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Contingency (philosophy) In logic, contingency is the feature of a statement making it neither necessary nor impossible. [ 1 ][ 2 ] Contingency is a fundamental concept of modal logic. Modal logic concerns the manner, or mode, in which statements are true. Contingency is one of three basic modes alongside necessity and possibility.
A formula of propositional logic is a tautology if the formula itself is always true, regardless of which valuation is used for the propositional variables. There are infinitely many tautologies. In many of the following examples A represents the statement "object X is bound", B represents "object X is a book", and C represents "object X is on ...
Tautological consequence can also be defined as ∧ ∧ ... ∧ → is a substitution instance of a tautology, with the same effect. [2]It follows from the definition that if a proposition p is a contradiction then p tautologically implies every proposition, because there is no truth valuation that causes p to be true and so the definition of tautological implication is trivially satisfied.
Modal logic. Modal logic is a kind of logic used to represent statements about necessity and possibility. It plays a major role in philosophy and related fields as a tool for understanding concepts such as knowledge, obligation, and causation. For instance, in epistemic modal logic, the formula can be used to represent the statement that is known.
Analytic truth defined as a true statement derivable from a tautology by putting synonyms for synonyms is near Kant's account of analytic truth as a truth whose negation is a contradiction. Analytic truth defined as a truth confirmed no matter what, however, is closer to one of the traditional accounts of a priori .
Logical truth is one of the most fundamental concepts in logic. Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity of its constituent propositions. In other words, a logical truth is a statement which is not only true, but one which is true under all interpretations of its logical components (other ...
In propositional logic, tautology is either of two commonly used rules of replacement. [1][2][3] The rules are used to eliminate redundancy in disjunctions and conjunctions when they occur in logical proofs. They are: The principle of idempotency of disjunction: and the principle of idempotency of conjunction: Where " " is a metalogical symbol ...
A graphical representation of a partially built propositional tableau. In proof theory, the semantic tableau [1] (/ t æ ˈ b l oʊ, ˈ t æ b l oʊ /; plural: tableaux), also called an analytic tableau, [2] truth tree, [1] or simply tree, [2] is a decision procedure for sentential and related logics, and a proof procedure for formulae of first-order logic. [1]