A general conservative extension theorem in process algebras with inequalities

We prove a general conservative extension theorem for transition system based process theories with easy-to-check and reasonable conditions. The core of this result is another general theorem which gives sufficient conditions for a system of operational rules and an extension of it in order to ensure conservativity, that is, provable transitions from an original term in the extension are the same as in the original system. As a simple corollary of the conservative extension theorem we prove a completeness theorem. We also prove a general theorem giving sufficient conditions to reduce the question of ground confluence modulo some equations for a large term rewriting system associated with an equational process theory to a small term rewriting system under the condition that the large system is a conservative extension of the small one. We provide many applications to show that our results are useful. The applications include (but are not limited to) various real and discrete time settings in ACP, ATP, and CCS and the notions projection, renaming, stage operator, priority, recursion, the silent step, autonomous actions, the empty process, divergence, etc

How to Moore a Gettier: Notes on the Dark Side of Knowledge

The Gettier Problem and Moore’s Paradox are related in a way that is unappreciated by philosophers. If one is in a Gettier situation, then one is also in a Moorean situation. The fact that S is in a Gettier situation (the fact that S is “Gettiered”), like the fact that S is in a Moorean situation (the fact that S is “Moored”), cannot (in the logical sense of “cannot”) be known by S while S is in that situation. The paper starts the job of mapping what can be said about this feature of Gettier situations. The goal is to stimulate further exploration into this yet uncharted territory

Cut Elimination for a Logic with Induction and Co-induction

Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles are based on a proof theoretic (rather than set-theoretic) notion of definition. Definitions are akin to logic programs, where the left and right rules for defined atoms allow one to view theories as "closed" or defining fixed points. The use of definitions and free equality makes it possible to reason intentionally about syntax. We add in a consistent way rules for pre and post fixed points, thus allowing the user to reason inductively and co-inductively about properties of computational system making full use of higher-order abstract syntax. Consistency is guaranteed via cut-elimination, where we give the first, to our knowledge, cut-elimination procedure in the presence of general inductive and co-inductive definitions.Comment: 42 pages, submitted to the Journal of Applied Logi

What Would Zero Look Like? A Treaty for the Abolition of Nuclear Weapons

Nuclear disarmament-the comprehensive, universal, and permanent abolition of all nuclear weapons, pursuant to a verifiable, legally binding international agreement-has long been one of the most ambitious, controversial, and urgent items on the agenda for arms control. To date, however, most of the discussion of getting to zero has highlighted the political, military, technical and diplomatic dimensions of this complex problem, and there has been relatively little attention to the legal requirements for drafting such a novel treaty. This Article fills that gap by offering two proposed agreements. The first, a non-legally-bindingfr amework accord, would be designedf or signature relatively soon (e.g., in 2015) to re-commit states to the goal of nuclear elimination and to energize their concerted individual and collective action on a set of prescribed steps in pursuit of it. The second, a legally-binding document, would be concluded at some point in the more distant future, when states had accomplished great reductions in their current nuclear arsenals and were ready, at last, to plunge forward to true abolition. The Article describes the conditions necessary for the further articulation of these two novel agreements, and the text of each instrument carries numerous annotations that identify competing options, describe the negotiating range, and illuminate the drafter\u27s choices. The hope is that something novel can be gained-fresh insights can be suggested, and new questions can be raised (even if answering them remains elusive)-by advancing the dialogue about nuclear disarmament to the concrete stage of treaty drafting

Program transformations using temporal logic side conditions

This paper describes an approach to program optimisation based on transformations, where temporal logic is used to specify side conditions, and strategies are created which expand the repertoire of transformations and provide a suitable level of abstraction. We demonstrate the power of this approach by developing a set of optimisations using our transformation language and showing how the transformations can be converted into a form which makes it easier to apply them, while maintaining trust in the resulting optimising steps. The approach is illustrated through a transformational case study where we apply several optimisations to a small program

Results on formal stepwise design in Z

Stepwise design involves the process of deriving a concrete model of a software system from a given abstract one. This process is sometimes known as refinement. There are numerous refinement theories proposed in the literature, each of which stipulates the nature of the relationship between an abstract specification and its concrete counterpart. This paper considers six refinement theories in Z that have been proposed by various people over the years. However, no systematic investigation of these theories, or results on the relationships between them, have been presented or published before. This paper shows that these theories fall into two important categories and proves that the theories in each category are equivalent