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Dependently Typed Functional Programs and their Proofs
, 1999
"... Research in dependent type theories [ML71a] has, in the past, concentrated on its use in the presentation of theorems and theoremproving. This thesis is concerned mainly with the exploitation of the computational aspects of type theory for programming, in a context where the properties of programs ..."
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Cited by 70 (13 self)
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Research in dependent type theories [ML71a] has, in the past, concentrated on its use in the presentation of theorems and theoremproving. This thesis is concerned mainly with the exploitation of the computational aspects of type theory for programming, in a context where the properties of programs may readily be specified and established. In particular, it develops technology for programming with dependent inductive families of datatypes and proving those programs correct. It demonstrates the considerable advantage to be gained by indexing data structures with pertinent characteristic information whose soundness is ensured by typechecking, rather than human effort. Type theory traditionally presents safe and terminating computation on inductive datatypes by means of elimination rules which serve as induction principles and, via their associated reduction behaviour, recursion operators [Dyb91]. In the programming language arena, these appear somewhat cumbersome and give rise to unappealing code, complicated by the inevitable interaction between case analysis on dependent types and equational reasoning on their indices which must appear explicitly in the terms. Thierry Coquand’s proposal [Coq92] to equip type theory directly with the kind of
Methodological Principles for Structuring an "Ontology"
, 1995
"... The knowledge used in most AI applications does not rely on a formal model of the domain. Therefore, it has to be normalized to ensure that the formal exploitation of its representation conforms to its meaning in the domain. Considering the intensional (non extensional) nature of concepts, whi ..."
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Cited by 19 (1 self)
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The knowledge used in most AI applications does not rely on a formal model of the domain. Therefore, it has to be normalized to ensure that the formal exploitation of its representation conforms to its meaning in the domain. Considering the intensional (non extensional) nature of concepts, which reflects the essences of the objects they denote, this normalization relies on a commitment on type definitions by necessary and sufficient conditions at the knowledge level. Our claim is that the taxonomic structure that accounts for the intensional nature of the ontology can be nothing but a tree. From this starting point, we derive methodological principles to constrain and justify the structuring of ontological types. Based on this methodology, we advocate understandability of an ontology rather than a putative reusability. 1 Introduction The ontology is the heart of any knowledge description: knowledge is intimately related to the ontology, since it is necessarily expre...
Functional dynamics I: Articulation process
 Physica D 138
, 2000
"... The articulation process of dynamical networks is studied with a functional map, a minimal model for the dynamic change of relationships through iteration. The model is a dynamical system of a function f, not of variables, having a selfreference term f ◦ f, introduced by recalling that operation in ..."
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Cited by 5 (1 self)
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The articulation process of dynamical networks is studied with a functional map, a minimal model for the dynamic change of relationships through iteration. The model is a dynamical system of a function f, not of variables, having a selfreference term f ◦ f, introduced by recalling that operation in a biological system is often applied to itself, as is typically seen in rules in the natural language or genes. Starting from an inarticulate network, two types of fixed points are formed as an invariant structure with iterations. The function is folded with time, until it has finite or infinite piecewiseflat segments of fixed points, regarded as articulation. For an initial logistic map, attracted functions are classified into step, folded step, fractal, and random phases, according to the degree of folding. Oscillatory dynamics are also found, where function values are mapped to several fixed points periodically. The significance of our results to prototype categorization in language is discussed. 1
Languages Of Analogical Strings
, 2000
"... this paper is to establish some fundamental, commonsense hypotheses (axioms) about analogies in general; then to draw from them basic results (theorems) on analogies between strings of symbols in particular; so as to propose a possible definition for languages of analogical strings; and to prove th ..."
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this paper is to establish some fundamental, commonsense hypotheses (axioms) about analogies in general; then to draw from them basic results (theorems) on analogies between strings of symbols in particular; so as to propose a possible definition for languages of analogical strings; and to prove that some famous languages of particular interest to the language processing community are very simple languages in this respect. We further argue that the fact that the property of bounded growth is verified by any such language is in favour of modelling part of natural language using such languages. Our feeling is that analogy between strings of symbols is an operation as fundamental as, e.g.,
The SnowBall Effect of Analogy
"... In previous work, a computational explanation of analogy, a phenomenon by which a new sentence is generated from three other sentences, has been proposed. For a given set of sentences, the number of analogy relations in which a new sentence may be involved is thus a priori proportional to the ..."
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In previous work, a computational explanation of analogy, a phenomenon by which a new sentence is generated from three other sentences, has been proposed. For a given set of sentences, the number of analogy relations in which a new sentence may be involved is thus a priori proportional to the cube of the size of the set. In this paper, we study this number while reading a corpus, sentence by sentence. We also study the smallest number of previously read sentences which would ensure just a certain number of analogies. We also show how to construct a significantly reduced set of sentences from which any sentence of the corpus can be generated by analogy.