Category: Algebraic logic

Composition of relations
In the mathematics of binary relations, the composition of relations is the forming of a new binary relation R; S from two given binary relations R and S. In the calculus of relations, the composition
Action algebra
In algebraic logic, an action algebra is an algebraic structure which is both a residuated semilattice and a Kleene algebra. It adds the star or reflexive transitive closure operation of the latter to
Ockham algebra
In mathematics, an Ockham algebra is a bounded distributive lattice with a dual endomorphism, that is, an operation ~ satisfying ~(x ∧ y) = ~x ∨ ~y, ~(x ∨ y) = ~x ∧ ~y, ~0 = 1, ~1 = 0. They were intro
Łukasiewicz–Moisil algebra
Łukasiewicz–Moisil algebras (LMn algebras) were introduced in the 1940s by Grigore Moisil (initially under the name of Łukasiewicz algebras) in the hope of giving algebraic semantics for the n-valued
Lindenbaum–Tarski algebra
In mathematical logic, the Lindenbaum–Tarski algebra (or Lindenbaum algebra) of a logical theory T consists of the equivalence classes of sentences of the theory (i.e., the quotient, under the equival
Residuated Boolean algebra
In mathematics, a residuated Boolean algebra is a residuated lattice whose lattice structure is that of a Boolean algebra. Examples include Boolean algebras with the monoid taken to be conjunction, th
Canonical normal form
In Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form (CDNF) or minterm canonical form and its dual canonical conjunctive normal form (CCNF) or maxterm can
Leibniz operator
In abstract algebraic logic, a branch of mathematical logic, the Leibniz operator is a tool used to classify deductive systems, which have a precise technical definition and capture a large number of
Elliptic algebra
In algebra, an elliptic algebra is a certain regular algebra of a Gelfand–Kirillov dimension three (quantum polynomial ring in three variables) that corresponds to a cubic divisor in the projective sp
Algebraic logic
In mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with free variables. What is now usually called classical algebraic logic focuses on the identification and a
Cylindric algebra
In mathematics, the notion of cylindric algebra, invented by Alfred Tarski, arises naturally in the algebraization of first-order logic with equality. This is comparable to the role Boolean algebras p
De Morgan algebra
In mathematics, a De Morgan algebra (named after Augustus De Morgan, a British mathematician and logician) is a structure A = (A, ∨, ∧, 0, 1, ¬) such that: * (A, ∨, ∧, 0, 1) is a bounded distributive
Relation algebra
In mathematics and abstract algebra, a relation algebra is a residuated Boolean algebra expanded with an involution called converse, a unary operation. The motivating example of a relation algebra is
Polyadic algebra
Polyadic algebras (more recently called Halmos algebras) are algebraic structures introduced by Paul Halmos. They are related to first-order logic analogous to the relationship between Boolean algebra
In abstract algebra, a branch of pure mathematics, an MV-algebra is an algebraic structure with a binary operation , a unary operation , and the constant , satisfying certain axioms. MV-algebras are t
Predicate functor logic
In mathematical logic, predicate functor logic (PFL) is one of several ways to express first-order logic (also known as predicate logic) by purely algebraic means, i.e., without quantified variables.
Monadic Boolean algebra
In abstract algebra, a monadic Boolean algebra is an algebraic structure A with signature ⟨·, +, ', 0, 1, ∃⟩ of type ⟨2,2,1,0,0,1⟩, where ⟨A, ·, +, ', 0, 1⟩ is a Boolean algebra. The monadic/unary ope
Abstract algebraic logic
In mathematical logic, abstract algebraic logic is the study of the algebraization of deductive systemsarising as an abstraction of the well-known Lindenbaum–Tarski algebra, and how the resulting alge
Higher-dimensional algebra
In mathematics, especially (higher) category theory, higher-dimensional algebra is the study of categorified structures. It has applications in nonabelian algebraic topology, and generalizes abstract
Boolean algebra
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, u
Kleene algebra
In mathematics, a Kleene algebra (/ˈkleɪni/ KLAY-nee; named after Stephen Cole Kleene) is an idempotent (and thus partially ordered) semiring endowed with a closure operator. It generalizes the operat
Heyting algebra
In mathematics, a Heyting algebra (also known as pseudo-Boolean algebra) is a bounded lattice (with join and meet operations written ∨ and ∧ and with least element 0 and greatest element 1) equipped w