Paraconsistency, self-extensionality, modality

Paraconsistent logics are logics that, in contrast to classical and intuitionistic logic, do not trivialize inconsistent theories. In this paper we take a paraconsistent view on two famous modal logics: B and S5. We use for this a well-known general method for turning modal logics to paraconsistent logics by defining a new (paraconsistent) negation as $\neg \varphi =_{Def} \sim \Box \varphi$ (where $\sim$ is the classical negation). We show that while that makes both B and S5 members of the well-studied family of paraconsistent C-systems, they differ from most other C-systems in having the important replacement property (which means that equivalence of formulas implies their congruence). We further show that B is a very robust C-system in the sense that almost any axiom which has been considered in the context of C-systems is either already a theorem of B or its addition to B leads to a logic that is no longer paraconsistent. There is exactly one notable exception, and the result of adding this exception to B leads to the other logic studied here, S5.

Jual Beli Benda Wakaf Untuk Pembangunan Masjid Istiqlal di Desa Palengaan Daja Pamekasan

Muslim jurists agree that selling waqf property is forbidden A case happened when concrete pillars of a waqf mosque was sold in a mosque called Istiqlal in Daja village. The pillars were initially planned to be installed during rebuilding of the mosque. The research discovered that this pillar originated from charity. These pillars were re-sold to collect more fund from community to continue the rebuilding. Majority of sunni schools of law (Shafii, Maliki and Hanbali) view that such transaction is forbidden because there is no valid reason for selling the pillar. In addition, the seller is not the rightful person to do so. Meanwhile, Hanafi jurists allow such practice as long as all requirements are met, especially the availability of replacement property as well as fulfilment of all terms and conditions of selling. Key words: Waqf, selling property, mosque

Finding a Port in a Non-Safe Harbor: Implications for Reverse Exchanges after Bartell

ABSTRACT Revenue Procedure 2000-37 provides a safe harbor for reverse like-kind exchanges to qualify for deferral of gain under Section 1031. In a reverse exchange, the replacement property is acquired before the relinquished property is transferred. The taxpayer transfers title to replacement property to a third-party accommodator to hold until the exchange takes place. In a landmark ruling for the taxpayer in Bartell v. Commissioner, the Tax Court held in favor of form over substance: although the taxpayer had possession and control of the replacement property for 17 months, the accommodator with the title had tax ownership. The IRS nonacquiesced with the decision, emphasizing substance over form: the accommodator must have benefits and burdens of ownership, rather than holding mere title. This paper proposes that the IRS's nonacquiescence is problematic because it could result in inconsistency across different Circuits, and recommends that Congress adopt a consistent timing rule for all exchanges.

Sequent Systems for Negative Modalities

Non-classical negations may fail to be contradictory-forming operators in more than one way, and they often fail also to respect fundamental meta-logical properties such as the replacement property. Such drawbacks are witnessed by intricate semantics and proof systems, whose philosophical interpretations and computational properties are found wanting. In this paper we investigate congruential non-classical negations that live inside very natural systems of normal modal logics over complete distributive lattices; these logics are further enriched by adjustment connectives that may be used for handling reasoning under uncertainty caused by inconsistency or undeterminedness. Using such straightforward semantics, we study the classes of frames characterized by seriality, reflexivity, functionality, symmetry, transitivity, and some combinations thereof, and discuss what they reveal about sub-classical properties of negation. To the logics thereby characterized we apply a general mechanism that allows one to endow them with analytic ordinary sequent systems, most of which are even cut-free. We also investigate the exact circumstances that allow for classical negation to be explicitly defined inside our logics.

SYMMETRIES OF FRACTAL TILINGS

Self-similar tilings of the plane can be generated by an iterative replacement property using squares and triangles. We show tilings with tiles that are topological disks and others whose tiles are connected but have an interior that is disconnected. In each example we note the symmetries of the individual tiles and describe how each tiling exhibits a property common to crystallographic tilings.