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For example, in describing O–A relationships for common British birds, Quinn et al. [7] found that the occupancy at the finest resolution (10 x 10 km squares) best explained abundance patterns. In a similar manner, Zuckerberg et al. [ 8 ] used Breeding Bird Atlas data measured on cells 5 × 5 km to describe breeding bird occupancy in New York ...
The prime example of a modal logic for which hypersequents provide an analytic calculus is the logic S5. In a standard hypersequent calculus for this logic [1] the formula interpretation is as above, and the propositional and structural rules are the ones from the previous section. Additionally, the calculus contains the modal rules
A sequent is said to be an intuitionistic sequent if there is at most one formula in the succedent (although multi-succedent calculi for intuitionistic logic are also possible). More precisely, the restriction of the general sequent calculus to single-succedent-formula sequents, with the same inference rules as for general sequents, constitutes ...
The weakening rule may be expressed as a natural deduction sequent: Γ ⊢ C Γ , A ⊢ C {\displaystyle {\frac {\Gamma \vdash C}{\Gamma ,A\vdash C}}} This can be read as saying that if, on the basis of a set of assumptions Γ {\displaystyle \Gamma } , one can prove C, then by adding an assumption A, one can still prove C.
In functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers.Equivalently, it is a function space whose elements are functions from the natural numbers to the field K of real or complex numbers.
In proof theory and mathematical logic, sequent calculus is a family of formal systems sharing a certain style of inference and certain formal properties. The first sequent calculi systems, LK and LJ, were introduced in 1934/1935 by Gerhard Gentzen [1] as a tool for studying natural deduction in first-order logic (in classical and intuitionistic versions, respectively).
In the BitTorrent file distribution system, a torrent file or meta-info file is a computer file that contains metadata about files and folders to be distributed, and usually also a list of the network locations of trackers, which are computers that help participants in the system find each other and form efficient distribution groups called swarms. [1]
A type 1 sequence boundary is defined to be a sequence boundary "characterized by subaerial exposure and concurrent subaerial erosion associated with stream rejuvenation, a basinward shift of facies, a downward shift in coastal onlap, and onlap of overlying strata". [3]