In algebra and logic, a modal algebra is a structure ⟨ A , ∧ , ∨ , − , 0 , 1 , ◻ ⟩ {\displaystyle \langle A,\land ,\lor ,-,0,1,\Box \rangle } such that...

the modal logic S4 what Boolean algebras are to set theory and ordinary propositional logic. Interior algebras form a variety of modal algebras. An interior...

mathematical structure of modal logic, namely Boolean algebras augmented with unary operations (often called modal algebras), began to emerge with J....

representation of modal algebras by general modal frames is possible for any normal modal algebra, it is only in the case of interior algebras (which correspond...

Derivative algebras provide an algebraic abstraction of the derived set operator in topology. They also play the same role for the modal logic wK4 =...

their construction is a special case of the construction of a modal algebra from a modal frame i.e. from a set with a single binary relation. (The latter...

extensions thereof. Modal and other nonclassical logics are typically modeled by what are called "Boolean algebras with operators." Algebraic formalisms going...

provides algebraic semantics for the modal logic wK3. In abstract algebra, the derivative algebra of a not-necessarily associative algebra A over a field...

Ultrafilter Lemma. Heyting algebras and interior algebras are the Lindenbaum–Tarski algebras for intuitionistic logic and the modal logic S4, respectively...

S4 algebra, a variety of modal algebras, also called Interior algebra Tetrahedral symmetry, the symmetric group S4 S4 (modal logic), a normal modal logic...

non-existent before Kripke (algebraic semantics existed, but were considered 'syntax in disguise'). The language of propositional modal logic consists of a countably...

fixed point operators; from this viewpoint, the modal μ-calculus is over the lattice of a power set algebra. The game semantics of μ-calculus is related...

treatment of monadic Boolean algebra. Monadic Boolean algebras also have an important connection to modal logic. The modal logic S5, viewed as a theory...

In linear algebra, the modal matrix is used in the diagonalization process involving eigenvalues and eigenvectors. Specifically the modal matrix M {\displaystyle...

are used to model modal and intermediate logics. The general frame semantics combines the main virtues of Kripke semantics and algebraic semantics: it shares...

backbone of modal analysis. They allow, through linear algebra, specifically through least square methods to fit large amounts of data to find the modal constants...

completeness of a logic: every normal modal logic is complete wrt a class of modal algebras, and a finite modal algebra can be transformed into a Kripke frame...

Boolean algebra Free Boolean algebra Monadic Boolean algebra Residuated Boolean algebra Two-element Boolean algebra Modal algebra Derivative algebra (abstract...

A modal connective (or modal operator) is a logical connective for modal logic. It is an operator which forms propositions from propositions. In general...

abstract algebraic logic is the study of the algebraization of deductive systems arising as an abstraction of the well-known Lindenbaum–Tarski algebra, and...

mathematical logic, algebraic semantics is a formal semantics based on algebras studied as part of algebraic logic. For example, the modal logic S4 is characterized...

was a Dutch logician who made major contributions to algebraic logic, universal algebra, and modal logic. His important achievements over the course of...

The goal of modal analysis in structural mechanics is to determine the natural mode shapes and frequencies of an object or structure during free vibration...

In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid...

"modal" operations ∇ j {\displaystyle \nabla _{j}} are lattice endomorphisms. LM2 algebras are the Boolean algebras. The canonical Łukasiewicz algebra...

semantics for intensional and modal logic. Their metaphysical status has been a subject of controversy in philosophy, with modal realists such as David Lewis...

been drawn between the monad-comonad theory, and modal logic via closure operators, interior algebras, and their relation to models of S4 and intuitionistic...

defined in the early 20th century by Jan Łukasiewicz as a three-valued modal logic; it was later generalized to n-valued (for all finite n) as well as...

dynamic logic and other modal logics of programs, for which programs and propositions form two distinct sorts, action algebra combines the two into a...

non-normal. Both algebraic and neighborhood semantics characterize familiar classical modal systems that are weaker than the weakest normal modal logic K. Every...