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Whether a decision problem has an effective method to derive the answer
S2CID 798307. Retrieved 5 August 2014. Mathoverflow.net/Decidability-of-chess-on-an-infinite-board Decidability-of-chess-on-an-infinite-board Brumleve, Dan; Hamkins
Decidability_(logic)
Topics referred to by the same term
Look up decidability in Wiktionary, the free dictionary. The word decidable may refer to: Decidable language Decidability (logic) for the equivalent in
Decidability
System of resource-aware logic
EXPSPACE-hard, although decidability itself has had the status of a longstanding open problem. In 2015, a proof of decidability was published in the journal
Linear_logic
Overview of and topical guide to logic
the metatheory of logic. Completeness (logic) Syntax (logic) Consistency Decidability (logic) Deductive system Interpretation (logic) Cantor's theorem
Outline_of_logic
Set with algorithmic membership test
total computable function, or the empty set. Computably enumerable Decidability (logic) Recursively enumerable language Recursive language Recursion That
Computable_set
Yes/no problem in computer science
Computational problem Counting problem (complexity) Decidability (logic) – for the problem of deciding whether a formula is a consequence of a logical theory
Decision_problem
Problem-solving procedures with certain characteristics
function that is effectively calculable is recursively computable. Decidability (logic) Decision problem Effective results in number theory Function problem
Effective_method
cardinal Unfoldable cardinal Entscheidungsproblem Decision problem Decidability (logic) Church–Turing thesis Computable function Algorithm Recursion Primitive
List of mathematical logic topics
List_of_mathematical_logic_topics
Formal systems of logic that significantly differ from standard logical systems
connectives in various logics; decidability and complexity aspects are generally omitted though. Video of Graham Priest & Maureen Eckert on Deviant Logic
Non-classical_logic
Study of correct reasoning
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical
Logic
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
Yes-or-no question that cannot ever be solved by a computer
whose learnability in EMX is undecidable in standard set theory. Decidability (logic) Entscheidungsproblem Proof of impossibility Unknowability Wicked
Undecidable_problem
Theory of logic to account for observations from quantum theory
In the mathematical study of logic and the physical analysis of quantum foundations, quantum logic is a set of rules for manipulation of propositions
Quantum_logic
Subfield of mathematics
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory
Mathematical_logic
System for reasoning about vagueness
Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept
Fuzzy_logic
Study of the properties of logical systems
Ackermann 1928) Major decidability results include: Decidability of truth-functional propositional logic (Emil Post 1920) Decidability of first-order monadic
Metalogic
Limitative results in mathematical logic
theories of paraconsistent logic. Philosophy portal Mathematics portal Chaitin's incompleteness theorem Decidability (logic) Gödel, Escher, Bach Gödel
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Formal language in mathematics and computer science
algorithms. The concept of decidability may be extended to other models of computation. For example, one may speak of languages decidable on a non-deterministic
Recursive_language
two-variable logic, such as satisfiability and finite satisfiability, are decidable. This result generalizes results about the decidability of fragments
Two-variable_logic
Branch of logic
Propositional logic is a branch of classical logic. It is also called statement logic, sentential calculus, propositional calculus, sentential logic, or sometimes
Propositional_logic
Existence of values making formula true
In mathematical logic, a formula is satisfiable if it is true under some assignment of values to its variables. For example, the formula x + 3 = y {\displaystyle
Satisfiability
Resource-sensitive logic allowing each assumption to be used at most once
comprehension axiom. Likewise, the logic formed the basis of a decidable sub-theory of predicate logic, called 'Direct logic' (Ketonen & Wehrauch, 1984; Ketonen
Affine_logic
Approach to logic
In logic and formal semantics, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to
Term_logic
Fragment of first-order logic
In logic, the monadic predicate calculus (also called monadic first-order logic) is the fragment of first-order logic (also called predicate calculus)
Monadic_predicate_calculus
System including an indeterminate value
three-valued logic (also trinary logic, trivalent, ternary, or trilean, sometimes abbreviated 3VL) is any of several many-valued logic systems in which
Three-valued_logic
{\displaystyle \vdash _{L}} and R. Notice that decidability of admissible rules of a decidable logic is equivalent to the existence of recursive (or
Admissible_rule
Method of deriving conclusions
of deriving conclusions from premises. They are integral parts of formal logic, serving as the logical structure of valid arguments. If an argument with
Rule_of_inference
logic, various sublanguages of set theory are decidable. They are referred to as syllogistics. Together with the operations of set algebra, decidable
Decidable sublanguages of set theory
Decidable_sublanguages_of_set_theory
In logic, a statement which is always true
In mathematical logic, a tautology (from Ancient Greek: ταυτολογία) is a formula that is true regardless of the interpretation of its component terms
Tautology_(logic)
Decidable theory of equality
first-order logic, all valid formulas are provable using axioms of first-order logic and the equality axioms (see also equational logic). Decidability can be
Theory_of_pure_equality
Family of formal knowledge representation
expressive than first-order logic. In contrast to the latter, the core reasoning problems for DLs are (usually) decidable, and efficient decision procedures
Description_logic
robust decidability of guarded logic could be generalized with a tree model property. The tree model can also be a strong indication that guarded logic extends
Guarded_logic
the most expressive natural decidable theories known, with many decidable theories interpretable in S2S. Its decidability was proved by Rabin in 1969
S2S_(mathematics)
Alfred Tarski: Life and Logic (Cambridge: Cambridge University Press, 2008). Macintyre, A.J.; Wilkie, A.J. (1995), "On the decidability of the real exponential
Decidability of first-order theories of the real numbers
Decidability_of_first-order_theories_of_the_real_numbers
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
Shapirovsky, "PSPACE-decidability of Japaridze's polymodal logic". Advances in Modal Logic 7 (2008), pp. 289–304. G. Japaridze, "The polymodal logic of provability"
Japaridze's_polymodal_logic
International specialist organization
Association for Symbolic Logic (ASL) is an international organization of specialists in mathematical logic and philosophical logic. The ASL was founded in
Association for Symbolic Logic
Association_for_Symbolic_Logic
such as completeness, decidability, consistency and definability. According to Anita Feferman, Tarski "changed the face of logic in the twentieth century"
History_of_logic
School of thought in philosophy of mathematics
is an extension of logic, some or all of mathematics is reducible to logic, or some or all of mathematics may be modelled in logic. Bertrand Russell and
Logicism
Set of sentences in a formal language
+, ×, 0, 1, =) was shown by Tarski to be decidable; it is the theory of real closed fields (see Decidability of first-order theories of the real numbers
Theory_(mathematical_logic)
Mathematical structure
runs on an infinite tree was first used by Michael Rabin for proving decidability of S2S, the monadic second-order theory with two successors. It has been
Infinite-tree_automaton
Study of the scope and nature of logic
Philosophy of logic is the branch of philosophy that studies the scope and nature of logic. It investigates the philosophical problems raised by logic, such as
Philosophy_of_logic
for the Decidability Problem on Finite Classes". The theorem is related to Church's result that the set of valid formulas in first-order logic is not decidable
Trakhtenbrot's_theorem
Term in mathematical logic
to be undecidable from T. (This concept is unrelated to the idea of "decidability" as in a decision problem.) A theory T is independent if no axiom in
Independence (mathematical logic)
Independence_(mathematical_logic)
Formal system of logic
In mathematics and logic, a higher-order logic (abbreviated HOL) is a form of logic that is distinguished from first-order logic by additional quantifiers
Higher-order_logic
Impossible task in computing
be viewed as asking for an algorithm to decide whether a given statement is provable using the rules of logic. In 1936, Alonzo Church and Alan Turing
Entscheidungsproblem
Form of logic that allows quantification over predicates
In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic
Second-order_logic
Logical formalism using combinators instead of variables
Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell
Combinatory_logic
Class of formal logics
Classical logic (or standard logic) or Frege–Russell logic is the intensively studied and most widely used class of deductive logic. Classical logic has had
Classical_logic
Process of drawing correct inferences
would find convincing. The main discipline studying logical reasoning is logic. Distinct types of logical reasoning differ from each other concerning the
Logical_reasoning
Formal semantics for non-classical logic systems
notion is the decidability question: it follows from Post's theorem that a recursively axiomatized modal logic L which has FMP is decidable, provided it
Kripke_semantics
Symbol representing a property or relation in logic
In logic, a predicate is a non-logical symbol that represents a property or a relation, though, formally, does not need to represent anything at all.
Predicate_(logic)
Form of second-order logic
In mathematical logic, monadic second-order logic (MSO) is the fragment of second-order logic where the second-order quantification is limited to quantification
Monadic_second-order_logic
Mathematical model for deduction or proof systems
arithmetic. Early logic systems includes Indian logic of Pāṇini, syllogistic logic of Aristotle, propositional logic of Stoicism, and Chinese logic of Gongsun
Formal_system
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
System for representing and reasoning about time
In logic, a temporal logic is any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time (for example
Temporal_logic
Algebraic manipulation of "true" and "false"
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the
Boolean_algebra
Type of non-monotonic logic
Default logic is a non-monotonic logic proposed by Raymond Reiter to formalize reasoning with default assumptions. Default logic can express facts like
Default_logic
Computer science and logic conference
Parosh A. Abdulla, Karlis Cerans, Bengt Jonsson, Yih-Kuen Tsay, "General decidability theorems for infinite-state systems" Iliano Cervesato, Frank Pfenning
Symposium on Logic in Computer Science
Symposium_on_Logic_in_Computer_Science
Symbolic logic system
Minimal logic, or minimal calculus, is a symbolic logic system originally developed by Ingebrigt Johansson under the name "Minimalkalkül". It is a paraconsistent
Minimal_logic
Fragment of metric temporal logic
In model checking, the Metric Interval Temporal Logic (MITL) is a fragment of Metric Temporal Logic (MTL). This fragment is often preferred to MTL because
Metric interval temporal logic
Metric_interval_temporal_logic
Simplification technique in mathematical logic
decidability and completeness. A common technique was to show first that a theory admits elimination of quantifiers and thereafter prove decidability
Quantifier_elimination
the Löwenheim-Skolem-Tarski theorem to problems of completeness and decidability", Indagationes Mathematicae, 16: 467–472, doi:10.1016/S1385-7258(54)50058-2
Łoś–Vaught_test
of mathematical logic; see also history of logic. 1847 – George Boole proposes symbolic logic in The Mathematical Analysis of Logic, defining what is
Timeline of mathematical logic
Timeline_of_mathematical_logic
Mathematical use of "for all" and "there exists"
In mathematical logic, quantifiers are formal counterparts of natural-language adjectives like all, some, most, few, etc. which indicate the number of
Quantifier_(logic)
Language to express rules and logic with semantic web
full power of OWL DL, but at the price of decidability and practical implementations. However, decidability can be regained by restricting the form of
Semantic_Web_Rule_Language
South African philosopher
Modern Logic and its Applications. Edited by Evandro Agazzi, Mind, New Series, Vol. 92, No. 366 (Apr. 1983), pp. 286–288 Deducibility and Decidability, Routledge:
R._R._Rockingham_Gill
Logic with discrete truth values
finite-valued logic can be applied in Boolean-valued modeling, description logics, and defuzzification of fuzzy logic. A finite-valued logic is decidable (sure
Finite-valued_logic
American esports organization
Counter Logic Gaming (CLG) was an American esports organization headquartered in Los Angeles, California. It was founded in April 2010 by George "HotshotGG"
Counter_Logic_Gaming
Logical problem studied in computer science
are often implemented directly in SMT solvers; see, for instance, the decidability of Presburger arithmetic. SMT can be thought of as a constraint satisfaction
Satisfiability modulo theories
Satisfiability_modulo_theories
Argument whose conclusion must be true if its premises are
In logic, specifically in deductive reasoning, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true
Validity_(logic)
Russian-Israeli mathematician
delay". Algebra and Logic (in Russian). 3 (4): 33–48. Boris Trakhtenbrot (1950). "The Impossibility of an Algorithm for the Decidability Problem on Finite
Boris_Trakhtenbrot
Russian mathematician (1909–1967)
school in model theory and decidability of elementary theories. During the early 1960s, Maltsev worked on problems of decidability of elementary theories
Anatoly_Maltsev
Academic journal
on non-classical logic, in particular formal aspects (completeness, decidability, complexity), applications to artificial Intelligence and cognitive science
Journal of Applied Non-Classical Logics
Journal_of_Applied_Non-Classical_Logics
Look up Appendix:Glossary of logic in Wiktionary, the free dictionary. This is a glossary of logic. Logic is the study of the principles of valid reasoning
Glossary_of_logic
Inference rule in logic, proof theory, and automated theorem proving
theorem-proving technique for sentences in propositional logic and first-order logic. For propositional logic, systematically applying the resolution rule acts
Resolution_(logic)
Mathematical logic
non-negative integers with the multiset sum operation, whose decidability reduces to the decidability of the theory of elements. In more detail, according to
Skolem_arithmetic
Theoretical perspective explaining human decision-making
rightful, expected, and legitimate. In other words, the logic of appropriateness assumes that actors decide on the basis of what social norms deem right rather
Logic_of_appropriateness
Syntactically correct logical formula
In mathematical logic, propositional logic, and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence
Well-formed_formula
Mathematical logician and philosopher
Bertrand Russell, Alfred North Whitehead, and David Hilbert were using logic and set theory to investigate the foundations of mathematics), building
Kurt_Gödel
Logic principle
general equivalence relation (which generally has poor constructibility or decidability properties). There are various extensionality principles in mathematics
Extensionality
Puzzle in Douglas Hofstadter's book "Gödel, Escher, Bach"
three rules.) The MIU system illustrates several important concepts in logic by means of analogy. It can be interpreted as an analogy for a formal system
MU_puzzle
Basic framework of mathematics
either provable or refutable; that is, its negation is provable), and decidability (there is a decision procedure to test every statement). By near the
Foundations_of_mathematics
Assignment of meaning to the symbols of a formal language
formal semantics. The most commonly studied formal logics are propositional logic, predicate logic and their modal analogs, and for these there are standard
Interpretation_(logic)
Characteristic of some logical systems
In mathematical logic and metalogic, a formal system is called complete with respect to a particular property if every formula having the property can
Completeness_(logic)
British mathematician and logician
extensions of Ax's work to this setting (including model-companions and decidability). Independently Ehud Hrushovski has proved model-theoretic results on
Angus_Macintyre
Mathematical logic concept
In logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent
Contraposition
Concept in first-order logic
and Frank P. Ramsey, is a fragment of first-order logic formulas where satisfiability is decidable. It is the set of sentences that, when written in prenex
Bernays–Schönfinkel_class
Translation of a text into a logical system
Logic translation is the process of representing a text in the formal language of a logical system. If the original text is formulated in ordinary language
Logic_translation
Property of logical theories
Venema Modal Logic. Cambridge University Press, 2001. Alasdair Urquhart. Decidability and the Finite Model Property. Journal of Philosophical Logic, 10 (1981)
Finite_model_property
Study of general and fundamental questions
self-cultivation. Major branches of philosophy are epistemology, ethics, logic, and metaphysics. Epistemology studies what knowledge is and how to acquire
Philosophy
Logical formulation of recursion
In mathematical logic, fixed-point logics are extensions of classical predicate logic that have been introduced to express recursion. Their development
Fixed-point_logic
In mathematical logic, zero-one law is a property of a logic saying that any property is either almost surely true or almost surely false. Zero-one law
Zero–one_law_(logic)
Applications of logic under uncertainty
Probabilistic logic (also probability logic and probabilistic reasoning) involves the use of probability and logic to deal with uncertain situations. Probabilistic
Probabilistic_logic
American philosopher and logician (1940–2022)
notion is the decidability question: it follows from Post's theorem that a recursively axiomatized modal logic L which has FMP is decidable, provided it
Saul_Kripke
Logical connective AND
In logic, mathematics and linguistics, and ( ∧ {\displaystyle \wedge } ) is the truth-functional operator of conjunction or logical conjunction. The logical
Logical_conjunction
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
Swiss mathematician
"Algorithmic aspects of branched coverings II/V: sphere bisets and decidability of Thurston equivalence". Inventiones Mathematicae. 223 (3): 895–994
Laurent_Bartholdi
Subfield of automated reasoning and mathematical logic
automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated
Automated_theorem_proving
Method of depicting causal relationships
A logic model is a hypothesized description of the causal chains in certain plans, used to show social programs and the results desired from them. They
Logic_model
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