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...

Langford in their 1932 book Symbolic Logic. It is a normal modal logic, and one of the oldest systems of modal logic of any kind. It is formed with propositional...

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...

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 later...

In logic, a modal companion of a superintuitionistic (intermediate) logic L is a normal modal logic that interprets L by a certain canonical translation...

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

non-normal world. For more discussion of the interpretation of the language of modal logic in models with worlds, see the entries on modal logic and on...

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

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...

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

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

Modal clausal form, also known as separated normal form by modal levels (SNFml) and Mints normal form, is a normal form for modal logic formulae. Such...

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)...

four-man sprint kayak K4, a model of the British red telephone box K4, a normal modal logic K4, in graph theory, the complete graph of four vertices K4, in abstract...

formula in disjunctive normal form, its dual is a formula in conjunctive normal form.) dynamic modal logic A branch of modal logic that studies necessary...

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

intensely investigated system in provability logic. Löb's theorem can be proved within normal modal logic using only some basic rules about the provability...

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

example, infinitary logics permit formulas of infinite size, and modal logics add symbols for possibility and necessity. First-order logic can be studied in...

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...

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...

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

lattice of normal modal logics. Stone's representation theorem can be generalized to the Jónsson–Tarski duality, which ensures that each modal algebra can...

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

semantics, also known as Scott–Montague semantics, is a formal semantics for modal logics. It is a generalization, developed independently by Dana Scott and Richard...

eleventh letter of the English alphabet. K may also refer to: K, a normal modal logic K (programming language), an array processing language developed by...

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

philosopher born in Sheffield, England. He is most well known for his work on modal logic, particularly his joint text with Dana Scott published posthumously (Lemmon...

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