We describe a polymorphic, typed lambda calculus with substructural features. This calculus extends the first-order substructural lambda calculus αλ associated with bunched logic. A particular novelty of our new calculus is the substructural treatment of second-order variables. This is accomplished through the use of bunches of type variables in typing contexts. Both additive and multiplicative forms of polymorphic abstraction are then supported. The calculus has sensible proof-theoretic properties and a straightforward categorical semantics using indexed categories. We produce a model for additive polymorphism with first-order bunching based on partial equivalence relations. We consider additive and multiplicative existential quantifiers separately from the universal quantifiers.

We introduce a notion of reducibility of representations of topological spaces and study some basic properties of this notion for domain representations.

A representation reduces to another if its representing map factors through the other representation. Reductions form a pre-order on representations. A spectrum is a class of representations divided by the equivalence relation induced by reductions. We establish some basic properties of spectra, such as, non-triviality. Equivalent representations represent the same set of functions on the represented space.

Within a class of representations, a representation is universal if all representations in the class reduce to it. We show that notions of admissibility, considered both for domains and within Weihrauch's TTE, are universality concepts in the appropriate spectra. Viewing TTE representations as domain representations, the reduction notion here is a natural generalisation of the one from TTE.

To illustrate the framework, we consider some domain representations of real numbers and show that the usual interval domain representation, which is universal among dense representations, does not reduce to various Cantor domain representations. On the other hand, however, we show that a substructure of the interval domain more suitable for efficient computation of operations is equivalent to the usual interval domain with respect to reducibility.

The simulation of synthetic humans inhabiting virtual environments is a current research topic with a great number of behavioral problems to be tackled. Semantical virtual environments (SVEs) have recently been proposed not only to ease world modeling but also to enhance the agent–object and agent–agent interaction. Thus, we propose the use of ontologies to define the world’s knowledge base and to introduce semantic levels of detail that help the sensorization of complex scenes—containing lots of interactive objects. The object taxonomy also helps to create general and reusable operativity for autonomous characters—for example, liquids can be poured from containers such as bottles. On the other hand, we use the ontology to define social relations among agents within an artificial society. These relations must be taken into account in order to display socially acceptable decisions. Therefore, we have implemented a market-based social model that reaches coordination and sociability by means of task exchanges. This paper presents a multi-agent framework oriented to simulate socially intelligent characters in SVEs. The framework has been successfully tested in three-dimensional (3D) dynamic scenarios while simulating a virtual university bar, where groups of waiters and customers interact with both the objects in the scene and the other virtual agents, finally displaying complex social behaviors.

We have developed two different art applications as a way of guiding and testing of our technical work in crowd simulation and interface devices. In this paper, we describe both of them as well as the systems used to implement them. ‘Crowds’ is an immersive art installation with stereo projection based on our development of the specification of crowd behavior using XML and images, a proprietary tangible wind interface, and interactive real-time navigation. ‘UnderCrowds’ deals with large crowds, implemented in the graphics processor, and uses a crowd sensor to make the size of the virtual crowd proportional to the number of spectators crossing in front of the said sensor.

We develop a formal apparatus to be used as a tool in analyzing common kinds of context dependence in natural language, and their interaction with temporal and spatial modalities. It is based on context-operators, which act on wffs. The interplay between the various modalities and the context-operators is one of the main targets of the analysis. Statements made by different people at different times in different places, using the same personal temporal and spatial indexicals, can be represented in the system, and can be combined by sentential connectives and be subject to quantification. The use of spatial modality and the suggested treatment of adverbial phrases are new as far as we know. So is a certain variant of temporal modality. In the nontechnical part, consisting of Sections 1 and 2, we discuss the role that formalisms can, in principle, play in the analysis of linguistic usage; this is followed by a philosophical discussion of various kinds of context dependence. The semitechnical part, Section 3, introduces the system's components, the context, and the modal operators, and explains their use via natural language examples. In Section 4 the formal language and its semantics are defined, in full detail. The temporal and spatial sublanguages constitute separate sorts, which interact through the modal operators and the context-operators. A sound deductive system is given and a completeness result is stated, without proof.

We propose a model for belief which is free of presuppositions. Current models for belief suffer from two difficulties. One is the well known problem of logical omniscience which tends to follow from most models. But a more important one is the fact that most models do not even attempt to answer the question what it means for someone to believe something, and just what it is that is believed. We provide a flexible model which allows us to give meaning to beliefs in general contexts, including the context of animal belief (where action is usually our only clue to a belief), and of human belief which is expressed in language.

The three classical process algebras CCS, CSP and ACP present several differences in their respective technical machinery. This is due, not only to the difference in their operators, but also to the terminology and ‘way of thinking’ of the community that has been (and still is) working with them. In this paper we will first discuss these differences and try to clarify the different usage of terminology and concepts. Then, as a result of this discussion, we define a generic process algebra where each of the basic mechanisms of the three process algebras (including minimal fixpoint based unguarded recursion) is expressed by an operator, and which can be used as an underlying common language. We show an example of the advantages of adopting such a language instead of one of the three more specialised algebras: producing a complete axiomatisation for Milner's observational congruence in the presence of (unguarded) recursion and static operators. More precisely, we provide a syntactical characterisation (allowing as many terms as possible) for the equations involved in recursion operators, which guarantees that transition systems generated by the operational semantics are finite state. Conversely, we show that every process admits a specification in terms of such a restricted form of recursion. We then present an axiomatisation that is ground complete over such a restricted signature. Notably, we also show that the two standard axioms of Milner for weakly unguarded recursion can be expressed using a single axiom only.

We describe several technical tools that prove to be efficient for investigating the rewrite systems associated with an equational specification. These tools consist of introducing a monoid of partial maps, listing the monoid relations corresponding to the local confluence diagrams of the rewrite system, introducing the group presented by these relations, and, finally, replacing the initial rewrite system with an internal process entirely sitting in this group. When the approach can be completed, one typically obtains a practical method for constructing algebras satisfying prescribed equations and for solving the associated word problem. The above techniques have been developed by the first author in a context of general algebra. The goal of this paper is to bring them to the attention of the rewrite system community. We hope that these techniques may be useful for more general rewrite systems.

This paper analyses the interpretation of mathematical entities in the formalisations of languages. Four case studies are considered, covering both denotational and axiomatic approaches. We argue that the usual interpretation consists of direct statements about the language concepts and, occasionally, about the real world; some problems of this approach are discussed. Applying results from philosophical studies into the structure of scientific theories, we propose an alternative interpretation of mathematical entities as statements defining constructed concepts, which can be employed in turn as theoretical models of the language concepts and the world. Though this approach requires us to write hypotheses claiming some similarity between the models and the represented subjects, we reason that it is more adequate for formalising certain languages.

We tackle the problem of studying which kind of functions can occur as complexity functions of formal languages of a certain type. We prove that an important narrow subclass of rational languages contains languages of polynomial complexity of any integer degree over any non-trivial alphabet.

Episturmian morphisms constitute a powerful tool to study episturmian words. Indeed, any episturmian word can be infinitely decomposed over the set of pure episturmian morphisms. Thus, an episturmian word can be defined by one of its morphic decompositions or, equivalently, by a certain directive word. Here we characterize pairs of words directing the same episturmian word. We also propose a way to uniquely define any episturmian word through a normalization of its directive words. As a consequence of these results, we characterize episturmian words having a unique directive word.

To evaluate our three-axis tactile sensor developed in preceding papers, a tactile sensor is mounted on a robotic finger with 3-degrees of freedom. We develop a dual computer system that possesses two computers to enhance processing speed: one is for tactile information processing and the other controls the robotic finger; these computers are connected to a local area network. Three kinds of experiments are performed to evaluate the robotic finger's basic abilities required for dexterous hands. First, the robotic hand touches and scans flat specimens to evaluate their surface condition. Second, it detects objects with parallelepiped and cylindrical contours. Finally, it manipulates a parallelepiped object put on a table by sliding it. Since the present robotic hand performed the above three tasks, we conclude that it is applicable to the dexterous hand in subsequent studies.

The development of a fuzzy wavelet neural network (FWNN) for the prediction of electricity consumption is presented. The fuzzy rules that contain wavelets are constructed. Based on these rules, the structure of FWNN-based system is described. The FWNN system is applied for modeling and prediction of complex time series. The gradient algorithm and genetic algorithm are used for learning of FWNN parameters. The developed FWNN is applied for prediction of electricity consumption. This process has high-order nonlinearity. The statistical data for the last 10 years are used for the development of FWNN prediction model. The effectiveness of the proposed system is evaluated with the results obtained from the simulation of FWNN-based prediction system and with the comparative simulation results of previous related models.

Digital-to-analog converters (DAC) transform signals from the abstract digital domain to the real analog world. In many applications, DACs play a crucial role. Due to variability in the production, various errors arise that influence the performance of the DAC. We focus on the current errors, which describe the fluctuations in the currents of the various unit current elements in the DAC. A key performance measure of the DAC is the Integrated Nonlinearity (INL), which we study in this article. There are several DAC architectures. The most widely used architectures are the thermometer and the binary and the segmented architectures. We study the two extreme architectures, namely the thermometer and the binary architectures. We assume that the current errors are independent and identically normally distributed and reformulate the INL as a functional of a Brownian bridge. We then proceed by investigating these functionals. For the thermometer case, the functional is the maximal absolute value of the Brownian bridge, which has been investigated in the literature. For the binary case, we investigate properties of the functional, such as its mean, variance, and density.

In this article we investigate less restrictive conditions on the model parameters and the underlying distribution function upon which the generalized order statistics are based, which enable one to establish the likelihood ratio and the hazard ratio orderings for p-spacings of generalized order statistic. Some previous works in the literature are extended.

We consider a single-server Markovian queue with synchronized services and setup times. The customers arrive according to a Poisson process and are served simultaneously. The service times are independent and exponentially distributed. At a service completion epoch, every customer remains satisfied with probability p (independently of the others) and departs from the system; otherwise, he stays for a new service. Moreover, the server takes multiple vacations whenever the system is empty.

Some of the transition rates of the underlying two-dimensional Markov chain involve binomial coefficients dependent on the number of customers. Indeed, at each service completion epoch, the number of customers n is reduced according to a binomial (n, p) distribution. We show that the model can be efficiently studied using the framework of q-hypergeometric series and we carry out an extensive analysis including the stationary, the busy period, and the sojourn time distributions. Exact formulas and numerical results show the effect of the level of synchronization to the performance of such systems.

In this article we consider a stochastic game in which each player draws one or two random numbers between 0 and 1. Players can decide to stop after the first draw or to continue for a second draw. The decision is made without knowing the other players’ numbers or whether the other players continue for a second draw. The object of the game is to have the highest total score without going over 1. In the article, we will characterize the optimal stopping rule for each player.

Consider a continuous nonnegative random variable X with mean μ and hazard function h. Assume further that a≤h(t)≤b for all t≥0. Under these constraints, we obtain sharp two-sided bounds for . An application to birth and death processes is discussed.