Definitions for modal logic
modal log·ic

Princeton's WordNetRate this definition:0.0 / 0 votes

1. modal logicnoun

   the logical study of necessity and possibility

2. modal logicnoun

   a system of logic whose formal properties resemble certain moral and epistemological concepts

GCIDERate this definition:0.0 / 0 votes

1. modal logicnoun

   A system of logic which studies how to combine propositions which include the concepts of necessity, possibility, and obligation.

WiktionaryRate this definition:0.0 / 0 votes

1. modal logicnoun

   Any formal system that attempts to deal with modalities, such as possibility and necessity, but also obligation and permission.

WikipediaRate this definition:0.0 / 0 votes

1. Modal logic

   Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other systems by adding unary operators ◊ {\displaystyle \Diamond } and ◻ {\displaystyle \Box } , representing possibility and necessity respectively. For instance the modal formula ◊ P {\displaystyle \Diamond P} can be read as "possibly P {\displaystyle P} " while ◻ P {\displaystyle \Box P} can be read as "necessarily P {\displaystyle P} ". Modal logics can be used to represent different phenomena depending on what kind of necessity and possibility is under consideration. When ◻ {\displaystyle \Box } is used to represent epistemic necessity, ◻ P {\displaystyle \Box P} states that P {\displaystyle P} is epistemically necessary, or in other words that it is known. When ◻ {\displaystyle \Box } is used to represent deontic necessity, ◻ P {\displaystyle \Box P} states that P {\displaystyle P} is a moral or legal obligation.In the standard relational semantics for modal logic, formulas are assigned truth values relative to a possible world. A formula's truth value at one possible world can depend on the truth values of other formulas at other accessible possible worlds. In particular, ◊ P {\displaystyle \Diamond P} is true at a world if P {\displaystyle P} is true at some accessible possible world, while ◻ P {\displaystyle \Box P} is true at a world if P {\displaystyle P} is true at every accessible possible world. A variety of proof systems exist which are sound and complete with respect to the semantics one gets by restricting the accessibility relation. For instance, the deontic modal logic D is sound and complete if one requires the accessibility relation to be serial. While the intuition behind modal logic dates back to antiquity, the first modal axiomatic systems were developed by C. I. Lewis in 1912. The now-standard relational semantics emerged in the mid twentieth century from work by Arthur Prior, Jaakko Hintikka, and Saul Kripke. Recent developments include alternative topological semantics such as neighborhood semantics as well as applications of the relational semantics beyond its original philosophical motivation. Such applications include game theory, moral and legal theory, web design, multiverse-based set theory, and social epistemology.

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1. modal logic

   Modal logic is a type of formal logic primarily developed to evaluate statements about necessity and possibility. In essence, it extends classical propositional and predicate logic to include operators expressing modality. Modes of truth are expressed through modalities, such as necessity, possibility, obligation, permissibility, belief, knowledge, etc. These modalities modify the truth value of a proposition, introducing semantic dimensions beyond mere true or false - they give sentences the ability to express complex scenarios like "it might possibly rain later" or "it is necessarily true that all bachelors are unmarried".

WikidataRate this definition:0.0 / 0 votes

1. Modal logic

   Modal logic is a type of formal logic primarily developed in the 1960s 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 saying that John is usually happy, in which case the term "usually" is functioning as a modal. The traditional alethic modalities, or modalities of truth, include possibility, necessity, and impossibility. Other modalities that have been formalized in modal logic include temporal modalities, or modalities of time, deontic modalities, epistemic modalities, or modalities of knowledge and doxastic modalities, or modalities of belief. A formal modal logic represents modalities using modal operators. For example, "It might rain today" and "It is possible that rain will fall today" both contain the notion of possibility. In a modal logic this is represented as an operator, Possibly, attached to the sentence "It will rain today".

Matched Categories

1. • Logic
   • Symbolic Logic

How to pronounce modal logic?

1. Alex

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   Daniel

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How to say modal logic in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of modal logic in Chaldean Numerology is: 9

2. Pythagorean Numerology

   The numerical value of modal logic in Pythagorean Numerology is: 1

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=modal logic
2. ^ GCIDE
   https://gcide.gnu.org.ua/?q=modal logic
3. ^ Wiktionary
   https://en.wiktionary.org/wiki/Modal_Logic
4. ^ Wikipedia
   https://en.wikipedia.org/wiki/Modal_Logic
5. ^ ChatGPT
   https://chat.openai.com
6. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=modal logic