Alternative Translation Techniques for Propositional and First-Order Modal Logics

We describe and analyze techniques, other than the standard relational/functional methods, for translating validity problems of modal logics into first-order languages. For propositional modal logics we summarize the -as-Pow method, a complete and automatic translation into a weak set theory, and then describe an alternative method, which we call algebraic, that achieves the same full generality of -as-Pow but is simpler and computationally more attractive. We also discuss the relationships between the two methods, showing that -as-Pow generalizes to the first-order case. For first-order modal logics, we describe two extensions, of different degrees of generality, of -as-Pow to logics of rigid designators and constant domains.     

Hierarchies of modal and temporal logics with reference pointers

We introduce and study hierarchies of extensions of the propositional modal and temporal languages with pairs of new syntactic devices: point of reference-reference pointer which enable semantic references to be made within a formula. We propose three different but equivalent semantics for the extended languages, discuss and compare their expressiveness. The languages with reference pointers are shown to have great expressive power (especially when their frugal syntax is taken into account), perspicuous semantics, and simple deductive systems. For instance, Kamp's and Stavi's temporal operators, as well as nominals (names, clock variables), are definable in them. Universal validity in these languages is proved undecidable. The basic modal and temporal logics with reference pointers are uniformly axiomatized and a strong completeness theorem is proved for them and extended to some classes of their extensions.     

The dynamic clusters method in nonhierarchical clustering

Given a finite setE R ⁿ, the problem is to find clusters (or subsets of similar points inE) and at the same time to find the most typical elements of this set. An original mathematical formulation is given to the problem. The proposed algorithm operates on groups of points, called samplings (samplings may be called multiple centers or cores); these samplings adapt and evolve into interesting clusters. Compared with other clustering algorithms, this algorithm requires less machine time and storage. We provide some propositions about nonprobabilistic convergence and a sufficient condition which ensures the decrease of the criterion. Some computational experiments are presented.     

Branching versus linear logics yet again

A brief overview is given of the temporal logics used in concurrent program verification and in database and systems specification. The properties of the underlying modal frame structures are analysed. The relative advantages of the linear and branching approaches are discussed. The state versus path formulas controversy is revisited. A meta-linear operatorL is proposed and compared with the in all trajectories operator considered in the language CTL*. The usefulness of the new operator within the context of a layered methodology for database and information systems specification and verification is illustrated. The operator is seen as a frame change operator and other interesting operators of this class are referred. Finitary and infinitary axiomatisations are given for the operatorL. The proof of the completeness of the infinitary axiomatisation is briefly outlined. This proof requires an appropriate extension of the usual Henkin methods.     

Modalities in linear logic weaker than the exponential “of course”: Algebraic and relational semantics

We present a semantic study of a family of modal intuitionistic linear systems, providing various logics with both an algebraic semantics and a relational semantics, to obtain completeness results. We call modality a unary operator on formulas which satisfies only one rale (regularity), and we consider any subsetW of a list of axioms which defines the exponential of course of linear logic. We define an algebraic semantics by interpreting the modality as a unary operation on an IL-algebra. Then we introduce a relational semantics based on pretopologies with an additional binary relationr between information states. The interpretation of is defined in a suitable way, which differs from the traditional one in classical modal logic. We prove that such models provide a complete semantics for our minimal modal system, as well as, by requiring the suitable conditions onr (in the spirit of correspondence theory), for any of its extensions axiomatized by any subsetW as above. We also prove an embedding theorem for modal IL-algebras into complete ones and, after introducing the notion of general frame, we apply it to obtain a duality between general frames and modal IL-algebras.     

Modal Pure Type Systems

We present a framework for intensional reasoning in typed -calculus. In this family of calculi, called Modal Pure Type Systems (MPTSs), a propositions-as-types-interpretation can be given for normal modal logics. MPTSs are an extension of the Pure Type Systems (PTSs) of Barendregt (1992). We show that they retain the desirable meta-theoretical properties of PTSs, and briefly discuss applications in the area of knowledge representation.     

Extended topology and systems

In this paper is indicated the possible utility of isotonic spaces as a background language for discussing systems. In isotonic spaces the basic duality between neighborhood and convergent first achieves a proper background permitting applications beyond the scope of topological spaces. A generalization of continuity of mappings based on ancestral relations is presented and this definition is applied to establish a necessary and sufficient condition that mappings preserve connectedness. Fortunately for systems theory, it is not necessary to have infinite sets or infinitary operators to apply definitions of neighborhood, convergents, continuity and connectedness.This work was supported in part by a grant from the National Science Foundation.     

A modal contrastive logic: The logic of ‘but’

In this paper we present a modal approach to contrastive logic, the logic of contrasts as these appear in natural language conjunctions such as but. We use a simple modal logic, which is an extension of the well-knownS5 logic, and base the contrastive operators proposed by Francez in [2] on the basic modalities that appear in this logic. We thus obtain a logic for contrastive operators that is more in accord with the tradition of intensional logic, and that, moreover — we argue — has some more natural properties. Particularly, attention is paid to nesting contrastive operators. We show that nestings of but give quite natural results, and indicate how nestings of other contrastive operators can be done adequately. Finally, we discuss the example of the Hangman's Paradox and some similarities (and differences) with default reasoning. But but us no buts, as they say.Also partially supported by Nijmegen University, Toernooiveld, 6525 ED Nijmegen, The Netherlands.     

Interpretations of open default theories in non-monotonic logics

It is shown that the translation of an open default into a modal formula x(L(x)LM ₁ (x)...LM _m (x)w(x)) gives rise to an embedding of open default systems into non-monotonic logics.     

Deep X-ray lithography using mask with integrated electrothermal actuator

We present a deep X-ray mask with integrated bent-beam electrothermal actuator for the fabrication of 3D microstructures with curved surface. The mask absorber is electroplated on the shuttle mass, which is supported by a pair of 20-m-thick single crystal silicon bent-beam electrothermal actuators and oscillated in a rectilinear direction due to the thermal expansion of the bent-beams. The width of each bent-beam is 10 m or 20 m and the length and bending angle are 1 mm and 0.1 rad, respectively, and the shuttle mass size is 1 mm × 1 mm. For 10-m-wide bent-beams, the shuttle mass displacement is around 15 m at 180 mW (3.6 V) dc input power. For 20-m-wide bent-beams, the shuttle mass displacement is around 19 m at 336 mW (4.2 V) dc input power. Sinusoidal cross-sectional PMMA microstructures with a pitch of 40 m and a height of 20 m are fabricated by 0.5 Hz, 20-m-amplitude sinusoidal shuttle mass oscillation.This research, under the contract project code MS-02-338-01, has been supported by the Intelligent Microsystem Center, which carries out one of the 21st centurys Frontier R & D Projects sponsored by the Korea Ministry of Science & Technology. Experiments at PLS were supported in part by MOST and POSCO.     

Mesh Selection for a Nearly Singular Boundary Value Problem

In this paper, we investigate the numerical solution of a model equation u _xx = exp(– ) (and several slightly more general problems) when 1 using the standard central difference scheme on nonuniform grids. In particular, we are interested in the error behaviour in two limiting cases: (i) the total mesh point number N is fixed when the regularization parameter 0, and (ii) is fixed when N. Using a formal analysis, we show that a generalized version of a special piecewise uniform mesh 12 and an adaptive grid based on the equidistribution principle share some common features. And the optimal meshes give rates of convergence bounded by |log()| as 0 and N is given, which are shown to be sharp by numerical tests.     

Recognition of handwritten musical notes by a modified Neocognitron

A neural network for recognition of handwritten musical notes, based on the well-known Neocognitron model, is described. The Neocognitron has been used for the what pathway (symbol recognition), while contextual knowledge has been applied for the where (symbol placement). This way, we benefit from dividing the process for dealing with this complicated recognition task. Also, different degrees of intrusiveness in learning have been incorporated in the same network: More intrusive supervised learning has been implemented in the lower neuron layers and less intrusive in the upper one. This way, the network adapts itself to the handwriting of the user. The network consists of a 13×49 input layer and three pairs of simple and complex neuron layers. It has been trained to recognize 20 symbols of unconnected notes on a musical staff and was tested with a set of unlearned input notes. Its recognition rate for the individual unseen notes was up to 93%, averaging 80% for all categories. These preliminary results indicate that a modified Neocognitron could be a good candidate for identification of handwritten musical notes.     

Specification and verification of database dynamics

Summary A framework is proposed for the structured specification and verification of database dynamics. In this framework, the conceptual model of a database is a many sorted first order linear tense theory whose proper axioms specify the update and the triggering behaviour of the database. The use of conceptual modelling approaches for structuring such a theory is analysed. Semantic primitives based on the notions of event and process are adopted for modelling the dynamic aspects. Events are used to model both atomic database operations and communication actions (input/output). Nonatomic operations to be performed on the database (transactions) are modelled by processes in terms of trigger/reaction patterns of behaviour. The correctness of the specification is verified by proving that the desired requirements on the evolution of the database are theorems of the conceptual model. Besides the traditional data integrity constraints, requirements of the form Under condition W, it is guaranteed that the database operation Z will be successfully performed are also considered. Such liveness requirements have been ignored in the database literature, although they are essential to a complete definition of the database dynamics.

Notation

Classical Logic Symbols (Appendix 1) for all (universal quantifier) - exists at least once (existential quantifier) - ¬ no (negation) - implies (implication) - is equivalent to (equivalence) - and (conjunction) - or (disjunction) Tense Logic Symbols (Appendix 1) G always in the future - G ₀ always in the future and now - F sometime in the future - F ₀ sometime in the future or now - H always in the past - H ₀ always in the past and now - P sometime in the past - P ₀ sometime in the past or now - X in the next moment - Y in the previous moment - L always - M sometime Event Specification Symbols (Sects. 3 and 4.1) (x) means immediately after the occurrence of x - (x) means immediately before the occurrence of x - (x) means x is enabled, i.e., x may occur next - { } ({w ₁} x{w ₂}) states that if w ₁ holds before the occurrence of x, then w ₂ will hold after the occurrence of x (change rule) - [ ] ([oa₁, ..., oa_n]x) states that only the object attributes oa₁, ..., oa _n are modifiable by x (scope rule) - {{ }} ({{w}}x) states that if x may occur next, then w holds (enabling rule) Process Specification Symbols (Sects. 5.3 and 5.4) :: for causal rules - for behavioural rules Transition-Pattern Composition Symbols (Sects. 5.2 and 5.3) ; sequential composition - ¦ choice composition - parallel composition - :| guarded alternative composition Location Predicates (Sect. 5.2) (z) means immediately after the occurrence of the last event of z (after) - (z) means immediately before the occurrence of the first event of z (before) - (z) means after the beginning of z and before the end of z (during) - ( z) means before the occurrence of an event of z (at)     

Context-free text grammars

A text is a triple=(, ₁, ₂) such that is a labeling function, and ₁ and ₂ are linear orders on the domain of ; hence may be seen as a word (, ₁) together with an additional linear order ₂ on the domain of . The order ₂ is used to give to the word (, ₁) itsindividual hierarchical representation (syntactic structure) which may be a tree but it may be also more general than a tree. In this paper we introducecontext-free grammars for texts and investigate their basic properties. Since each text has its own individual structure, the role of such a grammar should be that of a definition of a pattern common to all individual texts. This leads to the notion of ashapely context-free text grammar also investigated in this paper.     

The impact of artificial intelligence on leisure

Two views of AI in leisure and the work-place and two views of society are discussed. There is a conceptualisation of AI systems enhancing people in their work and leisure and another of AI automata which tends to degrade and replace human activity. Researchers tend to resolve into Optimists who work within a micro-sociological view and see AI systems as inevitable and beneficent. Others are Pessimists who adopt a macro-sociological view and see AI in its automata role and deliterious social consequences. These polarised perspectives must be integrated as only enhancing AI is socially acceptable.     

Redesign of a Systems Engineering Language: Formalisation of χ

This paper describes the redesign of a systems engineering language called . This is an engineering language designed to specify and analyse industrial systems. The main objective of this redesign was to enable mathematical reasoning about specifications. We discuss the original language, the requirements and design decisions, and the resulting syntax and semantics of the new version of , called . In particular, we elaborate on semantical aspects of s time model.     

Adding a temporal dimension to a logic system

We introduce a methodology whereby an arbitrary logic system L can be enriched with temporal features to create a new system T(L). The new system is constructed by combining L with a pure propositional temporal logic T (such as linear temporal logic with Since and Until) in a special way. We refer to this method as adding a temporal dimension to L or just temporalising L. We show that the logic system T(L) preserves several properties of the original temporal logic like soundness, completeness, decidability, conservativeness and separation over linear flows of time. We then focus on the temporalisation of first-order logic, and a comparison is make with other first-order approaches to the handling of time.     

On characterizing the “knee” of the Pareto curve based on Normal-Boundary Intersection

This paper deals with the issue of generating one Pareto optimal point that is guaranteed to be in a desirable part of the Pareto set in a given multicriteria optimization problem. A parameterization of the Pareto set based on the recently developed normal-boundary intersection technique is used to formulate a subproblem, the solution of which yields the point of maximum bulge, often referred to as the knee of the Pareto curve. This enables the identification of the good region of the Pareto set by solving one nonlinear programming problem, thereby bypassing the need to generate many Pareto points. Further, this representation extends the concept of the knee for problems with more than two objectives. It is further proved that this knee is invariant with respect to the scales of the multiple objective functions.The generation of this knee however requires the value of each objective function at the minimizer of every objective function (the pay-off matrix). The paper characterizes situations when approximations to the function values comprising the pay-off matrix would suffice in generating a good approximation to the knee. Numerical results are provided to illustrate this point. Further, a weighted sum minimization problem is developed based on the information in the pay-off matrix, by solving which the knee can be obtained.     

Grain Filters

Motivated by operators simplifying the topographic map of a function, we study the theoretical properties of two kinds of grain filters. The first category, discovered by L. Vincent, defines grains as connected components of level sets and removes those of small area. This category is composed of two filters, the maxima filter and the minima filter. However, they do not commute. The second kind of filter, introduced by Masnou, works on shapes, which are based on connected components of level sets. This filter has the additional property that it acts in the same manner on upper and lower level sets, that is, it commutes with an inversion of contrast. We discuss the relations of Masnou's filter with other classes of connected operators introduced in the literature. We display some experiments to show the main properties of the filters discussed above and compare them.     

A priori Probability That Two Qubits Are Unentangled

In a previous study (P. B. Slater, Eur. Phys. J. B. 17, 471 (2000)), several remarkably simple exact results were found, in certain specialized m-dimensional scenarios (m 4), for the a priori probability that a pair of qubits is unentangled/separable. The measure used was the volume element of the Bures metric (identically one-fourth the statistical distinguishability [SD] metric). Here, making use of a newly-developed (Euler angle) parameterization of the 4 × 4 density matrices of Tilma, Byrd and Sudarshan, we extend the analysis to the complete 15-dimensional convex set (C) of arbitrarily paired qubits—the total SD volume of which is known to be ⁸ / 1680 = ⁸/2⁴ 3 5 7 5.64794. Using advanced quasi-Monte Carlo procedures (scrambled Halton sequences) for numerical integration in this high-dimensional space, we approximately (5.64851) reproduce that value, while obtaining an estimate of 0.416302 for the SD volume of separable states. We conjecture that this is but an approximation to ⁶/2310 = ⁶ / (2 3 5 7 11) 0.416186. The ratio of the two volumes, 8/11²2 .0736881, would then constitute the exact Bures/SD probability of separability. The SD area of the 14-dimensional boundary of C is 142⁷/12285 = 2 71⁷/3³ 5 7 13 34.911, while we obtain a numerical estimate of 1.75414 for the SD area of the boundary of separable states. PACS: 03.67.-; 03.65.Ud; 02.60.Jh; 02.40.Ky