modal logic

modal logic
A logic studying the notions of necessity and possibility. Modal logic was of great importance historically, particularly in the light of various doctrines concerning the necessary properties of the deity, but was not a central topic of modern logic in its golden period at the beginning of the 20th century. It was, however, revived by C. I. Lewis, by adding to a propositional or predicate calculus two operators, ⎕ and ⋄ (sometimes written N and M), meaning necessarily and possibly, respectively. Theses like p →⋄p and ⎕p →p will be wanted. Controversial theses include ⎕p →⎕h p (if a proposition is necessary, it is necessarily necessary, characteristic of the system known as S4) and ⋄p →⎕⋄p (if a proposition is possible, it is necessarily possible, characteristic of the system known as S5). The classical model theory for modal logic, due to Kripke and the Swedish logician Stig Kanger, involves valuing propositions not as true or false simpliciter, but as true or false at possible worlds, with necessity then corresponding to truth in all worlds, and possibility to truth in some world.

Philosophy dictionary. . 2011.

Игры ⚽ Нужна курсовая?

Look at other dictionaries:

  • Modal logic — is a type of formal logic that extends classical propositional and predicate logic to include operators expressing modality. Modals words that express modalities qualify a statement. For example, the statement John is happy might be qualified by… …   Wikipedia

  • modal logic — mo dal log ic, n. A system of logic which studies how to combine propositions which include the concepts of necessity, possibility, and obligation. [PJC] …   The Collaborative International Dictionary of English

  • modal logic — Formal systems incorporating modalities such as necessity, possibility, impossibility, contingency, strict implication, and certain other closely related concepts. The most straightforward way of constructing a modal logic is to add to some… …   Universalium

  • modal logic — noun 1. the logical study of necessity and possibility • Hypernyms: ↑logic 2. a system of logic whose formal properties resemble certain moral and epistemological concepts • Hypernyms: ↑symbolic logic, ↑mathematical logic, ↑formal logic • …   Useful english dictionary

  • modal logic — noun Any formal system that attempts to deal with modalities, such as possibility and necessity, but also obligation and permission. See Also: deontic logic, doxastic logic, epistemic logic …   Wiktionary

  • Epistemic modal logic — is a subfield of modal logic that is concerned with reasoning about knowledge. While epistemology has a long philosophical tradition dating back to Ancient Greece, epistemic logic is a much more recent development with applications in many fields …   Wikipedia

  • Dynamic logic (modal logic) — For the subject in digital electronics also known as clocked logic, see dynamic logic (digital electronics). Dynamic logic is an extension of modal logic originally intended for reasoning about computer programs and later applied to more general… …   Wikipedia

  • Classical modal logic — In modal logic, a classical modal logic L is any modal logic containing (as axiom or theorem) the duality of the modal operators which is also closed under the rule Alternatively one can give a dual definition of L by which L is classical iff it… …   Wikipedia

  • S5 (modal logic) — In logic and philosophy, S5 is one of five systems of modal logic proposed by Clarence Irving Lewis and Cooper Harold Langford in their 1932 book Symbolic Logic . It is a normal modal logic, and one of the oldest systems of modal logic of any… …   Wikipedia

  • Regular modal logic — In modal logic, a regular modal logic L is a modal logic closed underDiamond A equiv lnotBoxlnot Aand the rule(Aland B) o C vdash (Box AlandBox B) oBox C.Every regular modal logic is classical, and every normal modal logic is regular and hence… …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”