Formal-Language-Oriented Foundation of Dynamics of Human Crowds Using Topos-Theory

2011 ◽  
pp. 21-113
Author(s):  
Vladimir G. Ivancevic ◽  
Darryn J. Reid
Keyword(s):  
Formal Language ◽  
Topos Theory

A proof of the associated sheaf theorem by means of categorical logic

1981 ◽  
Vol 46 (1) ◽  
pp. 45-55 ◽  
Author(s):  
Barbara Veit
Keyword(s):  
Formal Language ◽  
Precise Description ◽  
Topos Theory ◽  
Categorical Logic ◽  
Categorical Methods ◽  
Close Relationship ◽  
Basic Facts ◽  
Double Nature ◽  
Geometric Fact

The double nature, both logical and geometrical, of topos theory is one of the most fascinating aspects of this discipline. Consequently, it might be of some interest that an essentially “geometric” fact such as the associated sheaf theorem admits a proof entirely based on methods of categorical logic.The idea of this proof comes from a previous paper [V], where the same technique was used in the context of Grothendieck topoi. That paper used a generalized notion of forcing which leads directly from classical Tarski semantics in sets to Kripke-Joyal semantics in an arbitrary Grothendieck topos and gives a precise description of the links between the two. On account of this very close relationship, we thus could establish various basic facts on Grothendieck topoi without an extensive use of categorical methods, simply by viewing given subobjects as interpretations of appropriate formulas written in the formal language that had been used all along.

Automated Indexing of SNOMED Statements into ICD

1987 ◽  
Vol 26 (03) ◽  
pp. 93-98 ◽  
Author(s):  
F. Wingert
Keyword(s):  
Formal Language ◽  
Program System ◽  
Icd Codes

SummaryA formal language is presented which is used to generate a transformation table for mapping SNOMED statements to ICD codes. Non-terminal symbols define parts of the SNOMED space, the highest order of which corresponds to ICD categories. Performance of the corresponding program system and remaining problems are described.

Da eine oder mehrere betroffen …

2020 ◽  
Vol 48 (1) ◽  
pp. 47-100
Author(s):  
Melitta Gillmann
Keyword(s):  
High Frequency ◽  
Formal Language ◽  
Subordinate Clause ◽  
Matrix Clause ◽  
Very High Frequency ◽  
Corpus Study ◽  
Causal Relations ◽  
Legal Texts ◽  
The Matrix ◽  
Very High

AbstractBased on a corpus study conducted using the GerManC corpus (1650–1800), the paper sketches the functional and sociosymbolic development of subordinate clause constructions introduced by the subjunctor da ‘since’ in different text genres. In the second half of the 17th and the first half of the 18th century, the da clauses were characterized by semantic vagueness: Besides temporal, spatial and causal relations, the subjunctor established conditional, concessive, and adversative links between clauses. The corpus study reveals that different genres are crucial to the readings of da clauses. Spatial and temporal usages, for example, occur more often in sermons than in other genres. The conditional reading, in contrast, strongly tends to occur in legal texts, where it displays very high frequency. This could be the reason why da clauses carry indexical meaning in contemporary German and are associated with formal language. Over the course of the 18th century, the causal usages increase in all genres. Surprisingly, these causal da clauses tend to be placed in front of the matrix clause despite the overall tendency of causal clauses to follow the matrix clause.

scholarly journals Three Types of Architectural Educational Strategies (AES) in Sustainable Buildings for Learning Environments in Canada

2021 ◽  
Vol 13 (15) ◽  
pp. 8166
Author(s):  
Jean-Pierre Chupin ◽  
Morteza Hazbei ◽  
Karl-Antoine Pelchat
Keyword(s):  
Learning Environments ◽  
Formal Language ◽  
Quantitative Approach ◽  
Practical Approach ◽  
Future Research ◽  
Educational Strategies ◽  
Sustainable Buildings ◽  
Sustainable Architecture ◽  
Distinctive Features ◽  
Advanced Knowledge

This article explores a trend provisionally called “eco-didacticism” observable for nearly 15 years in art, design and architecture. The corpus concentrates on learning centres as buildings meant to diffuse advanced knowledge in the field of sustainable architecture. We found evidence of additional educational intentions to the pedagogical or scientific programs that these buildings have already been mandated to host and support. A variety of practices or devices have sometimes been added to the architecture, sometimes integrated, while others determine the overall structuring of these educational buildings. Seven cases of “learning centres” built in Canada between 2004 and 2018 have been screened through three epistemological filters distinguishing forms of “architectural didactics”: 1—a labeling often quantitative approach, 2—an experiential or practical approach, 3—a visually narrative or iconic approach. While outlining definitions of these Architectural Educational Strategies (AES), we offer initial explanations for their distinctive features. It appears that architects, designers and critics altogether operate on the belief that forms of architectural communication can operate as elements of a language that would be accessible to non-experts. Our conclusion indicates how future research could question the very possibility of giving lessons through formal language and aesthetic features.

scholarly journals Closed Structure

2021 ◽  
Author(s):  
Peter Fritz ◽  
Harvey Lederman ◽  
Gabriel Uzquiano
Keyword(s):  
Formal Language ◽  
Syntactic Structure ◽  
Natural Extension ◽  
Propositional Attitudes ◽  
Higher Order ◽  
Order Logic ◽  
Bertrand Russell ◽  
Structured Propositions ◽  
Higher Order Logic ◽  
Closed Structure

AbstractAccording to the structured theory of propositions, if two sentences express the same proposition, then they have the same syntactic structure, with corresponding syntactic constituents expressing the same entities. A number of philosophers have recently focused attention on a powerful argument against this theory, based on a result by Bertrand Russell, which shows that the theory of structured propositions is inconsistent in higher order-logic. This paper explores a response to this argument, which involves restricting the scope of the claim that propositions are structured, so that it does not hold for all propositions whatsoever, but only for those which are expressible using closed sentences of a given formal language. We call this restricted principle Closed Structure, and show that it is consistent in classical higher-order logic. As a schematic principle, the strength of Closed Structure is dependent on the chosen language. For its consistency to be philosophically significant, it also needs to be consistent in every extension of the language which the theorist of structured propositions is apt to accept. But, we go on to show, Closed Structure is in fact inconsistent in a very natural extension of the standard language of higher-order logic, which adds resources for plural talk of propositions. We conclude that this particular strategy of restricting the scope of the claim that propositions are structured is not a compelling response to the argument based on Russell’s result, though we note that for some applications, for instance to propositional attitudes, a restricted thesis in the vicinity may hold some promise.

A syntax controlled generator of formal language processors

1963 ◽  
Vol 6 (8) ◽  
pp. 451-455 ◽  
Author(s):  
J. Eickel ◽  
M. Paul ◽  
F. L. Bauer ◽  
K. Samuelson
Keyword(s):  
Formal Language

Spoken Greek

1944 ◽  
Vol 13 (38-39) ◽  
pp. 73-80
Author(s):  
W. R Loader
Keyword(s):  
Formal Language ◽  
Modern World ◽  
Grammatical Structure ◽  
Ancient Greek ◽  
Modern Greek ◽  
Law Courts ◽  
Business Correspondence

It has been suggested that there is less difference between ancient Greek and modern Greek than between present-day English and Chaucer's language. The suggestion is somewhat questionable. Broadly speaking, apart from dialects and local variations, there are presently three languages in Greece, the Kathareuousa, the Demotiki, and the popular newspaper language, which is a blend of the two.The Kathareuousa is the official and formal language, used in Government publications and statements, business correspondence, non-fictional books and treatises, law courts, University lectures, and in formal conversation. And although its grammatical structure is analytic as opposed to the synthesis of ancient Greek (a change which constitutes the main difference between classical and modern Greek, as it does between other modern and ancient languages), in the Kathareuousa the most strenuous attempt has been made to maintain the accidence and vocabulary of the ancient language.Words are declined and verbs conjugated (without some of their more difficult and less used moods and tenses) as in Attic Greek, pronouns and prepositions and the cases governed by them are the same, and while, naturally, many terms which describe things known only to the modern world are not to be found in Liddell and Scott, they are generally legitimate and intelligible compounds of words which are to be found in Liddell and Scott. Ἀɛροπλἁνoν for aeroplane, ἀɛρòσTαtoν for balloon, are instances which come easily to mind.

Model Theory: Geometrical and Set-Theoretic Aspects and Prospects

2003 ◽  
Vol 9 (2) ◽  
pp. 197-212 ◽  
Author(s):  
Angus Macintyre
Keyword(s):  
Model Theory ◽  
Category Theory ◽  
Theoretic Model ◽  
Topos Theory ◽  
Sheaf Theory ◽  
Special Cases ◽  
Algebraic Spaces ◽  
The Subject ◽  
Near Future ◽  
Modern Mathematics

I see model theory as becoming increasingly detached from set theory, and the Tarskian notion of set-theoretic model being no longer central to model theory. In much of modern mathematics, the set-theoretic component is of minor interest, and basic notions are geometric or category-theoretic. In algebraic geometry, schemes or algebraic spaces are the basic notions, with the older “sets of points in affine or projective space” no more than restrictive special cases. The basic notions may be given sheaf-theoretically, or functorially. To understand in depth the historically important affine cases, one does best to work with more general schemes. The resulting relativization and “transfer of structure” is incomparably more flexible and powerful than anything yet known in “set-theoretic model theory”.It seems to me now uncontroversial to see the fine structure of definitions as becoming the central concern of model theory, to the extent that one can easily imagine the subject being called “Definability Theory” in the near future.Tarski's set-theoretic foundational formulations are still favoured by the majority of model-theorists, and evolution towards a more suggestive language has been perplexingly slow. None of the main texts uses in any nontrivial way the language of category theory, far less sheaf theory or topos theory. Given that the most notable interactions of model theory with geometry are in areas of geometry where the language of sheaves is almost indispensable (to the geometers), this is a curious situation, and I find it hard to imagine that it will not change soon, and rapidly.

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