On Collective Self-Determination and a Palestinian State

Do the Palestinians deserve a state? To answer this question, one must first provide an account of collective self-determination (CSD) and when a group is entitled to it. This starts with looking at the origins of CSD, both to see if it truly is a right and, if so, what its nature is. I will argue that there is such a thing as a right to CSD, but due to its nature, it is not a universal right of all groups. Whether a group has a right to CSD depends on the conditions in which the group lives, and in this paper, I will tease out what these conditions are. The result of such an analysis will be a set of criteria by which one can judge whether or not a group is entitled to CSD, given the conditions in which the group lives. With this criteria, I will look at the Palestinian case in particular and determine whether or not the Palestinians have a right to CSD. If so, they have a right to an independent state, since any group that exercises true CSD can determine whether or not they choose to live in such a state

Tactics From Proofs

Proof guarantees the correctness of a formal specification with respect to formal requirements, and of an implementation with respect to a specification, and so provides valuable verification methods in high integrity system development. However, proof development by hand tends to be an erudite, error-prone and seemingly interminable task. Tactics are programs that drive theorem-provers, thus automating proof development and alleviating some of the problems mentioned above. The development of tactics for a particular application domain also extends the domain of application of the theorem-prover. A LCF-tactic is safe in that if it fails to be applicable to a particular conjecture, then it will not produce an incorrect proof. The current construction of tactics from proofs does not yield sufficiently robust tactics. Proofs tend to be specific to the details of a specification and so are not reusable in general, e.g. the same proof may not work when the definition of a conjecture is changed. The major challenges in proof development are deciding which proof rule and instantiations to apply in order to prove a conjecture. Discerning patterns in formal interactive proof development facilitates the construction of robust tactics that can withstand definitional changes in conjectures. Having developed an interactive proof for a conjecture, we develop the necessary abstractions of the proof steps used, to construct a tactic th at can be applicable to other conjectures in that domain. By so doing we encode human expertise used in the proof development, and make proofs robust and thus generally reusable. We apply our theory on the proofs of conjectures involving some set theory operators, and on the proof obligations that arise in the formal development of numerical specifications using the retrenchment method under the IEEE-854 floating-point standard in the PVS theorem-prover/proof-checker