An independent axiomatisation for free short-circuit logic

Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first argument does not suffice to determine the value of the expression. Free short-circuit logic is the equational logic in which compound statements are evaluated from left to right, while atomic evaluations are not memorised throughout the evaluation, i.e., evaluations of distinct occurrences of an atom in a compound statement may yield different truth values. We provide a simple semantics for free SCL and an independent axiomatisation. Finally, we discuss evaluation strategies, some other SCLs, and side effects.Comment: 36 pages, 4 tables. Differences with v2: Section 2.1: theorem Thm.2.1.5 and further are renumbered; corrections: p.23, line -7, p.24, lines 3 and 7. arXiv admin note: substantial text overlap with arXiv:1010.367

Propositional logic with short-circuit evaluation: a non-commutative and a commutative variant

Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first argument does not suffice to determine the value of the expression. Short-circuit evaluation is widely used in programming, with sequential conjunction and disjunction as primitive connectives. We study the question which logical laws axiomatize short-circuit evaluation under the following assumptions: compound statements are evaluated from left to right, each atom (propositional variable) evaluates to either true or false, and atomic evaluations can cause a side effect. The answer to this question depends on the kind of atomic side effects that can occur and leads to different "short-circuit logics". The basic case is FSCL (free short-circuit logic), which characterizes the setting in which each atomic evaluation can cause a side effect. We recall some main results and then relate FSCL to MSCL (memorizing short-circuit logic), where in the evaluation of a compound statement, the first evaluation result of each atom is memorized. MSCL can be seen as a sequential variant of propositional logic: atomic evaluations cannot cause a side effect and the sequential connectives are not commutative. Then we relate MSCL to SSCL (static short-circuit logic), the variant of propositional logic that prescribes short-circuit evaluation with commutative sequential connectives. We present evaluation trees as an intuitive semantics for short-circuit evaluation, and simple equational axiomatizations for the short-circuit logics mentioned that use negation and the sequential connectives only.Comment: 34 pages, 6 tables. Considerable parts of the text below stem from arXiv:1206.1936, arXiv:1010.3674, and arXiv:1707.05718. Together with arXiv:1707.05718, this paper subsumes most of arXiv:1010.367

The Hidden Costs of the Progressivity Debate

Progressive taxation-taxing high income individuals at a proportionally higher level than low income individuals-has sparked more than a century of controversy. Those who support progressive taxation have heralded it as a policy that promotes the greatest good for the greatest number in society protects traditional democratic values, reflects the communitarian world-view of women who see themselves as responsible for the well-being of all individuals, and reveals the aesthetic judgment that income inequality is distinctly evil or unlovely. At the same time, critics have condemned progressive income taxation as social policy that amounts to theft and involuntary servitude, reflects the democratic process gone awry, penalizes hard-working individuals, and produces economic waste throughout society. Theorists in almost every discipline have entered the progressivity debate, proposing a variety of different tax rates in order to disburse the costs of public goods and services. Despite their contending viewpoints, theorists on both sides of the debate have reached surprising consensus on the proper treatment of the truly poor. Both sides agree that legislators and policy-makers must avoid imposing tax costs on individuals living at or be- low subsistence levels of income. This agreement is notable in light of the widespread perception that advocates of progressivity worry about the poor while its detractors worry about the wealthy. In fact, all tax theorists have divided society into two groups-relatively wealthy individuals who pay taxes and poor individuals who are excluded from the face of the laws entirely. Of course, if the goal of tax policy is to distribute the costs of public goods, then offering an exemption to the poor might seem desirable and perhaps even an obvious policy choice, given that the poor have little or no income. While the practical difficulty of collecting the tax explains why theorists have advocated an exemption, it does not explain why they have failed to explore any positive rights beyond an exemption or, indeed, any responsibility the poor might have to society despite their lack of income. In this Article, I argue that.by reaching the agreement that the poor should have no tax liability, the contest over progressivity has centered improperly on the rights and responsibilities of relatively wealthy citizens. The wealthy are widely perceived to have valuable property that, if shared with society, will enable the smooth operation of the democratic state. At the same time, the wealthy are perceived to have liberty interests, which if violated, could lead to the ruin of the domestic economy

NH2-MIL-53(Al) and NH2-MIL-101(Al) in sulfur-containing copolyimide mixed matrix membranes for gas separation

Amino functionalized MOFs (NH2-MIL-53(Al) or NH2-MIL-101(Al)) were used as dispersed phase in the fabrication of mixed matrix membranes (MMMs) with a polymer matrix of sulfur-containing copolyimides (6FDA:DSDA/4MPD:4,4’-SDA 1:1 (polymer P1) or 6FDA/4MPD:4,4’-SDA 1:1 (polymer P2)). The gas separation properties of the MMMs obtained were tested for permeation of H2, CH4 and CO2. Membranes comprising polymer P1 showed better interaction with the fillers used than polymer P2, and therefore better separation properties, especially for NH2-MIL-101(Al). Upon NH2-MIL-101(Al) loading the performance of pure polymer was improved approaching the Robeson 1991 H2/CH4 and CO2/CH4 upper bound limits with high permeabilities, e.g. 114, 71 and 1.7 Barrer for H2, CO2 and CH4, respectively, using 10 wt.% NH2-MIL-101(Al)@P1. These improvements are related to the pore size of the filler, the flexibility and functional groups of sulfone-containing DSDA, and polymer rigidification