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...

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

Paraconsistent logic – Type of formal logic without explosion principle Paradox – Statement that apparently contradicts itself Tautology – In logic, a statement...

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...

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

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...

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...

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

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...

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

logic. It is also called (first-order) propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic....

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...

In logic, a normal modal logic is a set L of modal formulas such that L contains: All propositional tautologies; All instances of the Kripke schema: ◻...

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

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...

Syntax (logic) -- Synthese -- Systems of Logic Based on Ordinals -- T-schema -- Tacit assumption -- Tarski's undefinability theorem -- Tautology (logic) --...

mathematics, logicism is a programme comprising one or more of the theses that – for some coherent meaning of 'logic' – mathematics is an extension of logic, some...

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

explosion Presupposition, double question State of affairs (philosophy) Tautology (logic) – another type of true statement that also fails to convey any substantive...

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

evidence Superdeterminism – Class of theories in quantum mechanics Tautology (logic) – In logic, a statement which is always true Trial and error – Method of...

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

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

connectives are continuous. By definition, a formula is a tautology of infinite-valued Łukasiewicz logic if it evaluates to 1 under each valuation of propositional...

In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic...

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...

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

propositional logic, they are tautologies. A statement can be called valid, i.e. logical truth, in some systems of logic like in Modal logic if the statement...

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