Why is it called linear logic?

Why is it called linear logic?

font apparaître des structures logiques familières en algèbre linéaires […]” Translation: “Linear logic developed from systematically taking into consideration the categorical interpretation. So, in one sentence, it is called linear logic because it involves semantics which resemble structures from linear algebra.

What is classical logic philosophy?

From Wikipedia, the free encyclopedia. Classical logic (or standard logic) is the intensively studied and most widely used class of deductive logic. Classical logic has had much influence on analytic philosophy, the type of philosophy most often found in the English-speaking world.

What is non linear logic?

Linear-non-linear logic is a presentation of intuitionistic linear logic that decomposes the ! modality into an adjunction of between a syntax for a cartesian logic and a linear logic with cartesian variables.

What is linear deduction?

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. …

What are linear types?

Linear types corresponds to linear logic and ensures that objects are used exactly once. The Clean programming language makes use of uniqueness types (a variant of linear types) to help support concurrency, input/output, and in-place update of arrays. Linear type systems allow references but not aliases.

What is logical and linear?

Linear logic is a refinement of classical and intuitionistic logic. Instead of emphasizing truth, as in classical logic, or proof, as in intuitionistic logic, linear logic emphasizes the role of formulas as resources. Given its focus on resources, linear logic has found many applications in Computer Science.

What is the difference between symbolic logic and classical logic?

Answer: Symbolic logic originated in connection with mathematical theory. Symbolic logic has a short history and the traditional or classical Aristotelian logic has a long one. Classical logic is related to symbolic logic as embryo to adult organism.

What is linear thinking mean?

Linear thinking—or vertical thinking—is the traditional mode of ideation that designers problem-solve with by using logic, past data and existing solutions. They typically apply it when using convergent thinking methods to analyze the ideas they generate during divergent thinking sessions and see which might work best.

What is a linear thinker mean?

Linear thinking is an analytic, methodic, rational and logical thinking style. Linear thinkers use information they have learned from one situation to apply it to another situation in order to solve problems. They use consistency, rules, formulas or patterns to make decisions in life.

Is there a use for linear logic?

Linear logic restricted to \(L\) can be viewed as a linear logic programming language. As a consequence, it can serve as a specification language for computational systems, a role that is also occupied by, say, Petri nets, process calculi, \(\lambda\)-calculus, etc.

What is linear text?

Linear text refers to traditional text that needs to be read from beginning to the end while nonlinear text refers to text that does not need to be read from beginning to the end.

What is the meaning of linear logic?

Linear logic. 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.

What is intuitionistic linear logic?

The resource interpretation Lafont (1993) first showed how intuitionistic linear logic can be explained as a logic of resources, so providing the logical language with access to formalisms that can be used for reasoning about resources within the logic itself, rather than, as in classical logic, by means of non-logical predicates and relations.

What is Girard’s linear logic?

Answer Wiki. Jean-Yves Girard’s linear logic is resource aware, in the sense that premises represent resources that cannot be duplicated or discarded, rather than truth, which can be reused or ignored. Linear logic does this by removing several rules, known as the “structural rules,” from propositional logic.

What is linear thinking in psychology?

“Linear Thinking” is defined as follows: [Linear thinking is] a process of thought following known cycles or step-by-step progression where a response to a step must be elicited before another step is taken. Linear means “like a line”, and so a linear process moves forward in a line. If a = b, and b = c, then a = c.

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