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Linear logic is a substructural logic proposed by Jean-Yves Girard as a refinement of classical and intuitionistic logic, joining the dualities of the former with many of the constructive properties of the latter.[1] Although the logic has also been studied for its own sake, more broadly, ideas from linear logic have been influential in fields such as programming languages, game semantics, and quantum physics (because linear logic can be seen as the logic of quantum information theory),[2] as well as linguistics,[3] particularly because of its emphasis on resource-boundedness, duality, and interaction.
Linear logic lends itself to many different presentations, explanations, and intuitions.
Proof-theoretically, it derives from an analysis of classical sequent calculus in which uses of (the structural rules) contraction and weakening are carefully controlled. Operationally, this means that logical deduction is no longer merely about an ever-expanding collection of persistent "truths", but also a way of manipulating resources that cannot always be duplicated or thrown away at will. In terms of simple denotational models, linear logic may be seen as refining the interpretation of intuitionistic logic by replacing cartesian (closed) categories by symmetric monoidal (closed) categories, or the interpretation of classical logic by replacing Boolean algebras by C*-algebras.[citation needed]
Linearlogic is a substructural logic proposed by Jean-Yves Girard as a refinement of classical and intuitionistic logic, joining the dualities of the...
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...
Logic programming is a programming, database and knowledge representation paradigm based on formal logic. A logic program is a set of sentences in logical...
Affine logic is a substructural logic whose proof theory rejects the structural rule of contraction. It can also be characterized as linearlogic with weakening...
noncommutative logic where exchange, contraction and weakening are discarded. This can be used to model stack-based memory allocation (contrast with linear types...
logic and games, and Hanno Nickau who addressed the full abstraction problem in programming languages by means of games. New results in linearlogic by...
common alternative is the system of linearlogic, of which quantum logic is a fragment. Mathematically, quantum logic is formulated by weakening the distributive...
associativity. Two of the more significant substructural logics are relevance logic and linearlogic. In a sequent calculus, one writes each line of a proof...
intuitionistic logic known as linearlogic, via the so-called Dialectica spaces. Since linearlogic is a refinement of intuitionistic logic, the dialectica...
descriptions as a fallback Linearlogic – System of resource-aware logic Ordered logic (linearlogic) Relevance logic – mathematical logic system that imposes...
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...
temporal logic from computational verb logic. Temporal logic always has the ability to reason about a timeline. So-called "linear-time" logics are restricted...
by Yves Lafont in 1990 as a generalisation of the proof structures of linearlogic. An interaction net system is specified by a set of agent types and a...
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...
modalities, but can then also be unified in a single type system. Linear type Linearlogic Haller, P.; Odersky, M. (2010), "Capabilities for uniqueness and...
classical logic. Besides classical logic, independence-friendly (IF) logic and certain proper extensions of linearlogic and intuitionistic logic also turn...
logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by...
approach is to do both simultaneously. In many systems of relevant logic, as well as linearlogic, there are two separate disjunctive connectives. One allows...
the mechanic wants to see the codes while driving the car. In 2004, LinearLogic developed the ScanGauge, which at the time was the only easily installed...
mathematics, "?" commonly denotes Minkowski's question mark function. In linearlogic, the question mark denotes one of the exponential modalities that control...
derivation in linearlogic). The first such criterion is the long-trip criterion, which was described by Jean-Yves Girard. Linearlogic Ludics Geometry...
algebra. Also John Darlington and Y. K. Guo 1994 have attempted to relate linearlogic to Actor semantics. However, none of the above formalisms addresses the...