures Tautology (logic) Venn diagram Lundberg...

Philosophy of logic is the area of philosophy that studies the scope and nature of logic. It investigates the philosophical problems raised by logic, such as...

every interpretation. These formulas play a role similar to tautologies in propositional logic. A formula φ is a logical consequence of a formula ψ if every...

)} , where ⊤ {\displaystyle \top } stands for an arbitrary tautology of the underlying logic (which, in the case of SDL, is classical). The accessibility...

"semantically complete" when all its tautologies are theorems, whereas a formal system is "sound" when all theorems are tautologies (that is, they are semantically...

logic of any kind. It is formed with propositional calculus formulas and tautologies, and inference apparatus with substitution and modus ponens, but extending...

Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory...

theorem-proving technique for sentences in propositional logic and first-order logic. For propositional logic, systematically applying the resolution rule acts...

context-changing rules. Thus, if we are interested only in the derivability of tautologies, not hypothetical judgments, then we can formalize the Hilbert-style...

or symbols. According to Ayer, the statements of logic and mathematics are tautologies. Tautologies are true by definition, and thus their validity does...