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Type of formal logic
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
Modal_logic
One of five systems of 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
S5_(modal_logic)
Type of modal logic
Epistemic modal logic is a subfield of modal logic that is concerned with reasoning about knowledge. While epistemology has a long philosophical tradition
Epistemic_modal_logic
Type of modal logic
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: ◻
Normal_modal_logic
Method of deriving conclusions
instantiation. Modal logics are formal systems that extend propositional logic and first-order logic with additional operators. Alethic modal logic introduces
Rule_of_inference
Extension of modal logic
In logic, philosophy, and theoretical computer science, dynamic logic is an extension of modal logic capable of encoding properties of computer programs
Dynamic_logic_(modal_logic)
Phenomenon whereby language is used to discuss possible situations
and discourse effects of modal expressions using formal tools derived from modal logic. Within philosophy, linguistic modality is often seen as a window
Modality_(semantics)
In logic, a modal companion of a superintuitionistic (intermediate) logic L is a normal modal logic that interprets L by a certain canonical translation
Modal_companion
Bearer of truth values
and Metaphysical Modality, § 2. Metaphysical and Nomic Modality Garson 2024, Lead section, § 1. What is Modal Logic?, § 2. Modal Logics Newsome 2015, p
Proposition
American logician (born 1932)
approaches to the semantics of programming languages. He has also worked on modal logic, topology, and category theory. Scott received his B.A. in Mathematics
Dana_Scott
Application of logical methods to philosophical problems
systems like modal logic. Some theorists conceive of philosophical logic in a broader sense as the study of the scope and nature of logic in general. In
Philosophical_logic
Field of philosophical logic
can be used to formalize imperative logic, or directive modality in natural languages. Typically, a deontic logic uses O A {\displaystyle {\mathsf {O}}A}
Deontic_logic
Extension of propositional modal logic
propositional modal logic (with many modalities) by adding the least fixed point operator μ and the greatest fixed point operator ν, thus a fixed-point logic. The
Modal_μ-calculus
Study of correct reasoning
ethics, and epistemology. Modal logic is an extension of classical logic. In its original form, sometimes called "alethic modal logic", it introduces two new
Logic
Argument for the existence of God
ontological argument was formulated by Kurt Gödel in private notes, using modal logic. Although he never published or publicly presented it, a version was
Ontological_argument
Formal semantics for non-classical logic systems
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
Kripke_semantics
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
Regular_modal_logic
American philosopher and logician (1940–2022)
and original contributions to logic, especially modal logic. His principal contribution is a semantics for modal logic involving possible worlds, now
Saul_Kripke
Logical operator in modal logic
A modal connective (or modal operator) is a logical connective for modal logic. It is an operator which forms propositions from propositions. In general
Modal_operator
Concept in modal logic
In modal logic, modal collapse is the condition in which every true statement is necessarily true, and vice versa; that is to say, there are no contingent
Modal_collapse
Less-restrictive form of modal logic
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-normal_modal_logic
Subfield of mathematics
recursion theory and proof theory, but has also led to Löb's theorem in modal logic. The method of forcing is employed in set theory, model theory, and recursion
Mathematical_logic
Study of the scope and nature of logic
of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. But
Philosophy_of_logic
In modal logic, a classical modal logic L is any modal logic containing (as axiom or theorem scheme) the duality of the modal operators ◊ A ↔ ¬ ◻ ¬ A {\displaystyle
Classical_modal_logic
System for representing and reasoning about time
temporal logic. The term temporal logic is also sometimes used to refer specifically to tense logic, a modal logic-based system of temporal logic introduced
Temporal_logic
Translation of a text into a logical system
logic translations that convert formulas from one logical system into another, for example, from modal logic to first-order logic. This form of logic
Logic_translation
Possible truths which are not necessary
In logic, contingency is the feature of a statement making it neither necessary nor impossible. Contingency is a fundamental concept of modal logic. Modal
Contingency_(philosophy)
"If P then Q" and "Q", concluding "P". alethic modal logic A type of modal logic that deals with modalities of truth, such as necessity and possibility.
Glossary_of_logic
Various systems of symbolic logic
logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by
Intuitionistic_logic
Approach to predicate logic
such fine logical structures like modal, temporal, dynamic, epistemic ones). In order to achieve its special goal, logic was forced to develop its own formal
Intensional_logic
Tool for proving a logical formula
satisfiability of finite sets of formulas of various logics. It is the most popular proof procedure for modal logics. A method of truth trees contains a fixed set
Method_of_analytic_tableaux
American philosopher (1883–1964)
American academic philosopher. He is considered the progenitor of modern modal logic and the founder of conceptual pragmatism. First a noted logician, he
C._I._Lewis
System of logic in mathematics and philosophy
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 integers n) as
Łukasiewicz_logic
List of symbols used to express logical relations
contains logic symbols. Without proper rendering support, you may see question marks, boxes, or other symbols instead of logic symbols. In logic, a set
List_of_logic_symbols
Branch of philosophy
modal statements? In other words, even if modal logic explains how modal statements are evaluated, it does not explain why they are true. Modal logic
Modal_metaphysics
Ancient philosophy
"Stoic modal logic is not a logic of modal propositions (e.g., propositions of the type 'It is possible that it is day' ...) ... instead, their modal theory
Stoicism
German-born British philosopher (born 1960)
proposed logic is weaker than classical logic and stronger than intuitionistic logic. It is a modal companion to the superintuitionistic logic QH+KF. Determinism
Susanne_Bobzien
Type of logical system
first-order logic (FOL), also called predicate logic, predicate calculus, or quantificational logic, is a type of formal system. First-order logic uses quantified
First-order_logic
Modal logic relationship
values to sentences in the relational semantics for modal logic. In relational semantics, a modal formula's truth value at a possible world w {\displaystyle
Accessibility_relation
philosophical logic, particularly from the 1950s onwards, in subjects such as modal logic, temporal logic, deontic logic, and relevance logic. The Nasadiya
History_of_logic
Modal temporal logic with modalities referring to time
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
Linear_temporal_logic
American philosopher and logician (1941–2023)
philosopher and logician, known for his work in modal logic, deontic logic, conditional logic, and the logic of agency. He was a long-time member of the Department
Brian_Chellas
Overview of and topical guide to logic
Intuitionistic logic Linear logic Many-valued logic Mathematical logic Metalogic Minimal logic Modal logic Non-Aristotelian logic Non-classical logic Noncommutative
Outline_of_logic
Distinction in formal semantics
accessible possible worlds, and George Bush could not have been Al Gore. In modal logic the distinction between de dicto and de re is one of scope. In de dicto
De_dicto_and_de_re
Formal argument for the existence of God
attempted to clarify with his ontological argument. The argument uses modal logic, which deals with statements about what is necessarily true or possibly
Gödel's_ontological_proof
Formal systems of logic that significantly differ from standard logical systems
intuitionistic logic have an equivalent theorem in the classical modal logic S4. The result has been generalized to superintuitionistic logics and extensions
Non-classical_logic
New Zealand philosopher and logician (1939–2024)
a New Zealand philosopher and logician who was known for his work in modal logic. Cresswell received his B.A. in 1960 and M.A. in 1961 from the University
Max_Cresswell
Study of the semantics, or interpretations, of formal and natural languages
(developed by Saul Kripke and others for modal logic and related systems), algebraic semantics (connecting logic to abstract algebra), and game semantics
Semantics_(logic)
Type of logic regarding reasoning about beliefs
the set of beliefs of c {\displaystyle c} . In doxastic logic, belief is treated as a modal operator. There is complete parallelism between a person
Doxastic_logic
Modality in linguistics
Alethic modality (from Greek ἀλήθεια = truth) is a linguistic modality that indicates modalities of truth, in particular the modalities of logical necessity
Alethic_modality
Family of logics for natural-language and counterfactual conditionals
"basic conditional logic", corresponding to the core selection function semantics and serving as an analogue of the normal modal logic K for conditionals
Conditional_logic
Type of verb, such as "might", that is used to indicate modality
A modal verb is a type of verb that contextually indicates a modality such as a likelihood, ability, permission, request, capacity, suggestion, order
Modal_verb
Proof calculus based on introduction and elimination rules
proof-term calculus to classical logic. Natural deduction has also been extended to modal logic. Prawitz treated modal systems in his 1965 study, and many
Natural_deduction
Statement that players know and also know that other players know (ad infinitum)
Common knowledge can be given a logical definition in multi-modal logic systems in which the modal operators are interpreted epistemically. At the propositional
Common_knowledge_(logic)
Type of fallacy in modal logic
The modal fallacy or modal scope fallacy is a type of formal fallacy that occurs in modal logic. It is the fallacy of placing a proposition in the wrong
Modal_fallacy
logic is a modal logic that has more than one primitive modal operator. They find substantial applications in theoretical computer science. A modal logic
Multimodal_logic
Modal logic
Provability logic is a branch of proof theory and a modal logic, in which the box (or "necessity") operator is interpreted as 'it is provable that'. The
Provability_logic
Algorithm in modal logic
In modal logic, standard translation is a logic translation that transforms formulas of modal logic into formulas of non-modal first-order logic that
Standard_translation
Term used to model separate circumstances that cannot exist together
advent of possible world semantics for modal logic, as well as world based semantics for non-classical logics, but have yet to find the ubiquitous acceptance
Impossible_world
Philosophical concept
Modal realism is the view propounded by the philosopher David Lewis that all possible worlds are real in the same way as is the actual world: they are
Modal_realism
Family of formal knowledge representation
exist. For example, a description logic might be combined with a modal temporal logic such as linear temporal logic. Philosophy portal Formal concept
Description_logic
2001 textbook by Graham Priest
propositional logics, which are logical systems that differ from standard classical propositional logic. It covers a wide range of topics including modal logic, intuitionistic
An Introduction to Non-Classical Logic
An_Introduction_to_Non-Classical_Logic
American philosopher (1941–2001)
literature. His metaphysics incorporated seminal contributions to quantified modal logic, the development of counterpart theory, counterfactual causation, and
David_Lewis_(philosopher)
Propositional logic extending intuitionistic logic
In mathematical logic, a superintuitionistic logic is a propositional logic extending intuitionistic logic. A logic is a set of propositional formulas
Intermediate_logic
Formal system of logic
assumed in some context to refer to classical higher-order logic. However, modal higher-order logic has been studied as well. According to several logicians
Higher-order_logic
Concept of philosophy and logic used to express modal claims
used as a formal device in logic, philosophy, and linguistics in order to provide a semantics for intensional and modal logic. Their metaphysical status
Possible_world
British logician and philosopher (1930 – 1966)
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
John_Lemmon
Algebraic structure
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.
Interior_algebra
Topics referred to by the same term
modes (media) in a single artifact Multimodal logic modal logic that has more than one primitive modal operator Evolutionary multimodal optimization,
Multimodal
Concept in philosophical logic
including as a model of traditional logic, quantifications, modal logic, order theory, or paraconsistent logic. For instance, the statement A may be
Logical_hexagon
responsible for the introduction of hypothetical syllogism, temporal modal logic and inductive logic. Other important developments in early Islamic philosophy include
Logic_in_Islamic_philosophy
Formal semantics based on algebras
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
Algebraic semantics (mathematical logic)
Algebraic_semantics_(mathematical_logic)
Mathematician and philosopher (1906–1978)
theory by clarifying the connections between classical logic, intuitionistic logic, and modal logic. Born into a wealthy German-speaking family in Brno,
Kurt_Gödel
Concept in modal logic
In quantified modal logic, the Buridan formula and the converse Buridan formula (more accurately, schemata rather than formulas) (i) syntactically state
Buridan_formula
System including an indeterminate value
(unsuccessful) Tarski–Łukasiewicz attempt to axiomatize modal logic using a three-valued logic, "it is possible that..." L is read "it is true that..."
Three-valued_logic
Principles in the philosophy of Aristotle
philosophy regards possibility, as studied by modal metaphysics, to be an aspect of modal logic. Modal logic as a named subject owes much to the writings
Potentiality_and_actuality
Modal logic term
In modal logic, the modal depth of a formula is the deepest nesting of modal operators (commonly ◻ {\displaystyle \Box } and ◊ {\displaystyle \Diamond
Modal_depth
Logician and philosopher (1914–1969)
were subsequently published as Time and Modality (1957). This is a seminal contribution to the study of tense logic and the metaphysics of time, in which
Arthur_Prior
Founder(s): K F. Gödel (1933) showed that intuitionistic logic can be embedded into modal logic S4. (other systems) Interpretation (Gödel): ◻ P {\displaystyle
Constructive_logic
the line. Before the use of guarded logic there were two major terms used to interpret modal logic. Mathematical logic and database theory (Artificial Intelligence)
Guarded_logic
Boolean algebra with unary operators expressing necessity and possibility modalities
In algebra and logic, a modal algebra is a structure ⟨ A , ∧ , ∨ , − , 0 , 1 , ◻ ⟩ {\displaystyle \langle A,\land ,\lor ,-,0,1,\Box \rangle } such that
Modal_algebra
Branch of mathematical logic
predicate logic of either the classical or intuitionistic flavour, almost any modal logic, and many substructural logics, such as relevance logic or linear
Proof_theory
Normal form for modal logic formulas
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
Modal_clausal_form
Certain kind of modal formula
In modal logic, Sahlqvist formulas are a certain kind of modal formula with remarkable properties. The Sahlqvist correspondence theorem states that every
Sahlqvist_formula
American writer (1962–2008)
philosophy, Wallace pursued modal logic and mathematics, and presented in 1985 a senior thesis in philosophy and modal logic that was awarded the Gail Kennedy
David_Foster_Wallace
Theorem in mathematical logic
first-order logics extended with Lindström quantifiers. Lindström's theorem has been extended to various other systems of logic, in particular modal logics by
Lindström's_theorem
Assignment of meaning to the symbols of a formal language
semantics. The most commonly studied formal logics are propositional logic, predicate logic and their modal analogs, and for these there are standard ways
Interpretation_(logic)
Philosophical study of being
Section, § 1. Possible Worlds and Modal Logic Kuhn 2010, p. 13 Garson 2024, Lead section, § 1. What is Modal Logic? Kirwan 2005, pp. 417–418 Noonan &
Ontology
Branch of applied mathematics
used in natural language processing. Logic is used to model syntax, formal semantics, and pragmatics. Modal logic can model syntax that employs different
Mathematical_linguistics
Provability logic
then ⊢ P {\displaystyle \vdash P} . The provability logic GL that results from taking the modal logic K4 (or K, since the axiom schema 4, ◻ A → ◻ ◻ A {\displaystyle
Löb's_theorem
British philosopher (born 1955)
theoretical interpretation of the Barcan formula, which is a theorem of the modal logic S5. However, Williamson has also developed an ontology of “bare possibilia”
Timothy_Williamson
Inference seeking the simplest and most likely explanation
first-order logic, without requiring any preliminary reduction of formulae into normal forms. These methods have also been extended to modal logic. Abductive
Abductive_reasoning
Field of philosophical and mathematical logic studying agency and action
case. Agentive logics generalise modal logic by adding modalities indexed to agents and to actions. Typical examples include: STIT logics (from sees to
Agentive_logic
1947 book by Rudolf Carnap
Necessity: A Study in Semantics and Modal Logic (1947; enlarged edition 1956) is a book about semantics and modal logic by the philosopher Rudolf Carnap
Meaning_and_Necessity
That which makes or defines an entity
one's duty (express one's essence). Avicenna Essentialism Hypokeimenon Modal logic Phenomenon Physical ontology Smarana Theory of forms Transubstantiation
Essence
Topics referred to by the same term
connective Strict conditional or strict implication, a connective of modal logic that expresses necessity modus ponens, or implication elimination, a
Implication
German philosopher (1889–1964)
Becker made contributions to modal logic (the logic of necessity and possibility) and Becker's postulate, the claim that modal status is necessary (for instance
Oskar_Becker
Logical proposition that cannot be disproved
as such, is often thought of as the broadest type of possibility. In modal logic, a logical proposition is possible if it is true in some possible world
Logical_possibility
Axiomatic system of formal deduction in logic
propositional and first-order logic. They are widely used for modal logic, intuitionistic logic, relevance logic, many-valued logics, and other non-classical
Hilbert_system
Pair of logical equivalences
alethic modalities of possibility and necessity, Aristotle observed this case, and in the case of normal modal logic, the relationship of these modal operators
De_Morgan's_laws
MODAL LOGIC
MODAL LOGIC
Girl/Female
Hindu, Indian
Moral
Boy/Male
Hindi
Moral.
Boy/Male
Hindi
Moral.
Girl/Female
Indian
Moral; Faithful
Girl/Female
Hindu
Bird
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Pleasing
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu
Attractive; Sweet; Lovable; Intelligent; Smart; Handsome
Boy/Male
Indian
New Generation
Girl/Female
Christian, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Sindhi, Tamil, Telugu
Bird; Amazing
Boy/Male
Chinese
Moral.
Boy/Male
Indian, Sanskrit
Bird; Lion
Boy/Male
Egyptian
To model.
Girl/Female
Indian
Beautiful
Girl/Female
Arabic
Moral
Boy/Male
British, English, Hindu, Indian
Limited
Boy/Male
Muslim
Model, Example
Boy/Male
Hindu
Attractive
Boy/Male
Gujarati, Hindu, Indian, Kannada, Marathi
Enjoyment
Girl/Female
Hindu, Indian
An Apsara's Name
Girl/Female
Hindu, Indian, Traditional
Moral
MODAL LOGIC
MODAL LOGIC
MODAL LOGIC
MODAL LOGIC
MODAL LOGIC
MODAL LOGIC
MODAL LOGIC
a.
Supported by reason or probability; practically sufficient; -- opposed to legal or demonstrable; as, a moral evidence; a moral certainty.
a.
Indicating, or pertaining to, some mode of conceiving existence, or of expressing thought.
a.
Suitable to be taken as a model or pattern; as, a model house; a model husband.
adv.
In a modal manner.
n.
The inner meaning or significance of a fable, a narrative, an occurrence, an experience, etc.; the practical lesson which anything is designed or fitted to teach; the doctrine meant to be inculcated by a fiction; a maxim.
a.
Of the nature of, or relating to, a node; as, a nodal point.
n.
Anything which serves, or may serve, as an example for imitation; as, a government formed on the model of the American constitution; a model of eloquence, virtue, or behavior.
a.
Conformed to accepted rules of right; acting in conformity with such rules; virtuous; just; as, a moral man. Used sometimes in distinction from religious; as, a moral rather than a religious life.
n.
A piece of metal in the form of a coin, struck with a device, and intended to preserve the remembrance of a notable event or an illustrious person, or to serve as a reward.
v. i.
To make a copy or a pattern; to design or imitate forms; as, to model in wax.
n.
Something intended to serve, or that may serve, as a pattern of something to be made; a material representation or embodiment of an ideal; sometimes, a drawing; a plan; as, the clay model of a sculpture; the inventor's model of a machine.
a.
Of or pertaining to a mode or mood; consisting in mode or form only; relating to form; having the form without the essence or reality.
n.
Attractive moral excellence; moral beauty.
n.
An oily liquid, Cl3.CHO, analogous to chloral and bromal.
v. i.
To moralize.
v. t.
To plan or form after a pattern; to form in model; to form a model or pattern for; to shape; to mold; to fashion; as, to model a house or a government; to model an edifice according to the plan delineated.
a.
Serving to teach or convey a moral; as, a moral lesson; moral tales.
a.
Acting upon or through one's moral nature or sense of right, or suited to act in such a manner; as, a moral arguments; moral considerations. Sometimes opposed to material and physical; as, moral pressure or support.
n.
A morality play. See Morality, 5.
v. t.
To honor or reward with a medal.