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: ◻...

Modal logic is a kind of logic used to represent statements about necessity and possibility. In philosophy and related fields it is used as a tool for...

A non-normal modal logic is a variant of modal logic that deviates from the basic principles of normal modal logics. Normal modal logics adhere to the...

In philosophical logic, the concept of an impossible world (sometimes called a non-normal world) is used to model certain phenomena that cannot be adequately...

for non-classical logic systems created in the late 1950s and early 1960s by Saul Kripke and André Joyal. It was first conceived for modal logics, and...

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

published a treatment of alethic and epistemic modalities that introduced some systems of non-normal modal logics that have proven to have had lasting interest...

Intuitionistic logic Linear logic Many-valued logic Mathematical logic Metalogic Minimal logic Modal logic Non-Aristotelian logic Non-classical logic Noncommutative...

and original contributions to logic, especially modal logic. His principal contribution is a semantics for modal logic involving possible worlds, now...

In modal logic, a classical modal logic L is any modal logic containing (as axiom or theorem) the duality of the modal operators ◊ A ↔ ¬ ◻ ¬ A {\displaystyle...

In logic, linear temporal logic or linear-time temporal logic (LTL) is a modal temporal logic with modalities referring to time. In LTL, one can encode...

semantics. The most commonly studied formal logics are propositional logic, predicate logic and their modal analogs, and for these there are standard ways...

philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain...

can be used to formalize imperative logic, or directive modality in natural languages. Typically, a deontic logic uses OA to mean it is obligatory that...

Epistemic modal logic is a subfield of modal logic that is concerned with reasoning about knowledge. While epistemology has a long philosophical tradition...

resembling the inference rules governing modalities in sequent calculus formalisations of the normal modal logic S4, and that there is no longer such a...

In modal logic, Sahlqvist formulas are a certain kind of modal formula with remarkable properties. The Sahlqvist correspondence theorem states that every...

propositional logic (IPC) may be translated into the language of the normal modal logic S4 as follows: ⊥ ∗ = ⊥ A ∗ = ◻ A if  A  is prime (a positive literal)...

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

philosophical logic, particularly from the 1950s onwards, in subjects such as modal logic, temporal logic, deontic logic, and relevance logic. The Nasadiya...

(normal and non-normal) modal logic, hybrid logic, first-order modal logic, paraconsistent logic, linear logic, relevance logic, connexive logic, belief...

Standpoint of Modern Formal Logic. New York: Garland Publishers. ISBN 0-8240-6924-2. OCLC 15015545. Malink, Marko. 2013. Aristotle's Modal Syllogistic. Cambridge...

reference work on natural deduction, and included applications for modal and second-order logic. In natural deduction, a proposition is deduced from a collection...

doi:10.1016/j.asoc.2014.10.035. Mironov, A. M. (August 2005). "Fuzzy Modal Logics". Journal of Mathematical Sciences. 128 (6): 3461–3483. doi:10.1007/s10958-005-0281-1...

alethic modalities of possibility and necessity, Aristotle observed this case, and in the case of normal modal logic, the relationship of these modal operators...

_{n}\mid \Box \Sigma \vdash \Box \Pi \mid \Omega \vdash \Theta }}} for modal logic S5, where ◻ Σ {\displaystyle \Box \Sigma } means that every formula in...

simultaneously. non-standard logic Logics that diverge from or extend classical logic, including non-classical logics, many-valued logics, and modal logics, among...

Default logic is a non-monotonic logic proposed by Raymond Reiter to formalize reasoning with default assumptions. Default logic can express facts like...

logic L with its standard consequence relation ⊢ L {\displaystyle \vdash _{L}} generated by modus ponens and axioms, and we identify a normal modal logic...

thereof, can be added to the language of modal logic, thus obtaining modal dependence logic. As it is, dependence logic lacks an implication. The intuitionistic...