Spelling suggestions: "subject:"logic (symbolic anda mathematical)"" "subject:"logic (symbolic ando mathematical)""
141 |
Circumscriptive reasoningHalland, Kenneth John 08 1900 (has links)
We show how the non-monotonic nature of common-sense reasoning can be formalised by
circumscription. Various forms of circumscription are discussed. A new form of circumscription,
namely naive circumscription, is introduced in order to facilitate the comparison of the various
forms. Finally, some issues connected with the automation of circumscriptive reasoning are
examined. / Computing / M. Sc. (Computer Science)
|
142 |
Ax-Schanuel type inequalities in differentially closed fieldsAslanyan, Vahagn January 2017 (has links)
In this thesis we study Ax-Schanuel type inequalities for abstract differential equations. A motivating example is the exponential differential equation. The Ax-Schanuel theorem states positivity of a predimension defined on its solutions. The notion of a predimension was introduced by Hrushovski in his work from the 1990s where he uses an amalgamation-with-predimension technique to refute Zilber's Trichotomy Conjecture. In the differential setting one can carry out a similar construction with the predimension given by Ax-Schanuel. In this way one constructs a limit structure whose theory turns out to be precisely the first-order theory of the exponential differential equation (this analysis is due to Kirby (for semiabelian varieties) and Crampin, and it is based on Zilber's work on pseudo-exponentiation). One says in this case that the inequality is adequate. Thus, by an Ax-Schanuel type inequality we mean a predimension inequality for a differential equation. Our main question is to understand for which differential equations one can find an adequate predimension inequality. We show that this can be done for linear differential equations with constant coefficients by generalising the Ax-Schanuel theorem. Further, the question turns out to be closely related to the problem of recovering the differential structure in reducts of differentially closed fields where we keep the field structure (which is quite an interesting problem in its own right). So we explore that question and establish some criteria for recovering the derivation of the field. We also show (under some assumptions) that when the derivation is definable in a reduct then the latter cannot satisfy a non-trivial adequate predimension inequality. Another example of a predimension inequality is the analogue of Ax-Schanuel for the differential equation of the modular j-function due to Pila and Tsimerman. We carry out a Hrushovski construction with that predimension and give an axiomatisation of the first-order theory of the strong Fraïssé limit. It will be the theory of the differential equation of j under the assumption of adequacy of the predimension. We also show that if a similar predimension inequality (not necessarily adequate) is known for a differential equation then the fibres of the latter have interesting model theoretic properties such as strong minimality and geometric triviality. This, in particular, gives a new proof for a theorem of Freitag and Scanlon stating that the differential equation of j defines a trivial strongly minimal set.
|
143 |
The basic structure of intelligent databaseYu, Chun-I January 1989 (has links)
The purpose of this paper is to study the basic theoretic structure of intelligent data base by means of logic. There are three parts of this paper. The first part introduces the concept and relational algebra in relational data base. The second part focuses on the relationship between logic and the structure of intelligent data base and compares the intelligent database application. The last part, a SQL (Structure Query Language) queries simulation program using logic programming language Prolog, demonstrates how logic applies to query languages. / Department of Computer Science
|
144 |
Isotone fuzzy Galois connections and their applications in formal concept analysisKonecny, Jan. January 2009 (has links)
Thesis (Ph. D.)--State University of New York at Binghamton, Thomas J. Watson School of Engineering and Applied Science, Department of Systems Science and Industrial Engineering, 2009. / Includes bibliographical references.
|
145 |
Natural deduction; a proof-theoretical study.Prawitz, Dag. January 1900 (has links)
Akademisk avhandling--Stockholm. Universitet. / Bibliography: p. [106]-109.
|
146 |
Algebraïese simbole : die historiese ontwikkeling, gebruik en onderrig daarvanStols, Gert Hendrikus. 06 1900 (has links)
Text in Afrikaans, abstract in Afrikaans and English / Die gebruik van simbole maak wiskunde eenvoudiger en kragtiger, maar ook
moeiliker verstaanbaar. Laasgenoemde kan voorkom word as slegs eenvoudige en
noodsaaklike simbole gebruik word, met die verduidelikings en motiverings in
woorde.
Die krag van simbole le veral in die feit dat simbole as substitute vir konsepte kan
dien. Omdat die krag van simbole hierin le, skuil daar 'n groot gevaar in die gebruik
van simbole. Wanneer simbole los is van sinvolle verstandsvoorstellings, is daar geen
krag in simbole nie. Dit is die geval met die huidige benadering in skoolalgebra.
Voordat voldoende verstandsvoorstellings opgebou is, word daar op die manipulasie
van simbole gekonsentreer.
Die algebraiese historiese-kenteoretiese perspektief maak algebra meer betekenisvol
vir leerders. Hiervolgens moet die leerlinge die geleentheid gegun word om
oplossings in prosavorm te skryf en self hul eie wiskundige simbole vir idees spontaan in te voer. Hulle moet self die voordeel van algebraiese simbole beleef. / The use of symbols in algebra both simplifies and strengthens the subject, but it also
increases its level of complexity.This problem can be prevented if only simple and
essential symbols are used and if the explanations are fully verbalised.
The power of symbols stems from their potential to be used as substitutes for
concepts. As this constitutes the crux of mathematical symbolic representation, it
also presents a danger in that the symbols may not be comprehended. If symbols are
not related to mental representations, the symbols are meaningless. This is the case in
the present approach to algebra. Before sufficient mental representations are built,
there is a concentration on the manipulation of symbols.
The algebraic historical epistemological perspective makes algebra more meaningful
for learners. Learners should be granted the opportunities to write their solutions in prose and to develop their own symbols for concepts. / Mathematics Education / M. Sc. (Wiskunde-Onderwys)
|
147 |
Circumscriptive reasoningHalland, Kenneth John 08 1900 (has links)
We show how the non-monotonic nature of common-sense reasoning can be formalised by
circumscription. Various forms of circumscription are discussed. A new form of circumscription,
namely naive circumscription, is introduced in order to facilitate the comparison of the various
forms. Finally, some issues connected with the automation of circumscriptive reasoning are
examined. / Computing / M. Sc. (Computer Science)
|
148 |
Lógicas abstratas e o primeiro teorema de Lindström / Abstract logics and the first Lindström's theoremAlmeida, Edgar Luis Bezerra de, 1976- 03 November 2013 (has links)
Orientador: Itala Maria Loffredo D'Ottaviano / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências Humanas / Made available in DSpace on 2018-08-22T15:04:13Z (GMT). No. of bitstreams: 1
Almeida_EdgarLuisBezerrade_M.pdf: 946200 bytes, checksum: e8e316a3ee7420c8d7f45a751651a436 (MD5)
Previous issue date: 2013 / Resumo: Esta Dissertação apresenta uma definição de lógica abstrata e caracteriza alguns sistemas lógicos bastante conhecidos na literatura como casos particulares desta. Em especial, mostramos que a lógica de primeira ordem, lógica de segunda ordem, lógica com o operador Q1 de Mostowski e a lógica infinitária L!1! são casos particulares de lógicas abstratas. Mais que isso, mostramos que tais lógicas são regulares. Na análise de cada uma das lógicas acima citadas, mostramos o comportamento das mesmas com relação às propriedades de Löwenheim-Skolem e compacidade enumerável, resultados estes centrais à teoria de modelos. Nossa análise permite-nos constatar que, dentre os quatro casos apresentados, o único que goza de ambas as propriedades é a lógica de primeira ordem; as demais falham em uma, na outra ou em ambas as propriedades. Mostramos que isso não é mera coincidência, mas sim um resultado profundo, que estabelece fronteiras bem delimitadas à lógica de primeira ordem, conhecido como primeiro teorema de Lindström: se uma lógica é regular, ao menos tão expressiva quanto à lógica de primeira ordem e satisfaz ambas as propriedades citadas, então esta é equivalente a lógica de primeira ordem. Realizamos uma prova cuidadosa do teorema, em que cada ideia e cada estratégia de prova é estabelecida criteriosamente. Com seu trabalho, Lindström inaugurou um novo e profícuo campo de estudo, a teoria abstrata de modelos que estabelece, com relação a diversas combinações de propriedades de sistemas lógicos, uma estratificação entre lógicas. Apresentamos um outro exemplo de tal estratificação através de uma versão modal do teorema de Lindström, versão esta que caracteriza a lógica modal básica como maximal quanto a bissimilaridade e compacidade. Encerramos esta Dissertação com algumas considerações acerca da influência do primeiro teorema de Lindström / Abstract: This thesis presents the definition of abstract logic and features some quite logical systems presented in the literature as particular cases of this. In particular, we show that first-order logic, second-order logic, the logic with Mostowski's operator Q1 and the infinitary logic L!1! are specific systems of abstract logic. Moreover, we show that such logics are regular. In the analysis of each above mentioned logical systems we analyses his performance with regard to the properties of compactness and Löwenheim-Skolem, results that have important role in model theory. Our analysis allows us to conclude that among the four cases, the only one who enjoys both properties is the first-order logic, and all others fail in one, other or both properties. We show that this is not mere coincidence, but rather a deep, well-defined boundaries establishing the first-order logic, known as first Lindström's theorem: a regular logic that is at least as expressive as first-order logic and satisfies both properties mentioned, then this is equivalent to first-order logic. We conducted a thorough proof of the theorem, in which each idea and each proof strategy is carefully established. With his work Lindström inaugurated a new and fruitful field of study, the abstract model theory, which establishes with respect to different combinations of properties of logical systems, stratification between logical. Here is another example of such stratification through one of the theorem of modal version Lindström, which characterizes this version of the logic basic modal such as maximal bissimimulation and compactness. We conclude the thesis with some considerations about the influence of the Lindström's theorem / Mestrado / Filosofia / Mestre em Filosofia
|
149 |
Automatically presentable structuresRas, Charl John 03 September 2012 (has links)
M.Sc. / In this thesis we study some of the propertie of a clas called automatic structures. Automatic structures are structures that can be encoded (in some defined way) into a set of regular languages. This encoding allows one to prove many interesting properties about automatic structures, including decidabilty results.
|
150 |
Validating reasoning heuristics using next generation theorem proversSteyn, Paul Stephanes 31 January 2009 (has links)
The specification of enterprise information systems using formal specification languages
enables the formal verification of these systems. Reasoning about the properties of a formal
specification is a tedious task that can be facilitated much through the use of an automated
reasoner. However, set theory is a corner stone of many formal specification languages and
poses demanding challenges to automated reasoners. To this end a number of heuristics has
been developed to aid the Otter theorem prover in finding short proofs for set-theoretic
problems. This dissertation investigates the applicability of these heuristics to next generation
theorem provers. / Computing / M.Sc. (Computer Science)
|
Page generated in 0.0892 seconds