Abstract. We distinguish three abstraction strata in software design statements: (i) Strategic design statements (‘architectural design’) determine global constraints, such as programming paradigms, architectural styles, component-based software engineering standards, design principles, and law-governed regularities. (ii) Tactical design statements (‘detailed design’) determine local constraints, such as design patterns, programming idioms, and refactorings. (iii) Implementation statements determine specific properties of the implementation, such as class diagrams and program documentation. Seeking to ground the distinction between Strategic, Tactical, and Implementation statements in a well-defined vocabulary, we define criteria of distinction in mathematical logic. We present the Intension/Locality Hypothesis, postulating that the spectrum of software design statements is divided into three well-defined ‘abstraction classes ’ as follows: (i) The class of non-local statements (a_) contains Strategic statements; (ii) The class of local and intensional statements (_\) contains Tactical statements; (iii) The class of ‘local and extensional ’ statements (_X) contains Implementation

So far in this book we have discussed symmetric and antisymmetric relationships between particular words in a graph or a hierarchy, described one way to learn symmetric relationships from text, and shown how to use ideas such as similarity measures and transitivity to find ‘nearest neighbours ’ of a particular word. But ideally we should be able to measure the similarity or distance between any pair of words or concepts. To some extent, this is possible in graphs and taxonomies by finding the lengths of paths between concepts, but there are problems with this. First of all, finding shortest paths is often computationally expensive and may take a long time. Secondly, we might not have a reliable taxonomy, and as we’ve seen already, that there is a short path between two words in a graph doesn’t necessarily mean that they’re very similar, because the links in this short path may have arisen from very different contexts. Thirdly, the meanings of words we encounter in documents and corpora may be very different from those given by a general taxonomy such as WordNet — for example, WordNet 2.0 only gives the fruit and tree meanings for the word apple, which is a stark contrast with the top 10 pages returned by Google when doing an internet search with the query apple, which are all about Apple Computers. Another limitation of our methods so far is that we have focussed our attention purely on individual concepts, mainly single words. Ideally, we should be able to find the similarity between two arbitrary collections of words, and quickly. For this, we need some process for semantic composition — working out how to represent the meaning of a sentence or document based on the meaning of the words it contains.

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In this article, we canvass a few of the interesting topics that philosophers can pursue as part of the simultaneous study of logic and metaphysics. To keep the discussion to a manageable length, we limit our survey to deductive, as opposed to inductive, logic. Though most of this article

The main objective of this paper is to examine how theories of truth and reference that are in a broad sense Fregean in character are threatened by antinomies; in particular by the Epimenides paradox and versions of the socalled Russell-Myhill antinomy, an intensional analogue of Russell’s more well-known paradox for extensions. Frege’s ontology of propositions and senses has recently received renewed interest in connection with minimalist theories that take propositions (thoughts) and senses (concepts) as the primary bearers of truth and reference. In this paper, I will present a rigorous version of Frege’s theory of sense and denotation and show that it leads to antinomies. I am also going to discuss ways of modifying Frege’s semantical and ontological framework in order to avoid the paradoxes. In this connection, I explore the possibility of giving up the Fregean assumption of a universal domain of absolutely all objects, containing in addition to extensional objects also abstract intensional ones like propositions and singular concepts. I outline a cumulative hierarchy of Fregean propositions and senses, in analogy with Gödel’s hierarchy of constructible sets. In this hierarchy, there is no domain of all objects. Instead, every domain of objects is extendible with new objects that, on pain of contradiction, cannot belong to the given domain. According to this approach, there is no domain containing absolutely all propositions or absolutely all senses. 1.