This is a glossary of logic. Logic is the study of the principles of valid reasoning and argumentation.
A
A-proposition A type of standard-form categorical proposition, asserting that all members of the subject category are included in the predicate category; symbolized as "All S are P".
abduction A form of reasoning characterized by drawing a conclusion based on the best available explanation for a set of premises. Often used in hypothesis formation.
Abelian logic A type of relevance logic that rejects contraction and accepts that ((A → B) → B) → A.
absorption A logical rule stating that if a proposition implies another, then adding any additional conjunction to the first proposition does not change the implication. Symbolized as P → Q ≡ ( P ∧ R ) → Q {\displaystyle P\rightarrow Q\equiv (P\land R)\rightarrow Q} .
abstract object An object that does not exist at any particular time or place but rather exists as a type of thing—i.e., an idea, or abstraction.
abstraction The process or result of generalization by reducing the information content of a concept or an observable phenomenon, typically to retain only information which is relevant for a particular purpose.
abstraction operator The function implicitly defined by an abstraction principle.
abstraction principle A formula of the form (∀α)(∀β)(Abst(α) = Abst(β) ↔ Equ(α, β)), where Abst is an abstraction operator mapping the type of entities ranged over by α and β to objects, and “Equ” is an equivalence relation on the type of entities ranged over by α and β. For instance, Hume's principle, and Basic Law V.
accessibility relation In modal logic, a relation that describes which worlds are accessible from other worlds in the semantics of possible world models.
actual world In modal logic, the world that is considered to be the real world, as opposed to possible worlds which are considered in modal reasoning.
addition A rule of inference in formal logic where from any proposition, a disjunction can be formed by disjoining it with any other proposition. Symbolized as P ⊢ P ∨ Q {\displaystyle P\vdash P\lor Q} .
ad hominem A fallacy in argumentation that targets the person making an argument rather than the argument itself.
ad ignorantium A logical fallacy where a proposition is considered true because it has not been proven false or vice versa.
ad infinitum An argument or process that is supposed to continue indefinitely, without ever reaching an end or conclusion.
adjunction See conjunction introduction.
affine logics A subfield of linear logic focusing on the study of affine transformations and their implications in logical reasoning.
affirmative proposition A proposition that asserts the truth of a statement, as opposed to negating it.
affirming the consequent A logical fallacy in which a conditional statement is incorrectly used to infer its converse. For example, from "If P then Q" and "Q", concluding "P".
alethic modal logic A type of modal logic that deals with modalities of truth, such as necessity and possibility.
ambiguity The property of a statement or phrase having more than one meaning or interpretation.
amphiboly A type of ambiguity resulting from ambiguous grammatical structure, rather than the ambiguity of individual words.
analethic logic A three-valued logic where the third truth value is the truth-value gap "neither true nor false" ("N"), and the designated values are "true" and "neither true nor false."
analysis 1. Analysis, the process of breaking a concept down into more simple parts, so that its logical structure is displayed. 2. Mathematical analysis
analytic A statement that is true by virtue of its meaning, such as definitions or statements grounded in logical laws.
anaphora A rhetorical device that consists of repeating a sequence of words at the beginnings of neighboring clauses, thereby lending them emphasis.
ancestral In logic and mathematics, the transitive closure of a relation, capturing the idea of indirect relationships across generations or iterations.
antecedent The first part of a conditional statement, the "if" clause, which specifies a condition for the consequent.
anti-extension In set theory and logic, the complement of the extension of a concept or predicate, consisting of all objects that do not fall under the concept.
antilogism A syllogism with three premises leading to a contradiction, showing the inconsistency of the premises.
antinomy A contradiction between two beliefs or conclusions that are in themselves reasonable; a paradox.
antisymmetry A property of a relation R {\displaystyle R} , where for any two elements a {\displaystyle a} and b {\displaystyle b} , if a R b {\displaystyle aRb} and b R a {\displaystyle bRa} , then a = b {\displaystyle a=b} .
a posteriori Knowledge or justification is said to be a posteriori if it depends on empirical evidence or experience.
a priori Knowledge or justification is said to be a priori if it is independent of empirical evidence or experience, such as logic or mathematics.
argument A series of statements typically used to persuade someone of something or to present reasons for accepting a conclusion.
Aristotelian comprehension schema This formula in second-order logic: (∃x)Φ → (∃Y)(∀x)(Yx ↔ Φ).
Aristotelian logic The traditional logic developed by Aristotle, based on the study of syllogism and the principle of non-contradiction.
Aristotle's sea battle A thought experiment by Aristotle to explore the concept of future contingents and the problem of determinism and free will.
Aristotle's theses The formulas ¬ (¬ A → A) and ¬ (A → ¬A) in propositional logic; they are theorems in connexive logic but not in classical logic. See also Boethius' theses.
arity The number of arguments or operands that a function, operation, or relation takes. In logic, it refers to the number of terms that a predicate has.
assertion The principle, or axiom, that (A ∧ (A → B)) → B. Also called pseudo modus ponens.
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