Defaults as restrictions on classical Hilbert-style proofs

Since the earliest formalisation of default logic by Reiter many contributions to this appealing approach to nonmonotonic reasoning have been given. The different formalisations are here presented in a general framework that gathers the basic notions, concepts and constructions underlying default logic. Our view is to interpret defaults as special rules that impose a restriction on the juxtaposition of monotonic Hubert-style proofs of a given logicL. We propose to describe default logic as a logic where the juxtaposition of default proofs is subordinate to a restriction condition . Hence a default logic is a pair (L, ) where properties of the logic , like compactness, can be interpreted through the restriction condition . Different default systems are then given a common characterization through a specific condition on the logicL. We also prove cumulativity for any default logic (L, ) by slightly modifying the notion of default proof. We extend, in fact, the language ofL in a way close to that followed by Brewka in the formulation of his cumulative default system. Finally we show the existence of infinitely many intermediary default logics, depending on and called linear logics, which lie between Reiter's and ukaszewicz' versions of default logic.Work carried out in the framework of the agreement between Italian PT Administration and FUBLaforia, Université Paris VI Pierre et Marie Curie, 4 Place Jussieu,Tour 46, 75252 Paris, France     

Inverse problems for granulometries by erosion

Let us associate to any binary planar shape X the erosion curve _X defined by _X: r IR^XA(XrB), where A(X) stands for the surface area of X and XrB for the eroded set of X with respect to the ball rB of size r. Note the analogy to shape quantification by granulometry. This paper describes the relationship between sets X and Y verifying _X = _Y. Under some regularity conditions on X, _X is expressed as an integral on its skeleton of the quench function q _X(distance to the boundary of X). We first prove that a bending of arcs of the skeleton of X does not affect _X: quantifies soft shapes. We then prove, in the generic case, that the five possible cases of behavior of the second derivative _X characterize five different situations on the skeleton Sk(X) and on the quench function q _X: simple points of Sk(X) where q _Xis a local minimum, a local maximum, or neither, multiple points of Sk(X) where q _Xis a local maximum or not. Finally, we give infinitesimal generators of the reconstruction process for the entire family of shapes Y verifying _X = _Y for a given X.     

Two and three-quarter dimensional meshing facilitators

This paper presents generated enhancements for robust two and three-quarter dimensional meshing, including: (1) automated interval assignment by integer programming for submapped surfaces and volumes, (2) surface submapping, and (3) volume submapping. An introduction to the simplex method, an optimization technique of integer programming, is presented. Simplification of complex geometry is required for the formulation of the integer programming problem. A method of i-j unfolding is defined which explains how irregular geometry can be realigned into a simplified form that is suitable for submap interval assignment solutions. Also presented is the processes by which submapping eliminates the decomposition of surface geometry, through a pseudodecomposition process, producing suitable mapped meshes. The process of submapping involves the creation of interpolated virtual edges, user defined vertex types and i-j-k space traversals. The creation of interpolated virtual edges is the method by which submapping automatically subdivides surface geometry. The interpolated virtual edge is formulated according to an interpolation scheme using the node discretization of curves on the surface. User defined vertex types allow direct user control of surface decomposition and interval assignment by modifying i-j-k space traversals. Volume submapping takes the geometry decomposition to a higher level by using mapped virtual surfaces to eliminate decomposition of complex volumes.     

Extremal Relations between Additive Loss Functions and the Kolmogorov Complexity

Conditions are presented under which the maximum of the Kolmogorov complexity (algorithmic entropy) K(₁... _N ) is attained, given the cost f( _i ) of a message ₁... _N . Various extremal relations between the message cost and the Kolmogorov complexity are also considered; in particular, the minimization problem for the function f( _i ) – K(₁... _N ) is studied. Here, is a parameter, called the temperature by analogy with thermodynamics. We also study domains of small variation of this function.     

Random sequences in Fréchet spaces

This article deals with the generation of arbitrarily distributed sequences of random variables in a Fréchet space, using sequences ofcanonical random variables (c.r.v.)-i.e., independently uniformly distributed random variables taking real values in the unit interval [0, 1)-orcanonical random digits (c.r.d.)-i.e., independently uniformly distributed random variables taking integer values in some finite interval [0,B–1]. Two main results are established. First, that the members of a sequence of real random variables in [0, 1) are c.r.v. if and only if all the digits of all thebase- B digital representations of the members of the sequence are c.r.d. Secondly, that, given any sequence of random variables in a Fréchet space, there is a sequence of functions _n( ₁, ₂, ..., _n), forn=1, 2, 3,... (where ₁, ₂,..., _n,... are c.r.v.) which is distributed identically to.     

A predicate transformer for the progress property ‘to-always’

The temporal property to-always has been proposed for specifying progress properties of concurrent programs. Although the to-always properties are a subset of the leads-to properties for a given program, to-always has more convenient proof rules and in some cases more accurately describes the desired system behavior. In this paper, we give a predicate transformerwta, derive some of its properties, and use it to define to-always. Proof rules for to-always are derived from the properties ofwta. We conclude by briefly describing two application areas, nondeterministic data flow networks and self-stabilizing systems where to-always properties are useful.     

Maintaining the visibility map of spheres while moving the viewpoint on a circle at infinity

We investigate three-dimensional visibility problems for scenes that consist ofn non-intersecting spheres. The viewing point moves on a flightpath that is part of a circle at infinity given by a planeP and a range of angles {(t)¦t[01]} [02]. At timet, the lines of sight are parallel to the ray inP, which starts in the origin ofP and represents the angle(t) (orthographic views of the scene). We give an algorithm that computes the visibility graph at the start of the flight, all time parameters at which the topology of the scene changes, and the corresponding topology changes. The algorithm has running time0(n + k + p) logn), wheren is the number of spheres in the scene;p is the number of transparent topology changes (the number of different scene topologies visible along the flight path, assuming that all spheres are transparent); andk denotes the number of vertices (conflicts) which are in the (transparent) visibility graph at the start and do not disappear during the flight.The second author was supported by the ESPRIT II Basic Research Actions Program, under Contract No. 3075 (project ALCOM).     

Exact Linear Thermodynamic Evolution Equations from the Robertson Formalism

A linear evolution equation for a thermodynamic variable F, odd under time-reversal, is obtained from the exact equation derived by Robertson from the Liouville equation for the information-theoretic phase-space distribution. One obtains an exact expression for , the relaxation time for F. For very short , is time-independent for t > if C(t) F{exp(-i t)}Fo, the equilibrium time correlation, decays exponentially for t > . is the Liouville operator. So long as C(t) is such that decays rapidly to a steady-state value, the t limit of agrees with the fluctuation-dissipation theorem in applications to fluid transport.     

Improving A Solution's Quality Through Parallel Processing

The primary purpose of parallel computation is the fast execution of computational tasks that are too slow to perform sequentially. However, it was shown recently that a second equally important motivation for using parallel computers exists: Within the paradigm of real-time computation, some classes of problems have the property that a solution to a problem in the class computed in parallel is better than the one obtained on a sequential computer. What represents a better solution depends on the problem under consideration. Thus, for optimization problems, better means closer to optimal. Similarly, for numerical problems, a solution is better than another one if it is more accurate. The present paper continues this line of inquiry by exploring another class enjoying the aforementioned property, namely, cryptographic problems in a real-time setting. In this class, better means more secure. A real-time cryptographic problem is presented for which the parallel solution is provably, considerably, and consistently better than a sequential one.It is important to note that the purpose of this paper is not to demonstrate merely that a parallel computer can obtain a better solution to a computational problem than one derived sequentially. The latter is an interesting (and often surprising) observation in its own right, but we wish to go further. It is shown here that the improvement in quality can be arbitrarily high (and certainly superlinear in the number of processors used by the parallel computer). This result is akin to superlinear speedup—a phenomenon itself originally thought to be impossible.     

A New Implementation of Automath

This paper presents aut, a modern Automath checker. It is a straightforward re-implementation of the Zandleven Automath checker from the seventies. It was implemented about five years ago, in the programming language C. It accepts both the AUT-68 and AUT-QE dialects of Automath. This program was written to restore a damaged version of Jutting's translation of Landau's Grundlagen. Some notable features: It is fast. On a 1 GHz machine it will check the full Jutting formalization (736 K of nonwhitespace Automath source) in 0.6 seconds. Its implementation of -terms does not use named variables or de Bruijn indices (the two common approaches) but instead uses a graph representation. In this representation variables are represented by pointers to a binder. The program can compile an Automath text into one big Automath single line-style -term. It outputs such a term using de Bruijn indices. (These -terms cannot be checked by modern systems like Coq or Agda, because the -typed -calculi of de Bruijn are different from the -typed -calculi of modern type theory.)The source of aut is freely available on the Web at the address .     

Constructing sets of functions which have a givenF-cardinality

The termF-cardinality of (=F-card()) is introduced whereF: ^{n n} is a partial function and is a set of partial functionsf: ^{n n} . TheF-cardinality yields a lower bound for the worst-case complexity of computingF if only functionsf can be evaluated by the underlying abstract automaton without conditional jumps. This complexity bound isindependent from the oracles available for the abstract machine. Thus it is shown that any automaton which can only apply the four basic arithmetic operations needs (n logn) worst-case time to sortn numbers; this result is even true if conditional jumps witharbitrary conditions are possible. The main result of this paper is the following: Given a total functionF: ^{n n} and a natural numberk, it is almost always possible to construct a set such that itsF-cardinality has the valuek; in addition, can be required to be closed under composition of functionsf,g . Moreover, ifF is continuous, then consists of continuous functions.     

Predicting Protein Secondary Structure Using Stochastic Tree Grammars

We propose a new method for predicting protein secondary structure of a given amino acid sequence, based on a training algorithm for the probability parameters of a stochastic tree grammar. In particular, we concentrate on the problem of predicting -sheet regions, which has previously been considered difficult because of the unbounded dependencies exhibited by sequences corresponding to -sheets. To cope with this difficulty, we use a new family of stochastic tree grammars, which we call Stochastic Ranked Node Rewriting Grammars, which are powerful enough to capture the type of dependencies exhibited by the sequences of -sheet regions, such as the parallel and anti-parallel dependencies and their combinations. The training algorithm we use is an extension of the inside-outside algorithm for stochastic context-free grammars, but with a number of significant modifications. We applied our method on real data obtained from the HSSP database (Homology-derived Secondary Structure of Proteins Ver 1.0) and the results were encouraging: Our method was able to predict roughly 75 percent of the -strands correctly in a systematic evaluation experiment, in which the test sequences not only have less than 25 percent identity to the training sequences, but are totally unrelated to them. This figure compares favorably to the predictive accuracy of the state-of-the-art prediction methods in the field, even though our experiment was on a restricted type of -sheet structures and the test was done on a relatively small data size. We also stress that our method can predict the structure as well as the location of -sheet regions, which was not possible by conventional methods for secondary structure prediction. Extended abstracts of parts of the work presented in this paper have appeared in (Abe & Mamitsuka, 1994) and (Mamitsuka & Abe, 1994).     

Design sensitivity analysis of nonlinear dynamic response of structural and mechanical systems

This paper describes a unified variational theory for design sensitivity analysis of nonlinear dynamic response of structural and mechanical systems for shape, nonshape, material and mechanical properties selection, as well as control problems. The concept of an adjoint system, the principle of virtual work and a Lagrangian-Eulerian formulation to describe the deformations and the design variations are used to develop a unified view point. A general formula for design sensitivity analysis is derived and interpreted for usual performance functionals. Analytical examples are utilized to demonstrate the use of the theory and give insights for application to more complex problems that must be treated numerically.Derivatives The comma notation for partial derivatives is used, i.e. G,_u = G/u. An upper dot represents material time derivative, i.e. ü = ²u/t². A prime implies derivative with respect to the time measured in the reference time-domain, i.e. u = du/d.     

Mechanizing set theory

Fairly deep results of Zermelo-Frænkel (ZF) set theory have been mechanized using the proof assistant Isabelle. The results concern cardinal arithmetic and the Axiom of Choice (AC). A key result about cardinal multiplications is =, where is any infinite cardinal. Proving this result required developing theories of orders, order-isomorphisms, order types, ordinal arithmetic, cardinals, etc.; this covers most of Kunen, Set Theory, Chapter I. Furthermore, we have proved the equivalence of 7 formulations of the Well-ordering Theorem and 20 formulations of AC; this covers the first two chapters of Rubin and Rubin, Equivalents of the Axiom of Choice, and involves highly technical material. The definitions used in the proofs are largely faithful in style to the original mathematics.     

Separating complexity classes related to bounded alternating ω-branching programs

We develop a theory of communication within branching programs that provides exponential lower bounds on the size of branching programs that are bounded alternating. Our theory is based on the algebraic concept of -branching programs, : , a semiring homomorphism, that generalizes ordinary branching programs, -branching programs [M2] andMOD _p-branching programs [DKMW].Due to certain exponential lower and polynomial upper bounds on the size of bounded alternating -branching programs we are able to separate the corresponding complexity classesN _ba ,co-N _{ba ba} , andMOD _p - _ba ,p prime, from each other, and from that classes corresponding to oblivious linear length-bounded branching programs investigated in the past.     

Unextendible Product Bases and Locally Unconvertible Bound Entangled States

Mutual convertibility of bound entangled states under local quantum operations and classical communication (LOCC) is studied. We focus on states associated with unextendible product bases (UPB) in a system of three qubits. A complete classification of such UPBs is suggested. We prove that for any pair of UPBs S and T the associated bound entangled states _S and _T cannot be converted to each other by LOCC, unless S and T coincide up to local unitaries. More specifically, there exists a finite precision (S,T) > 0 such that for any LOCC protocol mapping _S into a probabilistic ensemble (p, ), the fidelity between _T and any possible final state satisfies F(_T, ) = 1 - (S,T).PACS: 03.65.Bz; 03.67.-a; 89.70+c.     

Information Gaps as Communication Needs: A New Semantic Foundation for Some Non-Classical Logics

Semantics connected to some information based metaphor are well-known in logic literature: a paradigmatic example is Kripke semantic for Intuitionistic Logic. In this paper we start from the concrete problem of providing suitable logic-algebraic models for the calculus of attribute dependencies in Formal Contexts with information gaps and we obtain an intuitive model based on the notion of passage of information showing that Kleene algebras, semi-simple Nelson algebras, three-valued ukasiewicz algebras and Post algebras of order three are, in a sense, naturally and directly connected to partially defined information systems. In this way wecan provide for these logic-algebraic structures a raison dêetre different from the original motivations concerning, for instance, computability theory.     

The π-Calculus in Direct Style

We introduce a calculus which is a direct extension of both the and the calculi. We give a simple type system for it, that encompasses both Curry's type inference for the -calculus, and Milner's sorting for the -calculus as particular cases of typing. We observe that the various continuation passing style transformations for -terms, written in our calculus, actually correspond to encodings already given by Milner and others for evaluation strategies of -terms into the -calculus. Furthermore, the associated sortings correspond to well-known double negation translations on types. Finally we provide an adequate CPS transform from our calculus to the -calculus. This shows that the latter may be regarded as an assembly language, while our calculus seems to provide a better programming notation for higher-order concurrency. We conclude by discussing some alternative design decisions.     

A Fermat-like Principle for Chemical Reactions in Heterogeneous Systems

We formulate a variational principle of Fermat type for chemical kinetics in heterogeneous reacting systems. The principle is consistent with the notion of intrinsic reaction coordinate (IRC), the idea of chemical resistance (CR) and the second law of thermodynamics. The Lagrangian formalism applies a nonlinear functional of entropy production that follows from classical (single-phase) nonequilibrium thermodynamics of chemically reacting systems or its extension for multiphase systems involving interface reactions and transports. For a chemical flux, a law of bending is found which implies that — by minimizing the total resistance — the chemical ray spanned between two given points takes the shape assuring its relatively large part in a region of lower chemical resistivity (a rarer region of the medium). In effect, the chemical flux bends into the direction that ensures its shape consistent with the longest residence of the chemical complex in regions of lower resistivity. The dynamic programming method quantifies the chemical rays and related wavefronts along the reaction coordinate.     

Automatic Extraction of Collocations From Korean Text

In this paper, we propose a statistical method to automaticallyextract collocations from Korean POS-tagged corpus. Since a large portion of language is represented by collocation patterns, the collocational knowledge provides a valuable resource for NLP applications. One difficulty of collocation extraction is that Korean has a partially free word order, which also appears in collocations. In this work, we exploit four statistics, frequency,randomness, convergence, and correlation' in order to take into account the flexible word order of Korean collocations. We separate meaningful bigrams using an evaluation function based on the four statistics and extend the bigrams to n-gram collocations using a fuzzy relation. Experiments show that this method works well for Korean collocations.