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System of resource-aware logic
Linear logic is a substructural logic proposed by French logician Jean-Yves Girard as a refinement of classical and intuitionistic logic, joining the dualities
Linear_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
Programming paradigm based on formal logic
Logic programming is a programming, database, and knowledge representation paradigm based on formal logic. A logic program is a set of sentences in logical
Logic_programming
Family of type systems based on substructural logic
being used exactly once in the order it was introduced. Linear types correspond to linear logic and ensure that objects are used exactly once. This allows
Substructural_type_system
Resource-sensitive logic allowing each assumption to be used at most once
Affine logic is a substructural logic whose proof theory rejects the structural rule of contraction. It can also be characterized as linear logic with weakening
Affine_logic
American Mathematical Society. 19 (6): 191–194. Girard, Jean-Yves (1987). "Linear logic". Theoretical Computer Science. 50 (1). Elsevier: 1–101. doi:10
Constructive_logic
Arithmetical concept
intuitionistic logic known as linear logic, via the so-called Dialectica spaces. Since linear logic is a refinement of intuitionistic logic, the dialectica
Dialectica_interpretation
Formal systems of logic that significantly differ from standard logical systems
classical logic, which is a formal theory of truth—that integrates and extends classical, linear and intuitionistic logics. Dialectical logic is the system
Non-classical_logic
Extension of linear logic
Noncommutative logic is an extension of linear logic that combines the commutative connectives of linear logic with the noncommutative multiplicative
Noncommutative_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
Theory of logic to account for observations from quantum theory
alternative is the system of linear logic, of which quantum logic is a fragment.[citation needed] Mathematically, quantum logic is formulated by weakening
Quantum_logic
associated with linear logic. Based on that claim and the fact that the semantics induced a logic properly stronger than (affine) linear logic, Japaridze argued
Cirquent_calculus
Branch of non-classical logic
associativity. Two of the more significant substructural logics are relevance logic and linear logic. In a sequent calculus, one writes each line of a proof
Substructural_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
1990s and employs the techniques of proof theory, substructural logic, linear logic, model theory and recursion theory to prove bounds on the expressive
Implicit computational complexity
Implicit_computational_complexity
Rule of mathematical logic
logic (linear logic) – Extension of linear logicPages displaying short descriptions of redirect targets Relevance logic – Kind of non-classical logic
Structural_rule
French logician (born 1947)
réductibilité"). He is also credited with the discovery of Girard's paradox, linear logic, the geometry of interaction, ludics, and (satirically) the mustard watch
Jean-Yves_Girard
was introduced by Jean-Yves Girard shortly after his work on linear logic. In linear logic, proofs can be seen as various kinds of networks as opposed
Geometry_of_interaction
American computer scientist and author
Miller has also made use of linear logic within computer science. In particular, he has demonstrated applications of linear logic to natural language parsing
Dale_Miller_(academic)
Generalized topological space
λ(k, *) = k (Barr 1979). As such it is a model of Jean-Yves Girard's linear logic (Girard 1987). The more general enriched category Chu(V, k) originally
Chu_space
algebra. Also John Darlington and Y. K. Guo 1994 have attempted to relate linear logic to Actor semantics. However, none of the above formalisms addresses the
Actor_model_later_history
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
System of logic in mathematics and philosophy
Sequent calculi for finite and infinite-valued Łukasiewicz logics as an extension of linear logic were introduced by A. Prijatelj in 1994. However, these
Łukasiewicz_logic
non-normal) modal logic, hybrid logic, first-order modal logic, paraconsistent logic, linear logic, relevance logic, connexive logic, belief revision,
Dialogical_logic
System for representing and reasoning about time
temporal logic from computational verb logic. Temporal logic always has the ability to reason about a timeline. So-called "linear-time" logics are restricted
Temporal_logic
Graphical model of computation
mathematician Yves Lafont in 1989 as a generalisation of the proof structures of linear logic. An interaction net system is specified by a set of agent types and a
Interaction_nets
Typographic character indicating a question (?)
mathematics, "?" commonly denotes Minkowski's question mark function. In linear logic, the question mark denotes one of the exponential modalities that control
Question_mark
Topics referred to by the same term
in the Shadows MALL, a protein Multiplicative-additive linear logic, a fragment of linear logic with no exponential entailment rules Mall Airways, regional
Mall
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
Concept in computing
modalities, but can then also be unified in a single type system. Linear type Linear logic Haller, P.; Odersky, M. (2010), "Capabilities for uniqueness and
Uniqueness_type
Type of formal logic
approach is to do both simultaneously. In many systems of relevant logic, as well as linear logic, there are two separate disjunctive connectives. One allows
Paraconsistent_logic
Type of programming language
Concatenative languages can be made well-suited to an implementation inspired by linear logic where no garbage is ever generated. The first concatenative programming
Concatenative programming language
Concatenative_programming_language
Model of concurrent computation
Attempts to relate actor semantics to algebra and linear logic): Several different actor algebras Linear logic The actor model can be used as a framework for
Actor_model
System that manages the behavior of other systems
are several types of linear control systems with different capabilities. Fuzzy logic is an attempt to apply the easy design of logic controllers to the
Control_system
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
noncommutative logic. The calculus has since been applied to study linear logic, classical logic, modal logic, and process calculi, and many benefits are claimed to
Calculus_of_structures
derivation in linear logic). The first such criterion is the long-trip criterion, which was described by Jean-Yves Girard. Linear logic Ludics Geometry
Proof_net
Logic gate implementing negation
steep and approximately linear, a properly-biased CMOS inverter digital logic gate may be used as a high-gain analog linear amplifier or even combined
Inverter_(logic_gate)
List of unsolved computational problems
type system also strongly normalizing? Is multiplicative-exponential linear logic decidable? Is the Aanderaa–Karp–Rosenberg conjecture true? Černý conjecture:
List of unsolved problems in computer science
List_of_unsolved_problems_in_computer_science
Mathematical function conceived as a crude model
extensively used to develop such logic. The artificial neuron activation function should not be confused with a linear system's transfer function. An artificial
Artificial_neuron
Category admitting tensor products
used to define models for the multiplicative fragment of intuitionistic linear logic. They also form the mathematical foundation for the topological order
Monoidal_category
Mathematical methods
used to provide new models of set theory. Linear realizability extends realizability techniques to linear logic. The term was coined by Seiller to encompass
Realizability
Structural rule Weakening Contraction Linear logic Intuitionistic linear logic Proof net Affine logic Strict logic Relevant logic Proof-theoretic semantics Ludics
List of mathematical logic topics
List_of_mathematical_logic_topics
Transforming a function in such a way that it only takes a single argument
internal language of such categories is linear logic, a form of quantum logic; the corresponding type system is the linear type system. Such categories are suitable
Currying
Framework for studying interactive computational tasks through logic
classical logic. Besides classical logic, independence-friendly (IF) logic and certain proper extensions of linear logic and intuitionistic logic also turn
Computability_logic
Brazilian mathematician, logician, and computer scientist
introduced Dialectica spaces, a categorical way of constructing models of linear logic, based on Kurt Gödel's Dialectica interpretation. She worked for nine
Valeria_de_Paiva
Conceptual scheme detailing the types of documentary films
- Joris Ivans. The Diary Film; the linear logic of passing time is used to structure the narrative in either linear or episodic form. Examples: Tarnation
Documentary_mode
Gödel logics. Gödel logics have several alternative definitions. Specifically, Gödel logics are: logics of linearly-ordered Heyting algebras logics of (classes
Gödel_logic
Whether a decision problem has an effective method to derive the answer
logic where Gödel's completeness theorem establishes the equivalence of semantic and syntactic consequence. In other settings, such as linear logic,
Decidability_(logic)
Intermediate language
Journal of Logic and Computation. 24 (3): 615–654. doi:10.1093/logcom/exs025. Ehrhard, Thomas (2016). "Call-By-Push-Value from a Linear Logic Point of View"
Call-by-push-value
Faculty of the human mind
functions of linear logic and the patterns of formal logic the intellect also processes the non-linear functions of fuzzy logic and dialectical logic. Intellect
Intellect
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 logic
Proof_theory
Foundational theorem of quantum information processing
made from quantum mechanics to linear logic as the logic of quantum information theory (in exact analogy to classical logic being founded on Cartesian closed
No-deleting_theorem
Syntax-semantics interface
composition is constrained by a set of instructions stated within a formal logic (linear logic). These instructions, called meaning constructors, state how the
Glue_semantics
Subdiscipline of proof theory
(2002). Baaz, Matthias; Voronkov, Andrei (eds.). "A Local System for Linear Logic". Logic for Programming, Artificial Intelligence, and Reasoning. Berlin,
Structural_proof_theory
Topics referred to by the same term
linearity Linear–log (AKA lin–log) plot, a graph with a linear scale on the Y-axis and a log scale on the X-axis Linear logic, a substructural logic that
Linear_(disambiguation)
Property of many systems of logic
the conclusion. Linear logic, which lacks monotonicity and idempotency of entailment. Contraction Exchange rule Substructural logic No-cloning theorem
Monotonicity_of_entailment
Branch of logic
resources and so not rejected by bunched logic. The semantics is also related to the 'phase semantics' of linear logic, but again is differentiated by accepting
Bunched_logic
conclusion. adjunction See conjunction introduction. affine logics A subfield of linear logic focusing on the study of affine transformations and their
Glossary_of_logic
Cognitive activity
cause-and-effect relationships, diverging from the linear logic of Cartesian thought and the punctual logic of dialectical thought. Within such systems, seemingly
Strategic_thinking
Adjunction between a category of co/presheaf under the co/Yoneda embedding
S2CID 2716529 Pratt, Vaughan (1996), "Broadening the denotational semantics of linear logic", Electronic Notes in Theoretical Computer Science, 3: 155–166, doi:10
Isbell_duality
Face-to-face Classical logic Intermediate logic Intuitionistic logic Minimal logic Relevant logic Affine logic Linear logic Ordered logic Dialetheism Absurdism
Outline_of_philosophy
Cirquent calculus with that semantics can be seen as a logic of resources that, unlike linear logic, makes it possible to account for resource-sharing. As
Giorgi_Japaridze
of many other kinds of logic, such as modal logic and linear logic, and novel semantic models, such as game semantics, logics for computability have been
Logics_for_computability
French-American mathematical historian
founding paper on model theory. Jean-Yves Girard's seminal paper on Linear logic is dedicated in memory of Jean van Heijenoort. Van Heijenoort was murdered
Jean_van_Heijenoort
Dutch mathematician (1939–2019)
intuitionistic logic With Georg Kreisel, he was a developer of the theory of choice sequences. He wrote one of the first texts on linear logic, and, with
Anne_Sjerp_Troelstra
constructing models of linear logic. They were introduced by Valeria de Paiva in her doctoral thesis, as a way of modeling both linear logic and Gödel's Dialectica
Dialectica_space
British computer scientist
Computational Interpretations of Linear logic. in Theoretical Computer Science 111 1994. Domain Theory. (with A Jung). in Handbook of Logic in Computer Science 3
Samson_Abramsky
Intuitionistic type theory BHK interpretation Curry–Howard correspondence Linear logic Game semantics Typed lambda calculus Typed and untyped languages Type
List of functional programming topics
List_of_functional_programming_topics
Logical problem studied in computer science
designs). Subtheories are also possible: for example, difference logic is a sub-theory of linear arithmetic in which each inequality is restricted to have the
Satisfiability modulo theories
Satisfiability_modulo_theories
Type of category in mathematics
vector space of linear maps from one vector space to another. The internal language of closed symmetric monoidal categories is linear logic and the type
Closed_monoidal_category
The Kleene Award is awarded at the annual IEEE Symposium on Logic in Computer Science (LICS) to the author(s) of the best student paper(s). A paper qualifies
Kleene_Award
Type of formal logic
temporal logic include propositional dynamic logic (PDL), (propositional) linear temporal logic (LTL), computation tree logic (CTL), Hennessy–Milner logic, and
Modal_logic
Computer fitted to some cars
the mechanic wants to see the codes while driving the car. In 2004, Linear Logic developed the ScanGauge, which at the time was the only easily installed
Trip_computer
Topics referred to by the same term
protocols Lollipop, the name of the symbol (⊸), used to represent linear implication in Linear logic Chicken lollipop, an hors d'oeuvre Crossing guard, often described
Lollipop_(disambiguation)
Cryptocurrency project
the ability to define custom resource types with semantics inspired by linear logic: a resource can never be copied or implicitly discarded, only moved between
Diem_(digital_currency)
German-American mathematician (born 1947)
connections between game semantics and linear logic. He has authored more than 200 research articles in mathematical logic and theoretical computer science
Andreas_Blass
Relationship between programs and proofs
interpretation to linear, relevant and other resource logics". Journal of Symbolic Logic. Vol. 57. Association for Symbolic Logic. pp. 1319–1365. doi:10
Curry–Howard_correspondence
is an outline of topics related to linear algebra, the branch of mathematics concerning linear equations and linear maps and their representations in vector
Outline_of_linear_algebra
American computer scientist
contributions in garbage collection, functional programming languages, and linear logic. He was one of the founders of Symbolics, a company that designed and
Henry Baker (computer scientist)
Henry_Baker_(computer_scientist)
Phenomenon in natural language
free choice within nonclassical frameworks such as dynamic semantics, linear logic, alternative semantics, and inquisitive semantics. Others have proposed
Free_choice_inference
Study of programming languages via mathematical objects
development of programming languages based on linear logic, denotational semantics have been given to languages for linear usage (see e.g. proof nets, coherence
Denotational_semantics
Punctuation mark (!)
subfactorial. It is used to represent the uniqueness quantifier. In linear logic, the exclamation mark denotes one of the modalities that control weakening
Exclamation_mark
problems, but she did so in a manner that deviated from the more common linear logic). Kelly's comedic function tends to include blatant displays of naivety
List of Married... with Children characters
List_of_Married..._with_Children_characters
Concept in logic
original expression. Where ψ and φ represent formulas of propositional logic, ψ is a substitution instance of φ if and only if ψ may be obtained from
Substitution_(logic)
Programming language that uses first order logic
(CLP), object-oriented logic programming, concurrency, linear logic, functional and higher-order logic programming abilities, plus interoperability with knowledge
Prolog
Computer science concept
not type-check, causing the compilation to fail. Linear types, based on the theory of linear logic, and closely related to uniqueness types, are types
Type_system
their internal structure. Girard shows that for second-order affine linear logic, given a computational system with nontermination and error stops as
Ludics
Topics referred to by the same term
operator in object-oriented programming ?, the why not connective in linear logic �, the Unicode replacement character ⚳, the symbol for the dwarf planet
Question mark (disambiguation)
Question_mark_(disambiguation)
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
Class of non-classical logics
nonclassical logics in the past two decades—paraconsistent logics, linear logics, substructural logics, nonmonotonic logics, innumerable other logics for AI
Deviant_logic
Symmetric monoidal closed category equipped with a dualizing object
the tensor product ⊛ {\displaystyle \circledast } . Various models of linear logic form *-autonomous categories, the earliest of which was Jean-Yves Girard's
*-autonomous_category
Type of logical formula
mathematical logic and logic programming, a Horn clause is a logical formula of a particular rule-like form that gives it useful properties for use in logic programming
Horn_clause
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
LSAT question type
LSAT logic games, abbreviated LG, and officially referred to as analytical reasoning, was historically one of three types of sections that appeared on
LSAT_logic_games
Components of a mathematical or logical formula
In mathematical logic, a term is an arrangement of dependent/bound symbols that denotes a mathematical object within an expression/formula. In particular
Term_(logic)
Magnetic tape data storage technology
Linear Tape-Open (LTO), also known as the LTO Ultrium format, is a magnetic tape data storage technology used for backup, data archiving, and data transfer
Linear_Tape-Open
Rule in logic programming
SLD resolution (Selective Linear Definite clause resolution) is the basic inference rule used in logic programming. It is a refinement of resolution that
SLD_resolution
Work by Georg Wilhelm Friedrich Hegel
Science of Logic (German: Wissenschaft der Logik), first published between 1812 and 1816, is the work in which Georg Wilhelm Friedrich Hegel outlined
Science_of_Logic
(also coherence space) is a concept introduced in the semantic study of linear logic. In Proofs and Types, coherent spaces are called coherence spaces. A
Coherent_space
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