Rewriting Logic Semantics of a Plan Execution Language

The Plan Execution Interchange Language (PLEXIL) is a synchronous language developed by NASA to support autonomous spacecraft operations. In this paper, we propose a rewriting logic semantics of PLEXIL in Maude, a high-performance logical engine. The rewriting logic semantics is by itself a formal interpreter of the language and can be used as a semantic benchmark for the implementation of PLEXIL executives. The implementation in Maude has the additional benefit of making available to PLEXIL designers and developers all the formal analysis and verification tools provided by Maude. The formalization of the PLEXIL semantics in rewriting logic poses an interesting challenge due to the synchronous nature of the language and the prioritized rules defining its semantics. To overcome this difficulty, we propose a general procedure for simulating synchronous set relations in rewriting logic that is sound and, for deterministic relations, complete. We also report on two issues at the design level of the original PLEXIL semantics that were identified with the help of the executable specification in Maude

Dissociative photoionization of NO across a shape resonance in the XUV range using circularly polarized synchrotron radiation.

We report benchmark results for dissociative photoionization (DPI) spectroscopy and dynamics of the NO molecule in the region of the σ* shape resonance in the ionization leading to the NO+(c3Π) ionic state. The experimental study combines well characterized extreme ultraviolet (XUV) circularly polarized synchrotron radiation, delivered at the DESIRS beamline (SOLEIL), with ion-electron coincidence 3D momentum spectroscopy. The measured (N+, e) kinetic energy correlation diagrams reported at four discrete photon energies in the extended 23-33 eV energy range allow for resolving the different active DPI reactions and underline the importance of spectrally resolved studies using synchrotron radiation in the context of time-resolved studies where photoionization is induced by broadband XUV attosecond pulses. In the dominant DPI reaction which leads to the NO+(c3Π) ionic state, photoionization dynamics across the σ* shape resonance are probed by molecular frame photoelectron angular distributions where the parallel and perpendicular transitions are highlighted, as well as the circular dichroism CDAD(θe) in the molecular frame. The latter also constitute benchmark references for molecular polarimetry. The measured dynamical parameters are well described by multichannel Schwinger configuration interaction calculations. Similar results are obtained for the DPI spectroscopy of highly excited NO+ electronic states populated in the explored XUV photon energy range

A proposal for broad spectrum proof certificates

International audienceRecent developments in the theory of focused proof systems provide flexible means for structuring proofs within the sequent calculus. This structuring is organized around the construction of ''macro'' level inference rules based on the ''micro'' inference rules which introduce single logical connectives. After presenting focused proof systems for first-order classical logics (one with and one without fixed points and equality) we illustrate several examples of proof certificates formats that are derived naturally from the structure of such focused proof systems. In principle, a proof certificate contains two parts: the first part describes how macro rules are defined in terms of micro rules and the second part describes a particular proof object using the macro rules. The first part, which is based on the vocabulary of focused proof systems, describes a collection of macro rules that can be used to directly present the structure of proof evidence captured by a particular class of computational logic systems. While such proof certificates can capture a wide variety of proof structures, a proof checker can remain simple since it must only understand the micro-rules and the discipline of focusing. Since proofs and proof certificates are often likely to be large, there must be some flexibility in allowing proof certificates to elide subproofs: as a result, proof checkers will necessarily be required to perform (bounded) proof search in order to reconstruct missing subproofs. Thus, proof checkers will need to do unification and restricted backtracking search

A Focused Sequent Calculus Framework for Proof Search in Pure Type Systems

Basic proof-search tactics in logic and type theory can be seen as the root-first applications of rules in an appropriate sequent calculus, preferably without the redundancies generated by permutation of rules. This paper addresses the issues of defining such sequent calculi for Pure Type Systems (PTS, which were originally presented in natural deduction style) and then organizing their rules for effective proof-search. We introduce the idea of Pure Type Sequent Calculus with meta-variables (PTSCalpha), by enriching the syntax of a permutation-free sequent calculus for propositional logic due to Herbelin, which is strongly related to natural deduction and already well adapted to proof-search. The operational semantics is adapted from Herbelin's and is defined by a system of local rewrite rules as in cut-elimination, using explicit substitutions. We prove confluence for this system. Restricting our attention to PTSC, a type system for the ground terms of this system, we obtain the Subject Reduction property and show that each PTSC is logically equivalent to its corresponding PTS, and the former is strongly normalising iff the latter is. We show how to make the logical rules of PTSC into a syntax-directed system PS for proof-search, by incorporating the conversion rules as in syntax-directed presentations of the PTS rules for type-checking. Finally, we consider how to use the explicitly scoped meta-variables of PTSCalpha to represent partial proof-terms, and use them to analyse interactive proof construction. This sets up a framework PE in which we are able to study proof-search strategies, type inhabitant enumeration and (higher-order) unification

Implicit complexity for coinductive data: a characterization of corecurrence

We propose a framework for reasoning about programs that manipulate coinductive data as well as inductive data. Our approach is based on using equational programs, which support a seamless combination of computation and reasoning, and using productivity (fairness) as the fundamental assertion, rather than bi-simulation. The latter is expressible in terms of the former. As an application to this framework, we give an implicit characterization of corecurrence: a function is definable using corecurrence iff its productivity is provable using coinduction for formulas in which data-predicates do not occur negatively. This is an analog, albeit in weaker form, of a characterization of recurrence (i.e. primitive recursion) in [Leivant, Unipolar induction, TCS 318, 2004].Comment: In Proceedings DICE 2011, arXiv:1201.034

Circular dichroism in photoionization of H2

ABSTRACT: Circular dichroism is a consequence of chirality. However, nonchiral molecules can also exhibit it when the measurement itself introduces chirality, e.g., when measuring molecular-frame photoelectron angular distributions. The few such experiments performed on homonuclear diatomic molecules show that, as expected, circular dichroism vanishes when the molecular-frame photoelectron angular distributions are integrated over the polar electron emission angle. Here we show that this is not the case in resonant dissociative ionization of H2 for photons of 30–35 eV, which is the consequence of the delayed ionization from molecular doubly excited states into ionic states of different inversion symmetry

Circular dichrosim in photoionization of H2 and D2

ABSTRACT: In this work, circular dichroism in H2 (D2) photoionization is studied in detail. We have selected several photon energies for a case study: 19 eV for which only direct ionization to the 1s_g ionization channel is present, 27 eV where autoionization of Q1 doubly excited states takes place, and 32.5 eV for which autoionization from Q1 and doubly excited states and direct ionization to 1s_g and 2p_u channels strongly interfere. The latter case shows clear evidence of different behavior of the photoionization against radiation helicity

The play's the thing

For very understandable reasons phenomenological approaches predominate in the field of sensory urbanism. This paper does not seek to add to that particular discourse. Rather it takes Rorty’s postmodernized Pragmatism as its starting point and develops a position on the role of multi-modal design representation in the design process as a means of admitting many voices and managing multidisciplinary collaboration. This paper will interrogate some of the concepts underpinning the Sensory Urbanism project to help define the scope of interest in multi-modal representations. It will then explore a range of techniques and approaches developed by artists and designers during the past fifty years or so and comment on how they might inform the question of multi-modal representation. In conclusion I will argue that we should develop a heterogeneous tool kit that adopts, adapts and re-invents existing methods because this will better serve our purposes during the exploratory phase(s) of any design project that deals with complexity

Circular dichroism in molecular-frame photoelectron angular distributions in the dissociative photoionization of H2 and D2 molecules

ABSTRACT: The presence of net circular dichroism in the photoionization of nonchiral homonuclear molecules has been put in evidence recently through the measurement of molecular-frame photoelectron angular distributions in dissociative photoionization of H2 [Dowek et al., Phys. Rev. Lett. 104, 233003 (2010)]. In this work we present a detailed study of circular dichroism in the photoelectron angular distributions of H2 and D2 molecules, oriented perpendicularly to the propagation vector of the circularly polarized light, at different photon energies (20, 27, and 32.5 eV). Circular dichroism in the angular distributions at 20 and to a large extent 27 eV exhibits the usual pattern in which inversion symmetry is preserved. In contrast, at 32.5 eV, the inversion symmetry breaks down, which eventually leads to total circular dichroism after integration over the polar emission angle. Time-dependent ab initio calculations support and explain the observed results for H2 in terms of quantum interferences between direct photoionization and delayed autoionization from the Q1 and Q2 doubly excited states into ionic states (1sσg and 2pσu) of different inversion symmetry. Nevertheless, for D2 at 32.5 eV, there is a particular case where theory and experiment disagree in the magnitude of the symmetry breaking: when D+ ions are produced with an energy of around 5 eV. This reflects the subleties associated to such simple molecules when exposed to this fine scrutiny