Boundary Algebra: A Simple Notation for Boolean Algebra and the Truth Functors

RePEc Working Paper Series No. 02/2007Boundary algebra [BA] is a simpler notation for Spencer-Brown’s (1969) primary algebra [pa], the Boolean algebra 2, and the truth functors. The primary arithmetic [PA] is built up from the atoms, ‘()’ and the blank page, by enclosure between ‘(‘ and ‘)’, denoting the primitive notion of distinction, and concatenation. Inserting letters denoting the presence or absence of () into a PA formula yields a BA formula. The BA axioms are “()()=()” (A1), and “(()) [=⊥] may be written or erased at will” (A2). Repeated application of these axioms to a PA formula yields a member of B= {(),⊥} called its simplification. If (a)b [dually (a(b))] ⇔ a=b, then ⊥=() [()=⊥] follows trivially, so that B is a poset. (a) has two intended interpretations: (a) ⇔ a' (Boolean algebra 2), and (a) ⇔ ~a (sentential logic). BA is a self-dual notation for 2: () ⇔ 1 [0] so that B is the carrier for 2, and ab ⇔ a ⋃ b [a ⋂ b]. The BA basis abc=bca (Dilworth 1938), a(ab)= a(b), and a()=() (Bricken 2002) facilitates clausal reasoning and proof by calculation. BA also simplifies the usual normal forms and Quine’s (1982) truth value analysis. () ⇔ true [false] yields boundary logic

Does tenure review in New Zealand’s South Island give rise to rents?

Under “tenure review,” a New Zealand pastoral lessee surrenders part of his leasehold toconservation and acquires a freehold interest in the remainder. 28 new freeholders paid the Crown$6.9 million for freehold rights to 101,752ha, then sold 46$135.7 million. Wemodel tenure review as a sequential real option – first to acquire freehold, then to subdivide andsell all or part of their new freeholds. We find little evidence that the Crown accounted for theseoption values when negotiating tenure review, and conclude that the capital gains enjoyed byformer lessees are rents

Does tenure review in New Zealand's South Island give rise to rents?

We examine land prices arising from tenure review of South Island high country pastoral leases. Tenure review splits the leasehold – part is converted to freehold ownership, and part is converted to public conservation land. The Crown sells its residual interest in the most developable part of a leasehold, and buys the lessee’s interest in the part with conservation value. Of the 77 runs that completed tenure review from 1992-2008, at least 28 new landowners have on-sold 176 parcels of newly freeheld land. In gross, these 28 new owners paid the Crown $6.9M to freehold, and have realized$134 million after on-selling 45,266ha, 44% of their new freeholds

Contrast requirements of urban drivers. Phase I. Interim report.

Federal Highway Administration, Office of Research, Washington, D.C.Mode of access: Internet.COP: 2Author corporate affiliation: Franklin Institute Research Laboratories, Philadelphia, Pa.Subject code: NDISubject code: PMKHSubject code: WU*N