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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
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
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)
Logic of knowledge and information change
Dynamic epistemic logic (DEL) is a logical framework dealing with knowledge and information change. Typically, DEL focuses on situations involving multiple
Dynamic_epistemic_logic
Topics referred to by the same term
Dynamic logic may mean: In theoretical computer science, dynamic logic (modal logic) is a modal logic for reasoning about dynamic behaviour In digital
Dynamic_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
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
Guarded logic is a choice set of dynamic logic involved in choices, where outcomes are limited. A simple example of guarded logic is as follows: if X
Guarded_logic
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
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)
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
System for reasoning about vagueness
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
Fuzzy_logic
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
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
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
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)
Field of philosophical and mathematical logic studying agency and action
sees to it that φ {\displaystyle \varphi } holds; dynamic logics of action with program-like modalities [ α ] φ {\displaystyle [\alpha ]\varphi } and ⟨
Agentive_logic
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
Family of formal knowledge representation
composition, inversion, etc.) correspond to the modal operations used in dynamic logic. Temporal description logic represents—and allows reasoning about—time
Description_logic
Theory of logic to account for observations from quantum theory
Quantum logic embeds into linear logic and the modal logic B. Indeed, modern logics for the analysis of quantum computation often begin with quantum logic, and
Quantum_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 studied alongside
Modality_(semantics)
Family of modal logics for agency and choice
STIT logic (from seeing to it that) is a family of modal and branching-time logics for reasoning about agency and choice. A typical STIT operator has
STIT_logic
Approach to formal semantics
various logical systems, including classical logic, intuitionistic logic, linear logic, and modal logic. The approach bears conceptual resemblances to
Game_semantics
its dual is a formula in conjunctive normal form.) dynamic modal logic A branch of modal logic that studies necessary and possible connections between
Glossary_of_logic
Framework in logic and natural language semantics
Dynamic semantics is a framework in logic and natural language semantics that treats the meaning of a sentence as its potential to update a context. In
Dynamic_semantics
In computer science, Hennessy–Milner logic (HML) is a dynamic logic used to specify properties of a labeled transition system (LTS), a structure similar
Hennessy–Milner_logic
Linguistic modality expressing how the world should be
(wishes, desires, etc.; boulomaic logic would apply): "If only I were rich!" A related type of modality is dynamic modality, which indicates a subject's internal
Deontic_modality
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
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
Phenomenon in natural language
Q)} This symbolic logic formula above is not valid in classical modal logic: Adding this principle as an axiom to standard modal logics would allow one
Free_choice_inference
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
American computer scientist
at the intersection of logic and complexity. He is one of the fathers of dynamic logic and developed the version of the modal μ-calculus most used today
Dexter_Kozen
Symbol connecting formulas in logic
Boolean logic Boolean-valued function Catuṣkoṭi Dialetheism Four-valued logic List of Boolean algebra topics Logical conjunction Logical constant Modal operator
Logical_connective
Formal semantic phenomenon
couched in variants of dynamic semantics such as DRT and SDRT. Linguistic modality Anaphora (linguistics) Conditional sentence Modal logic Discourse representation
Modal_subordination
Canadian philosopher (1936–2023)
and in 2010 he gave the René Descartes Lectures at the Tilburg Center for Logic and Philosophy of Science (TiLPS). Hacking also gave the Howison lectures
Ian_Hacking
Principle of classical logic
In propositional logic, import-export is a name given to the propositional form of Exportation: ( P → ( Q → R ) ) ↔ ( ( P ∧ Q ) → R ) {\displaystyle (P\rightarrow
Import–export_(logic)
Israeli logician (born 1945)
Gabbay, Agi Kurucz, Frank Wolter, Michael Zakharyaschev: Many-dimensional modal logics: theory and applications. North-Holland, 2003. Dov M. Gabbay, Amir Pnueli
Dov_Gabbay
Model of logic based on matrix algebra
Vector logic is an algebraic model of elementary logic based on matrix algebra. Vector logic assumes that the truth values map on vectors, and that the
Vector_logic
Formal statement in logic
of modal logic. It is logically equivalent to the material conditional of classical logic, combined with the necessity operator from modal logic. For
Strict_conditional
Type of verb, such as "might", that is used to indicate modality
certainty) deontic modality, concerned with possibility and necessity in terms of freedom to act (including permission and duty) dynamic modality, which may be
Modal_verb
Methods in artificial intelligence research
logic, to handle time; epistemic logic, to reason about agent knowledge; modal logic, to handle possibility and necessity; and probabilistic logics to
Symbolic artificial intelligence
Symbolic_artificial_intelligence
American scientist (1839–1914)
having wavered earlier as to just how positively real the modalities are. In his 1897 "The Logic of Relatives" he wrote: I formerly defined the possible
Charles_Sanders_Peirce
Topics referred to by the same term
which replaces quantifiers with the epsilon operator Modal μ-calculus, a common temporal logic used by formal verification methods such as model checking
Calculus_(disambiguation)
Dutch professor, philosopher and logician
of modal logic. This research has resulted in Van Benthem's theorem, which states that propositional modal logic is the fragment of first-order logic that
Johan_van_Benthem_(logician)
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
declarative semantics. The important features of the logic include hypothetical and committed updates, dynamic constraints on transaction execution, non-determinism
Transaction_logic
implication operations of the former to the latter. Unlike dynamic logic and other modal logics of programs, for which programs and propositions form two
Action_algebra
and non-normal) modal logic, hybrid logic, first-order modal logic, paraconsistent logic, linear logic, relevance logic, connexive logic, belief revision
Dialogical_logic
Formal study of linguistic meaning
intensionality, modality, negation, plural expressions, and the influence of contextual factors. Formal semantics is relevant to various fields. In logic and computer
Formal semantics (natural language)
Formal_semantics_(natural_language)
Precisely specified semantic version of a statement
In logic, the logical form of a statement is a precisely specified semantic version of that statement in a formal system. Informally, the logical form
Logical_form
Conditionals that discuss what would have been if things were otherwise
analysis treats natural language counterfactuals as being equivalent to the modal logic formula ◻ ( P → Q ) {\displaystyle \Box (P\rightarrow Q)} . In this formula
Counterfactual_conditional
Sentence that resists simple formalization
Hindi, and analysis of complex and modal versions of donkey pronouns in English. The Handbook of Philosophical Logic Discourse Representation Theory Introduction
Donkey_sentence
Finnish and American philosopher and logician (1929–2015)
Introduction to the Logic of the Two Notions ISBN 1-904987-08-7 1969. Models for Modalities: Selected Essays ISBN 978-90-277-0598-3 1973 Logic, Language-Games
Jaakko_Hintikka
New Zealand philosopher and logician (1918–1994)
philosopher and logician whose principal scholarly works were concerned with modal logic and medieval philosophy. Hughes was born on 8 June 1918 in Waterford
George_Edward_Hughes
Formal verification tool
contain modalities is possible. There is also a dual modality ⟨ α ⟩ {\displaystyle \langle \alpha \rangle } which includes termination. This dynamic logic can
KeY
Branch of medieval logic
medieval logic that was probably aimed at giving accounts of issues similar to modern accounts of reference, plurality, tense, and modality, within an
Supposition_theory
American philosopher, logician, and computer scientist (born 1939)
Professorship. Thomason is known for his work on modal and tense logic, the semantics of natural language, deontic logic, and the logical foundations of knowledge
Richmond_Thomason
Scottish mathematician and novelist (1831–1909)
of Logic. Elsevier, vol. 4. Discusses MacColl's contributions to philosophy of language and logic including modal logic, logic of fictions and modal logic
Hugh_MacColl
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)
Linguistic theory
The language of representation in Dynamic Syntax consists of binary trees. These trees are underpinned by the Logic Of Finite Trees (LOFT, Blackburn &
Dynamic_syntax
Standard of Object Management Group
alethic modality or deontic modality and require elements of modal logic as formalization. SBVR Structural Business Rules use two alethic modal operators:
Semantics of Business Vocabulary and Business Rules
Semantics_of_Business_Vocabulary_and_Business_Rules
boolean formulas First-order logic of equality Provability in intuitionistic propositional logic Satisfaction in modal logic S4 First-order theory of the
List of PSPACE-complete problems
List_of_PSPACE-complete_problems
are modal or categorial. The immediate interpretant is a quality of impression which a sign is fitted to produce, a special potentiality. The dynamic interpretant
Semiotic theory of Charles Sanders Peirce
Semiotic_theory_of_Charles_Sanders_Peirce
German-American philosopher (1891–1970)
semantics (Carnap 1942, 1943, 1956), modal logic, and on the philosophical foundations of probability and inductive logic (Carnap 1950, 1952). After a stint
Rudolf_Carnap
Computer science professor
with recursive predicates, rewriting logic, Hoare logic, temporal logics, dynamic logic, and the modal μ-calculus. Roșu's Ph.D. thesis proposed circular
Grigore_Roșu
American philosopher and logician (1908–2000)
in logic was not logic for Quine. Formal systems involving intensional notions, especially modality. Quine was especially hostile to modal logic with
Willard_Van_Orman_Quine
Entities that are said to be either true or false
of Logic. Prentice Hall. ISBN 0-13-663625-X. QUINE, W.V. (1970). Philosophy of Logic. Prentice Hall. ISBN 0-13-663625-X. See also First-order logic#Semantics
Truth-bearer
Academic fields of study or professions
Mathematical logic Set theory Proof theory Model theory Recursion theory Modal logic Intuitionistic logic Philosophical logic Logical reasoning Modal logic Deontic
Outline of academic disciplines
Outline_of_academic_disciplines
Russian-American researcher
semantics for modal logic that also served as a formalization of the Brouwer–Heyting–Kolmogorov provability semantics for intuitionistic logic (1995). He
Sergei_N._Artemov
Linear temporal logic; a modal temporal logic with modalities referring to time. MCL: Model Checking Language; Alternation-Free Modal μ-calculus extended
List_of_model_checking_tools
Area of physical and philosophical debate
inconsistencies of classical Boolean logic with the facts related to measurement and observation in quantum mechanics. Modal interpretations of quantum mechanics
Interpretations of quantum mechanics
Interpretations_of_quantum_mechanics
German philosopher, logician, and mathematician (1848–1925)
father of analytic philosophy, concentrating on the philosophy of language, logic, and mathematics. Though he was largely ignored during his lifetime, Giuseppe
Gottlob_Frege
American philosopher (born 1940)
1968, pp. 98–112. "Modality and Reference" (with R. H. Thomason). Noûs 2 (1968): 359–372. "Abstraction in First-Order Modal Logic" (with R. H. Thomason)
Robert_Stalnaker
Book on mathematical logic
and equational forms), modal logic, and dynamic logic. It is organized into seven chapters. The first concerns second-order logic in its standard form,
Extensions of First Order Logic
Extensions_of_First_Order_Logic
Computer scientist at Carnegie Mellon University
the event calculus, a logic-based formalism for reasoning about events and their effects over time. Their work introduced modal variants of the event
Iliano_Cervesato
Type of linguistic modality
related to modality. Some languages mark evidentiality separately from epistemic modality. Alethic modality Deontic modality Epistemic logic Epistemology
Epistemic_modality
Philosophical tradition in Muslim culture
responsible for the introduction of hypothetical syllogism, temporal modal logic and inductive logic. Other important developments in early Islamic philosophy include
Islamic_philosophy
Russian mathematician (1939–2014)
Intuitionistic Logic" (University Series in Mathematics). Published by Kluwer Academic Publisher, 2001. Mints, G. (1992) "A Short Introduction to Modal Logic". Published
Grigori_Mints
Theoretical framework
world objects and events. It is a graphical representation of modal logic in which modal operators are used to distinguish statement about concepts from
Conceptual_model
Approach to semantics in analytic philosophy
Dimensional Semantics by David Chalmers The Two Dimensional Argument against Materialism by David Chalmers Two Dimensional Modal Logic by Gary Hardegree
Two-dimensionalism
1921 philosophical work by Ludwig Wittgenstein
Picture Theory of Language. "The Tractatus's notion of substance is the modal analogue of Immanuel Kant's temporal notion. Whereas for Kant, substance
Tractatus Logico-Philosophicus
Tractatus_Logico-Philosophicus
American philosopher (1855–1916)
Alfred Kempe. Students who learned logic at Royce's feet include Clarence Irving Lewis, who went on to pioneer modal logic, Edward Vermilye Huntington, the
Josiah_Royce
Art of persuasion
opinions or arguments. Since the time of Aristotle, logic has changed. For example, modal logic has undergone a major development that also modifies
Rhetoric
Study of meaning in language
meanings can be created by arranging words. Formal semantics relies on logic and mathematics to provide precise frameworks of the relation between language
Semantics
British philosopher (1925–2011)
mathematical logic, he developed an intermediate logic, a logical system intermediate between classical logic and intuitionistic logic that had already
Michael_Dummett
Belgian academic
and compared different techniques to derive dynamic bending stiffness of the experimentally determined modal characteristics of a reinforced concrete beam
Magd_Abdel_Wahab
20th-century tradition of Western philosophy
larger misunderstandings of the metaphysics of modality, or of necessity and possibility. Modal logic was developed by pragmatist C. I. Lewis to deal
Analytic_philosophy
first-order logic Causes and effects causal calculus – How one process influences another Knowledge about knowledge Belief revision Modal logics paraconsistent
Outline of artificial intelligence
Outline_of_artificial_intelligence
Philosophical system of Giovanni Gentile
solution. The "logic of thinking thought," understood as an archetypal-ontological instance, is a philosophical and dialectical logic; the "logic of thought
Actual_idealism
Computer science field
Addison-Wesley. ISBN 0-321-22862-6. Bradfield, Julian; Stirling, Colin (2001). "Modal Logics and mu-Calculi: An Introduction". Handbook of Process Algebra. Elsevier
Model_checking
Type of determiner that indicates quantity
formal analysis. Term logic treated All, Some and No in the 4th century BC, in an account also touching on the alethic modalities. Starting with Gottlob
Quantifier_(linguistics)
List of concepts in artificial intelligence
Philadelphia, 1995. Hughes, G. E., & Cresswell, M. J., A New Introduction to Modal Logic (London: Routledge, 1996), p. 161. Feigenbaum, Edward (1988). The Rise
Glossary of artificial intelligence
Glossary_of_artificial_intelligence
British philosopher, mathematician and economist (1903–1930)
logic. Alonzo Church would go on to show that the general case of the decision problem for first-order logic is unsolvable and that first-order logic
Frank_P._Ramsey
Branch of philosophy
artificial intelligence, logic of information, cybernetics, social theory, ethics and the study of language and information. The logic of information, also
Philosophy_of_information
German philosopher
of research include logic (theories of truth and modality, paradox, conditionals, nonmonotonic reasoning, dynamic doxastic logic), epistemology (belief
Hannes_Leitgeb
Intelligence in machines
calculus, modal logics: Russell & Norvig (2021, §10.4), Poole, Mackworth & Goebel (1998, pp. 275–277) Default reasoning, Frame problem, default logic, non-monotonic
Artificial_intelligence
Bulgarian scientist, statesman and diplomat
on mathematical logic and computer sciences. The Combinatory Dynamic Logic (Modal Logic with Nominals) was developed in Bulgaria by Passy and Professors
Solomon_Passy
British linguist (1922–2019)
Modality and Evidential Modality. Event Modality in turn can be of two types: Deontic Modality and Dynamic Modality. In Deontic Modality, the conditioning factors
Frank_R._Palmer
Adverb connecting two independent clauses
Ditransitive Dynamic Exceptional case-marking Frequentative Germanic strong Germanic weak Impersonal Inchoative Intransitive Labile Lexical Light Modal Negative
Conjunctive_adverb
travel, tourism, insurance
DYNAMIC LOGIC-MODAL-LOGIC
DYNAMIC LOGIC-MODAL-LOGIC
Boy/Male
Gujarati, Hindu, Indian, Kannada, Marathi
Enjoyment
Girl/Female
Arabic, Muslim, Pashtun
Logic; Reason
Girl/Female
Muslim
Dynamic, Moving
Girl/Female
British, English
15th Century
Boy/Male
Indian
New Generation
Girl/Female
Christian, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Sindhi, Tamil, Telugu
Bird; Amazing
Boy/Male
Hindu
Dynamic
Girl/Female
Hindu
Bird
Boy/Male
Hindu
Dynamic hero
Boy/Male
Tamil
Dynamic
Boy/Male
Hindu
Attractive
Girl/Female
Arabic, Muslim
Dynamic; Moving
Boy/Male
Tamil
Ruthwik Sai | à®°à¯à®¤à¯à®µà¯€à®•à¯à®¸à®¾à®ˆÂ     Â
Dynamic hero
Ruthwik Sai | à®°à¯à®¤à¯à®µà¯€à®•à¯à®¸à®¾à®ˆÂ     Â
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu
Attractive; Sweet; Lovable; Intelligent; Smart; Handsome
Boy/Male
Indian, Sanskrit
Bird; Lion
Boy/Male
Indian, Marathi
Dynamic Personality
Boy/Male
Arabic, Muslim
Dynamic; Bright
Girl/Female
Indian
Beautiful
Boy/Male
Hindu, Indian, Sanskrit
Intelligent; Dynamic; Ruler
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Pleasing
DYNAMIC LOGIC-MODAL-LOGIC
DYNAMIC LOGIC-MODAL-LOGIC
DYNAMIC LOGIC-MODAL-LOGIC
DYNAMIC LOGIC-MODAL-LOGIC
DYNAMIC LOGIC-MODAL-LOGIC
DYNAMIC LOGIC-MODAL-LOGIC
DYNAMIC LOGIC-MODAL-LOGIC
travel, tourism, insurance