The modal logic of set-theoretic potentialism and the potentialist maximality principles

We analyze the precise modal commitments of several natural varieties of set-theoretic potentialism, using tools we develop for a general model-theoretic account of potentialism, building on those of Hamkins, Leibman and L\"owe, including the use of buttons, switches, dials and ratchets. Among the potentialist conceptions we consider are: rank potentialism (true in all larger $V_\beta$); Grothendieck-Zermelo potentialism (true in all larger $V_\kappa$ for inaccessible cardinals $\kappa$); transitive-set potentialism (true in all larger transitive sets); forcing potentialism (true in all forcing extensions); countable-transitive-model potentialism (true in all larger countable transitive models of ZFC); countable-model potentialism (true in all larger countable models of ZFC); and others. In each case, we identify lower bounds for the modal validities, which are generally either S4.2 or S4.3, and an upper bound of S5, proving in each case that these bounds are optimal. The validity of S5 in a world is a potentialist maximality principle, an interesting set-theoretic principle of its own. The results can be viewed as providing an analysis of the modal commitments of the various set-theoretic multiverse conceptions corresponding to each potentialist account.Comment: 36 pages. Commentary can be made about this article at http://jdh.hamkins.org/set-theoretic-potentialism. Minor revisions in v2; further minor revisions in v

Automatic generation of hardware/software interfaces

Enabling new applications for mobile devices often requires the use of specialized hardware to reduce power consumption. Because of time-to-market pressure, current design methodologies for embedded applications require an early partitioning of the design, allowing the hardware and software to be developed simultaneously, each adhering to a rigid interface contract. This approach is problematic for two reasons: (1) a detailed hardware-software interface is difficult to specify until one is deep into the design process, and (2) it prevents the later migration of functionality across the interface motivated by efficiency concerns or the addition of features. We address this problem using the Bluespec Codesign Language~(BCL) which permits the designer to specify the hardware-software partition in the source code, allowing the compiler to synthesize efficient software and hardware along with transactors for communication between the partitions. The movement of functionality across the hardware-software boundary is accomplished by simply specifying a new partitioning, and since the compiler automatically generates the desired interface specifications, it eliminates yet another error-prone design task. In this paper we present BCL, an extension of a commercially available hardware design language (Bluespec SystemVerilog), a new software compiling scheme, and preliminary results generated using our compiler for various hardware-software decompositions of an Ogg Vorbis audio decoder, and a ray-tracing application.National Science Foundation (U.S.) (NSF (#CCF-0541164))National Research Foundation of Korea (grant from the Korean Government (MEST) (#R33-10095)

Linear superposition as a core theorem of quantum empiricism

Clarifying the nature of the quantum state $|\Psi\rangle$ is at the root of the problems with insight into (counterintuitive) quantum postulates. We provide a direct-and math-axiom free-empirical derivation of this object as an element of a vector space. Establishing the linearity of this structure-quantum superposition-is based on a set-theoretic creation of ensemble formations and invokes the following three principia: $(\textsf{I})$ quantum statics, $(\textsf{II})$ doctrine of a number in the physical theory, and $(\textsf{III})$ mathematization of matching the two observations with each other; quantum invariance. All of the constructs rest upon a formalization of the minimal experimental entity: observed micro-event, detector click. This is sufficient for producing the $\mathbb C$-numbers, axioms of linear vector space (superposition principle), statistical mixtures of states, eigenstates and their spectra, and non-commutativity of observables. No use is required of the concept of time. As a result, the foundations of theory are liberated to a significant extent from the issues associated with physical interpretations, philosophical exegeses, and mathematical reconstruction of the entire quantum edifice.Comment: No figures. 64 pages; 68 pages(+4), overall substantial improvements; 70 pages(+2), further improvement

On the Pursuit of Static and Coherent Weaving

Aspect-oriented programming (AOP) has been shown to be a useful model for software development. Special care must be taken when we try to adapt AOP to strongly typed functional languages which come with features like type inference mechanism, polymorphic types, higher-order functions and type-scoped pointcuts. Specifically, it is highly desirable that weaving of aspect-oriented functional programs can be performed statically and coherently. In [13], we showed a type-directed weaver which resolves all advice chainings coherently at static time. The novelty of this paper lies in the extended framework which supports static and coherent weaving in the presence of polymorphic recursive functions, advising advice bodies and higher-order advices