The language model is one of the most important knowledge sources for statistical machine translation. In this article, we present two extensions to standard n-gram language models in statistical machine translation: a backward language model that augments the conventional forward language model, and a mutual information trigger model which captures long-distance dependencies that go beyond the scope of standard n-gram language models. We introduce algorithms to integrate the two proposed models into two kinds of state-of-the-art phrase-based decoders. Our experimental results on Chinese/Spanish/Vietnamese-to-English show that both models are able to significantly improve translation quality in terms of BLEU and METEOR over a competitive baseline.

The authors have been involved in ontological modeling of function for over 15 years. As an instance of the revisionary approach discussed in Vermaas's position paper, we have proposed an ontological definition of function and a modeling framework based on it, which has been deployed in industry. In addition, as an instance of the overarching approach, we have proposed a reference ontology of function that explains some kinds, definitions, and practical expressions of functions. In this paper, we explain our methodology in an overarching approach based on perspectives for capturing functions. When one captures a function of an artifact, one focuses on a specific aspect of the artifact from a specific perspective. In this paper, we conceptualize such perspectives behind the reference ontology. In addition, based on our experiences in deployment in an industrial setting, we report some solutions, such as ontological modeling guidelines, for overcoming some of the difficulties faced in the practical functional modeling approach described in Eckert's position paper. Our findings suggest that such solutions will help engineers to describe consistent functional models compliant with a single definition of function.

Functions are important in designing. However, several issues hinder progress with the understanding and usage of functions: lack of a clear and overarching definition of function, lack of overall justifications for the inevitability of the multiple views of function, and scarcity of systematic attempts to relate these views with one another. To help resolve these, the objectives of this research are to propose a common definition of function that underlies the multiple views in literature and to identify and validate the views of function that are logically justified to be present in designing. Function is defined as a change intended by designers between two scenarios: before and after the introduction of the design. A framework is proposed that comprises the above definition of function and an empirically validated model of designing, extended generate, evaluate, modify, and select of state-change, and an action, part, phenomenon, input, organ, and effect model of causality (Known as GEMS of SAPPhIRE), comprising the views of activity, outcome, requirement–solution–information, and system–environment. The framework is used to identify the logically possible views of function in the context of designing and is validated by comparing these with the views of function in the literature. Describing the different views of function using the proposed framework should enable comparisons and determine relationships among the various views, leading to better understanding and usage of functions in designing.

Research on design and analysis of complex systems has led to many functional representations with several meanings of function. This work on conceptual design uses a family of representations called structure–behavior–function (SBF) models. The SBF family ranges from behavior–function models of abstract design patterns to drawing–shape–SBF models that couple SBF models with visuospatial knowledge of technological systems. Development of SBF modeling is an instance of cognitively oriented artificial intelligence research that seeks to understand human cognition and build intelligent agents for addressing complex tasks such as design. This paper first traces the development of SBF modeling as our perspective on design evolved from that of problem solving to that of memory and learning. Next, the development of SBF modeling as a case study is used to abstract some of the core principles of an artificial intelligence methodology for functional modeling. Finally, some implications of the artificial intelligence methodology for different meanings of function are examined.

Research into visual reasoning up to now has focused on images that are literal depictions of their objects. I argue in this article that an important further mode of visual reasoning operates on images that depict objects metaphorically. Such images form part of the class of expressive symbols: they are found, for example, in allegorical representations in works of visual art, studied by iconology. They were also a common way of encapsulating insights about the universe in natural philosophy in the Renaissance. Many writers assume that expressive symbols have vanished from modern science, but I argue in the second part of the article that mathematical law statements in present-day physics should be seen, in part, as images that constitute expressive symbols of the world. In support of this view, I offer evidence that law statements relate to their objects metaphorically and that physicists engage with them primarily through visual inspection and visual reasoning.

In this position paper, the ambiguity of functional descriptions in engineering is considered from a methodological point of view. Four responses to this ambiguity are discussed, ranging from defining a single meaning of function and rejecting the different meanings that are currently used in engineering to accepting these meanings as coexisting in engineering and taking function as a family resemblance concept. Rejecting the different meanings is described as the straightforward response to resolving the ambiguity of functional descriptions, yet in engineering research and design methodology it rather seems to be accepted that engineers do use the coexisting meanings side by side. In this paper, explanations are given of why this practice is beneficial to engineering. Then it is explored how the particular meaning that engineers attach to function depends on the tasks for which functional descriptions are used. Finally, the methodological implications of the four responses to the ambiguity of functional descriptions are discussed.

Visuo is an implemented Python program that models visual reasoning. It takes as input a description of a scene in words (e.g. ‘small dog on a sunny street’) and produces estimates of the quantitative magnitudes of the qualitative input (e.g. the size of the dog and the brightness of the street). We claim that reasoners transfer quantitative knowledge to new concepts from distributions of familiar concepts in memory. We also claim that visuospatial magnitudes should be stored as distributions over fuzzy sets. We show that Visuo successfully predicts quantitative knowledge to new concepts.

Function is an ambiguous concept, whereas having explicit and precise concepts is critical for building a systematic science of engineering design. Based on Bunge's scientific ontology, this paper is devoted to developing an explicit and precise concept of function for design science. First, we attempt to clarify the concept of behavior, which is closely related to function and is also shown as an ambiguous concept in engineering. Second, the concept of action is imported from scientific ontology into design science. Third, a scientific ontology based concept of function is proposed, together with an ontology-based functional taxonomy. A case of a function definition of a civil aircraft type demonstrates that the proposed concept of function is more explicit and precise than previous ones, and it can lead to better functional design results.

In this article I present and discuss some criteria to provide a diagrammatic classification. Such a classification is of use for exploring in detail the domain of diagrammatic reasoning. Diagrams can be classified in terms of the use we make of them—static or dynamic—and of the correspondence between their space and the space of the data they are intended to represent. The investigation is not guided by the opposition visual vs. non-visual, but by the idea that there is a continuous interaction between diagrams and language. Diagrammatic reasoning is characterized by a duality, since it refers both to an object, the diagram, having its spatial characteristics, and to a subject, the user, who interprets them. A particular place in the classification is occupied by constructional diagrams, which exhibit for the user instructions for the application of some procedures.

Functional modeling is a very significant part of many different well-known design methodologies. This paper investigates the questions of what functional modeling approaches people use in industry and how they conceptualize functions. Using interviews and the findings from an experiment where 20 individual designers were asked to generate a functional model of a product, the paper highlights the different notions designers associate with the word function. Difficulties associated with functional modeling arise from varied and inconsistent notions of functions as well as wider challenges associated with modeling and the introduction of methods in industry.

Understanding product functions is a key aspect of the work undertaken by engineers involved in complex system design. The support offered to these engineers by existing modeling tools such as the function tree and the function structure is limited because they are not intuitive and do not scale well to deal with real-world engineering problems. A research collaboration between two universities and a major power system company in the aerospace domain has allowed the authors to further develop a method for function analysis known as function analysis diagram that was already in use by line engineers. The capability to generate and edit these diagrams was implemented in the Decision Rationale editor, a software tool for capturing design rationale. This article presents the intended benefits of the method and justifies them using an engineering case study. The results of the research have shown that the function analysis diagram method has a simple notation, permits the modeling of product functions together with structure, allows the generation of rich and accurate descriptions of product functionality, is useful to work with variant and adaptive design tasks, and can coexist with other functional modeling methods.

Function-based design and modeling have been taught, studied, and practiced in various forms for several years with efforts centered on using function modeling to help designers understand problems or to facilitate idea generation. Only limited focus has been placed on potential use for qualitative and quantitative reasoning and analysis of the design concept. This potential for early stage analysis has not been fully explored partly because computational reasoning tools have not been developed for this express purpose. This paper presents a set of requirements and their justification to realize this design enabling tool. The requirements include coverage, consistency, validity against physics laws, domain neutrality, physics-based definitions, normative and descriptive modeling, and qualitative and quantitative modeling and reasoning. Each requirement is defined in concrete terms and illustrated with examples and logic. With the requirements for function-based reasoning and representation clearly identified, future research toward formalizing of function-based design will be more focused and objective validation of proposed representations against these requirements would be possible.

Authors across disciplines propose functional modeling as part of systematic design approaches, in order to support and guide designers during conceptual design. The presented research aims at contributing to a better understanding of the diverse functional modeling approaches proposed across disciplines. The article presents a literature review of 41 modeling approaches from a variety of disciplines. The analysis focuses on what is addressed by functional modeling at which point in the proposed conceptual design process (i.e., in which sequence). The gained insights lead to the identification of specific needs and opportunities, which could support the development of an integrated functional modeling approach. The findings suggest that there is no such shared sequence for functional modeling across disciplines. However, a shared functional modeling perspective has been identified across all reviewed disciplines, which could serve as a common basis for the development of an integrated functional modeling approach.

Let G be a finite graph with minimum degree r. Form a random subgraph Gp of G by taking each edge of G into Gp independently and with probability p. We prove that for any constant ε > 0, if $p=\frac{1+\epsilon}{r}$, then Gp is non-planar with probability approaching 1 as r grows. This generalizes classical results on planarity of binomial random graphs.

Are counterfactuals with true antecedents and consequents automatically true? That is, is Conjunction Conditionalization: (X ∧ Y) ⊃ (X > Y) valid? Stalnaker and Lewis think so, but many others disagree. We note here that the extant arguments for Conjunction Conditionalization are unpersuasive, before presenting a family of more compelling arguments. These arguments rely on some standard theorems of the logic of counterfactuals as well as a plausible and popular semantic claim about certain semifactuals. Denying Conjunction Conditionalization, then, requires rejecting other aspects of the standard logic of counterfactuals or else our intuitive picture of semifactuals.