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Study of computable functions and Turing degrees
Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated
Computability_theory
Framework for studying interactive computational tasks through logic
Computability logic (CoL) is a research program and mathematical framework for redeveloping logic as a systematic formal theory of computability, as opposed
Computability_logic
Logics for computability are formulations of logic that capture some aspect of computability as a basic notion. This usually involves a mix of special
Logics_for_computability
Ability to solve a problem by an effective procedure
Computability is the ability to solve a problem by an effective procedure. It is a key topic of the field of computability theory within mathematical logic
Computability
Overview of and topical guide to logic
Classical logic Computability logic Deontic logic Dependence logic Description logic Deviant logic Doxastic logic Epistemic logic First-order logic Formal
Outline_of_logic
Subfield of mathematics
(also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their
Mathematical_logic
Various systems of symbolic logic
Yurii Medvedev’s logic of finite problems, or Giorgi Japaridze’s computability logic. Yet such semantics persistently induce logics properly stronger
Intuitionistic_logic
1970s automated theorem prover
Logic for Computable Functions (LCF) is an interactive automated theorem prover developed at Stanford and Edinburgh by Robin Milner and collaborators in
Logic for Computable Functions
Logic_for_Computable_Functions
Formal systems of logic that significantly differ from standard logical systems
not use classical logic in the reasoning process. There are many kinds of non-classical logic, which include: Computability logic is a semantically constructed
Non-classical_logic
Japaridze is best known for his invention of computability logic, cirquent calculus, and Japaridze's polymodal logic. During 1985–1988 Japaridze elaborated
Giorgi_Japaridze
of mathematical logic topics. For traditional syllogistic logic, see the list of topics in logic. See also the list of computability and complexity topics
List of mathematical logic topics
List_of_mathematical_logic_topics
hard- and easy-play machines elaborated within the framework of computability logic, Dina Q. Goldin's Persistent Turing Machines (PTMs), and Yuri Gurevich's
Interactive_computation
Approach to formal semantics
atoms. Computability logic Dependence logic Ehrenfeucht–Fraïssé game Independence-friendly logic Interactive computation Intuitionistic logic Ludics J
Game_semantics
Thesis on the nature of computability
In computability theory, the Church–Turing thesis is a thesis about the nature of computable functions. It states that a function on the natural numbers
Church–Turing_thesis
Mathematical function that can be computed by a program
Computable functions are the basic objects of study in computability theory. Informally, a function is computable if there is an algorithm that computes
Computable_function
Whether a decision problem has an effective method to derive the answer
Modal logic, Oxford Logic Guides, vol. 35, Oxford University Press, ISBN 978-0-19-853779-3, MR 1464942 Davis, Martin (2013) [1958], Computability and Unsolvability
Decidability_(logic)
Academic subfield of computer science
Walter A. Carnielli (2000). Computability: Computable Functions, Logic, and the Foundations of Mathematics, with Computability: A Timeline (2nd ed.). Wadsworth/Thomson
Theory_of_computation
System of resource-aware logic
logic, whose formal development is somewhat standard (see first-order logic and higher-order logic). Philosophy portal Chu spaces Computability logic
Linear_logic
Set with algorithmic membership test
In computability theory, a set of natural numbers is computable (or decidable or recursive) if there is an algorithm that computes the membership of every
Computable_set
proof theory capable of "taming" various nontrivial fragments of his computability logic, which had otherwise resisted all axiomatization attempts within
Cirquent_calculus
Concept in computer science
this property that is referred to as charge recovery logic, adiabatic circuits, or adiabatic computing (see adiabatic process). Although in practice no nonstationary
Reversible_computing
Deductive system for computable functions by Dana Scott
Logic of Computable Functions (LCF) is a deductive system for computable functions proposed by Dana Scott in 1969 in a memorandum unpublished until 1993
Logic_of_Computable_Functions
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
Computer that uses photons or light waves
Ramesh; Senthilnathan, Krishnamoorthy. "All-Optical Logic Gates Show Promise for Optical Computing". Photonics. Photonics Spectra. Retrieved 8 April 2018
Optical_computing
Value indicating the relation of a proposition to truth
which in classical logic has only two possible values (true or false). Truth values are used in computing as well as various types of logic. In some programming
Truth_value
1989 monograph by Marian Pour-El and J. Ian Richards
Computability in Analysis and Physics is a monograph on computable analysis by Marian Pour-El and J. Ian Richards. It was published by Springer-Verlag
Computability in Analysis and Physics
Computability_in_Analysis_and_Physics
Computation model defining an abstract machine
each producing output data from given input data. Computability theory, which studies computability of functions from inputs to outputs, and for which
Turing_machine
Book by Raymond Smullyan
is a branch of symbolic logic having the expressive power of set theory, and with deep connections to questions of computability and provability. Smullyan's
To_Mock_a_Mockingbird
Device performing a Boolean function
A logic gate is a device that performs a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output
Logic_gate
Problem in computer science
In computability theory, the halting problem is the decision problem of, given an arbitrary computer program and an input, determining whether said program
Halting_problem
Logic circuitry that requires low temperatures to achieve superconductivity
Superconducting quantum computing is the application of superconducting logics in quantum computing. Superconducting digital logic circuits use single flux
Superconducting_computing
Study of correct reasoning
theory, and computability theory. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic. However, it
Logic
Problem-solving procedures with certain characteristics
In metalogic, mathematical logic, and computability theory, an effective method or effective procedure is a finite-time, deterministic procedure for solving
Effective_method
American company
and networking in data centers, mobile networks and client computing. In April 2007, LSI Logic merged with Agere Systems and rebranded the firm as LSI Corporation
LSI_Logic
Molecule that performs a logical operation
fields such as molecular electronics, biosensing, DNA computing, nanorobotics, and cell imaging. For logic gates with a single input, there are four possible
Molecular_logic_gate
Tarski "changed the face of logic in the twentieth century". Alonzo Church and Alan Turing proposed formal models of computability, giving independent negative
History_of_logic
In computability theory, a maximal set is a coinfinite computably enumerable subset A of the natural numbers such that for every further computably enumerable
Maximal set (computability theory)
Maximal_set_(computability_theory)
presents "Turing's Thesis", asserting the identity of computability in general with computability by Turing machines, as an equivalent form of Church's
Timeline of mathematical logic
Timeline_of_mathematical_logic
Realizability Theory: Ties constructive logic to computability — proofs correspond to algorithms. Topos Logic: Internal logics of topoi (generalized spaces) are
Constructive_logic
American mathematician (1928–2023)
computer scientist who contributed to the fields of computability theory and mathematical logic. His work on Hilbert's tenth problem led to the MRDP
Martin_Davis_(mathematician)
Logical formalism using combinators instead of variables
combinatory logic in the 1960s and 1970s. In computer science, combinatory logic is used as a simplified model of computation, used in computability theory
Combinatory_logic
Programmable digital computer used to control machinery
A programmable logic controller (PLC) or programmable controller is an industrial computer that has been ruggedized and adapted for the control of manufacturing
Programmable_logic_controller
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
Digital audio workstation
Notator Logic, or Logic, by German software developer C-Lab which later went by Emagic. Apple acquired Emagic in 2002 and rebranded Logic to Logic Pro, adding
Logic_Pro
Observation in computer circuit design
the organization of computing logic, specifically the relationship between the number of external signal connections to a logic block (i.e., the number
Rent's_rule
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)
Programming paradigm based on formal logic
learning Satisfiability Syntax and semantics of logic programming Tärnlund, S.Å. (1977). "Horn clause computability". BIT Numerical Mathematics. 17 (2): 215–226
Logic_programming
American mathematician
theory (particularly the idea of the set-theoretic multiverse), in computability theory, and in group theory. After earning a Bachelor of Science in
Joel_David_Hamkins
Study of mathematical analysis seen through computability theory
mathematics and computer science, computable analysis is the study of mathematical analysis from the perspective of computability theory. It is concerned with
Computable_analysis
1938 doctoral thesis by Alan Turing
Systems of Logic Based on Ordinals was the PhD dissertation of the mathematician Alan Turing. The thesis was completed at Princeton under Alonzo Church
Systems of Logic Based on Ordinals
Systems_of_Logic_Based_on_Ordinals
Mathematical logic concept
In computability theory, a set S of natural numbers is called computably enumerable (c.e.), recursively enumerable (r.e.), semidecidable, partially decidable
Computably_enumerable_set
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)
Impossible task in computing
and a discussion of, his proof. Soare, Robert I., "Computability and recursion", Bull. Symbolic Logic 2 (1996), no. 3, 284–321. Toulmin, Stephen, "Fall
Entscheidungsproblem
Programming language for industrial controllers
Ladder logic was originally a written method to document the design and construction of relay racks as used in manufacturing and process control. Each
Ladder_logic
Yes-or-no question that cannot ever be solved by a computer
In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct
Undecidable_problem
Typographic symbol
uses in mathematics, computing, and typography. It has many names, often related to particular meanings: Sheffer stroke (in logic), pipe, bar, or (literally
Vertical_bar
Array of logic gates that are reprogrammable
a subset of logic devices referred to as programmable logic devices (PLDs). They consist of a grid-connected array of programmable logic blocks that can
Field-programmable_gate_array
Academic discipline
logic that are particularly significant are computability theory (formerly called recursion theory), modal logic and category theory. The theory of computation
Logic_in_computer_science
In computability theory and mathematical logic the Tarski–Kuratowski algorithm is a non-deterministic algorithm that produces an upper bound for the complexity
Tarski–Kuratowski_algorithm
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
Computer that uses ternary logic
ternary computer, also called trinary computer, is one that uses ternary logic (i.e., base 3) instead of the more common binary system (i.e., base 2) in
Ternary_computer
Propositional calculus in which there are more than two truth values
Many-valued logic (also multi- or multiple-valued logic) is a propositional or predicate calculus in which there are more than two truth values. Traditionally
Many-valued_logic
Approach in philosophy of mathematics and logic
Anti-realism BHK interpretation Brouwer–Hilbert controversy Computability logic Conceptualism Constructive logic Constructivism (philosophy of mathematics) Curry–Howard
Intuitionism
This is a list of computability and complexity topics, by Wikipedia page. Computability theory is the part of the theory of computation that deals with
List of computability and complexity topics
List_of_computability_and_complexity_topics
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
American philosopher and mathematician
mathematician who worked in mathematical logic. In addition to his prolific technical work in proof theory, computability theory, and set theory, he was known
Solomon_Feferman
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
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
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)
Erasmus Mundus co-operative MSc program
artificial intelligence, formal specification and verification, logic and computability. This basic knowledge is then applied to areas like natural language
European Master Program in Computational Logic
European_Master_Program_in_Computational_Logic
Computer hardware technology that uses quantum mechanics
can be simulated by a Turing machine. Quantum computers provide no computability power over classical computers. Thus, quantum computers cannot solve
Quantum_computing
Type of formal logic
Paraconsistent logic is a type of non-classical logic that allows for the coexistence of contradictory statements without leading to a logical explosion
Paraconsistent_logic
Scientific organization
Connecting with Computability, Gent, Belgium (online). CiE 2022: Revolutions and Revelations in Computability, Swansea, Wales. CiE 2023: Unity of Logic and Computation
Computability_in_Europe
School of thought in philosophy of mathematics
logicism is a school of thought comprising one or more of the theses that—for some coherent meaning of 'logic'—mathematics is an extension of logic,
Logicism
Rules to verify computer program correctness
Hoare logic (also known as Floyd–Hoare logic or Hoare rules) is a formal system with a set of logical rules for reasoning rigorously about the correctness
Hoare_logic
German mathematician and logician
Steel. Cambridge : Cambridge University 2008. Logic and theory of algorithms : 4th Conference on Computability in Europe, CiE 2008, Athens, Greece, June 15
Benedikt_Löwe
Combinational digital circuit
In computing, an arithmetic logic unit (ALU) is a combinational digital circuit that performs arithmetic and bitwise operations on integer binary numbers
Arithmetic_logic_unit
Existence of values making formula true
Press). Boolos, George; Burgess, John; Jeffrey, Richard (2007). Computability and Logic (5th ed.). Cambridge University Press. Daniel Kroening; Ofer Strichman
Satisfiability
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
Overview of and topical guide to computer science
Automata theory – Different logical structures for solving problems. Computability theory – What is calculable with the current models of computers. Proofs
Outline_of_computer_science
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
In gate-based quantum computing, various sets of quantum logic gates are commonly used to express quantum operations. The following tables list several
List_of_quantum_logic_gates
Sequence of words formed by specific rules
In logic, mathematics, computer science, and linguistics, a formal language is a set of strings whose symbols are taken from a set called "alphabet".
Formal_language
Logic programming paradigm
Concurrent logic programming is a variant of logic programming designed for parallel computing in which programs are sets of guarded Horn clauses of the
Concurrent_logic_programming
Reprogrammable computer hardware technology
In computing, a logic block or configurable logic block (CLB) is a fundamental building block of field-programmable gate array (FPGA) technology.[citation
Logic_block
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)
Digital logic based on non-linear magnetic effects
Magnetic logic is digital logic made using the non-linear properties of wound ferrite cores. Magnetic logic represents 0 and 1 by magnetising cores clockwise
Magnetic_logic
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
1111/1467-8349.00076. Japaridze, G. (2003). "Introduction to computability logic". Annals of Pure and Applied Logic. 123 (1–3): 1–99. doi:10.1016/S0168-0072(03)00023-X
Dialogical_logic
reason about simplicial sets and cubical sets. Synthetic computability theory develops computability theory in constructive mathematics by postulating, among
Synthetic_mathematics
Basic circuit in quantum computing
In quantum computing and specifically the quantum circuit model of computation, a quantum logic gate (or simply quantum gate) is a basic quantum circuit
Quantum_logic_gate
Bulgarian mathematician
Doyen and pioneer of mathematical logic research in Bulgaria who developed a Bulgarian school in the theory of computability, namely the algebraic (or axiomatic)
Dimiter_Skordev
Mathematical-logic system
tb00919.x. Turing, Alan M. (December 1937). "Computability and λ-Definability". The Journal of Symbolic Logic. 2 (4): 153–163. doi:10.2307/2268280. JSTOR 2268280
Lambda_calculus
Concept in computability theory
Cenzer, Douglas (1999), "Π0 1 classes in computability theory", Handbook of computability theory, Stud. Logic Found. Math., vol. 140, Amsterdam: North-Holland
Computably_inseparable
Family of formal knowledge representation
Description logics (DL) are a family of formal knowledge representation languages. Many DLs are more expressive than propositional logic but less expressive
Description_logic
Mathematical model describing how an output of a function is computed given an input
In computer science, and more specifically in computability theory and computational complexity theory, a model of computation is a model that describes
Model_of_computation
computability theory, productive sets and creative sets are types of sets of natural numbers that have important applications in mathematical logic.
Creative_and_productive_sets
Description of non-logical symbols
In mathematical logic, a signature is a description of the non-logical symbols of a formal language. In universal algebra, a signature lists the operations
Signature_(logic)
Computer architecture that can be reprogrammed
configurable logic to act more like a coprocessor rather than a peripheral. This has brought reconfigurable computing into the high-performance computing sphere
Reconfigurable_computing
Programming paradigm
Probabilistic logic programming is a programming paradigm that combines logic programming with probabilities. Most approaches to probabilistic logic programming
Probabilistic logic programming
Probabilistic_logic_programming
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