constructive logicの例文

• He developed constructive logic, constructive type theory and constructive analysis.
• So then modus tollens wouldn't be included as an inference rule in constructive logics?
• Becker also showed how a constructive logic that denied unrestricted excluded middle could be used to reconstruct most of Euclid's proofs.
• Some authors have argued that this might be an indication of inadequacy of Heyting s calculus itself, deeming the latter incomplete as a constructive logic.
• Is there any theory of arithmetic within the framework of linear logic, analogous to how Heyting arithmetic is the arithmetic of intuitionistic or constructive logic?
• Intuitionistic logic is of great interest to computer scientists, as it is a constructive logic and can be applied for extracting verified programs from proofs.
• What results is essentially an intuitionistic ( i . e . constructive logic ) theory, its content being clarified by the existence of a " free topos ".
• A deep result in proof theory, the Curry-Howard correspondence, states that a proof of functional correctness in constructive logic corresponds to a certain program in the lambda calculus.
• One example is CosmicOS . Another is a second-generation " Lingua Cosmica " developed by the Dutch-Swedish astronomer and mathematician Alexander Ollongren of Leiden University, using constructive logic.
• From a constructivist point of view, Harrop formulae are " well-behaved . " For example, in Heyting arithmetic, Harrop formulae satisfy a classical equivalence not usually satisfied in constructive logic:
• It describes the way the logic of situations in human societies can be formulated in the lingua, also named LINCOS . This astrolinguistic system, also designed for use in interstellar communication, is based on modern constructive logic  which assures that all expressions are verifiable.
• Constructive proofs can be seen as defining certified mathematical algorithms : this idea is explored in the Brouwer Heyting Kolmogorov interpretation of constructive logic, the Curry Howard correspondence between proofs and programs, and such logical systems as Per Martin-L鰂's Intuitionistic Type Theory, and Thierry Coquand and G閞ard Huet's Calculus of Constructions.
• Accordingly, the " Journal " publishes papers in all of the traditional areas of philosophical logic, including : various versions of modal, temporal, epistemic, and deontic logic; constructive logics; relevance and other sub-classical logics; many-valued logics; logics of conditionals; quantum logic; decision theory, inductive logic, logics of belief change, and formal epistemology; defeasible and nonmonotonic logics; formal philosophy of language; vagueness; and theories of truth and validity.