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430 results on '"Logical theory"'

1. From Emptiness to Nonsense: the Constitution of the Number Zero (for Non-mathematicians).

Author

Hoogcarspel, Erik

Subjects
*ZERO (The number), *NUMBER systems, *NUMERALS, *SYMBOLISM
Abstract

The subject is introduced by a reflection on the different aspects of numbers and a review of a paper written by Andreas Nieder: Representing Something Out of Nothing: The Dawning of Zero. This is followed by a reflection on the precise nature of the transformation of zero from a signifier of quantity to a number. Edmund Husserl called this the constitution (Stiftung) of the zero as a new ideal object and he described the process in The Origin of Geometry. Zero as a number is an element of a self-contained symbolic deductive system that does not refer to the life world and has no sense at all; it is, in the words of the analytic philosophical tradition, nonsense. This implies that no meaning can possibly be transferred from zero as a quantity to zero as a number. The history of zero as a number coincides with the history of abstract mathematics and the development of calculation systems, the tremendous usefulness of which is precisely based on its very meaninglessness. All speculation about any eventual progress of the concept of zero as a quantity to zero as a number is therefore unsubstantiated. Marc Richir showed that the constitution of an ideal object is a leap; it leaves a gap between its new sense and its historical basis. This chapter will conclude with the question whether there is a link between this historical basis of zero as a quantity and the concept of emptiness in Buddhism; this supposed relation has been and still is the pet of quite a few Buddhologists. [ABSTRACT FROM AUTHOR]

Published
2023
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3. Logical Encoding of Argumentation Frameworks with Higher-order Attacks and Evidential Supports.

Author

Cayrol, Claudette and Lagasquie-Schiex, Marie-Christine

Subjects
*DEBATE, *ENCODING, *MODEL theory, *MANURES
Abstract

We propose a logical encoding of argumentation frameworks with higher-order interactions (i.e. attacks/supports whose targets are arguments or other attacks/supports) with an evidential meaning for supports. Our purpose is to separate the logical expression of the meaning of an attack or an evidential support (simple or higher-order) from the logical expression of acceptability semantics. We consider semantics which specify the conditions under which the arguments (resp. the attacks/supports) are considered as accepted, directly on the extended framework, without translating the original framework into a Dung's argumentation framework. We characterize the output of a given framework in logical terms (namely as particular models of a logical theory). Our proposal applies to the particular case of Dung's frameworks, enabling to recover standard extensions. [ABSTRACT FROM AUTHOR]

Published
2020
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4. Definability in First Order Theories of Graph Orderings

Author

Ramanujam, R., Thinniyam, R. S., Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Artemov, Sergei, editor, and Nerode, Anil, editor

Published
2016
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8. Definability in first-order theories of graph orderings ⋆.

Author

Ramanujam, R and Thinniyam, Ramanathan S

Subjects
DEFINITION (Logic), FINITE simple groups, ISOMORPHISM (Mathematics), TREE graphs, ORDERED sets
Abstract

We study definability in the first-order theory of graph order: i.e. the set of all isomorphism types of simple finite graphs ordered by either the minor, subgraph or induced subgraph relation. Natural graph families like cycles and trees are definable in these orders, as also notions like connectivity, maximum degree, etc. This machinery allows us to show mutual interpretability with arithmetic for all orders. We discuss implications for formalizing statements of graph theory in such theories of order. 1 [ABSTRACT FROM AUTHOR]

Published
2020
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11. Basics for a Grammar Engine to Verbalize Logical Theories in isiZulu

Author

Keet, C. Maria, Khumalo, Langa, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Kobsa, Alfred, Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Bikakis, Antonis, editor, Fodor, Paul, editor, and Roman, Dumitru, editor

Published
2014
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14. On the Automated Analysis of Safety in Usage Control: A New Decidability Result

Author

Ranise, Silvio, Armando, Alessandro, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Xu, Li, editor, Bertino, Elisa, editor, and Mu, Yi, editor

Published
2012
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15. PRAGMATISM AND PROBABILITY: RE-EXAMINING KEYNES’S THINKING ON PROBABILITY

Author

Bradley W. Bateman

Subjects
Pragmatism, General Arts and Humanities, Philosophy, media_common.quotation_subject, Biography, Context (language use), Logical theory, Epistemology, History and Philosophy of Science, General theory, Criticism, General Economics, Econometrics and Finance, Probability interpretations, media_common
Abstract

As we celebrate the centenary of John Maynard Keynes’s Treatise on Probability (1921), we are still faced with unresolved, fundamental questions about his foray into the philosophy of probability. One of these unresolved questions concerns whether Keynes (1931) later changed his mind in response to intense criticism from Frank Ramsey (1922, 1931) and abandoned the logical theory of probability. This essay draws from Cheryl Misak’s recent biography of Frank Ramsey (2020) to argue that Ramsey had an even wider influence on Keynes’s work than has been recognized, and that this influence was not just on his philosophy of probability but also on his economics. Understood in this fuller context, it seems even more clear that Keynes embraced and built upon Ramsey’s subjective theory of probability in The General Theory of Employment, Interest, and Money (1936).

Published
2021
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18. A Review of Mathematical Knowledge Management

Author

Carette, Jacques, Farmer, William M., Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Goebel, Randy, editor, Siekmann, Jörg, editor, Wahlster, Wolfgang, editor, Carette, Jacques, editor, Dixon, Lucas, editor, Coen, Claudio Sacerdoti, editor, and Watt, Stephen M., editor

Published
2009
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19. Mathematical Logic for Life Science Ontologies

Author

Lutz, Carsten, Wolter, Frank, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Goebel, Randy, editor, Siekmann, Jörg, editor, Wahlster, Wolfgang, editor, Ono, Hiroakira, editor, Kanazawa, Makoto, editor, and de Queiroz, Ruy, editor

Published
2009
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20. Logic and Metaphysics in Avicenna’s Modal Syllogistic

Author

Thom, Paul, Rahman, Shahid, editor, Symons, John, editor, van Bendegem, Jean Paul, editor, van Benthem, Johan, editor, Dubucs, Jacques, editor, Fagot-Largeault, Anne, editor, van Fraassen, Bas, editor, Gabbay, Dov, editor, Hintikka, Jaakko, editor, Lambert, Karel, editor, Priest, Graham, editor, Sandu, Gabriel, editor, Wansing, Heinrich, editor, Williamson, Timothy, editor, Street, Tony, editor, and Tahiri, Hassan, editor

Published
2008
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21. Learning and Memorizing Models of Logical Theories in a Hybrid Learning Device

Author

Gust, Helmar, Kühnberger, Kai-Uwe, Geibel, Peter, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Ishikawa, Masumi, editor, Doya, Kenji, editor, Miyamoto, Hiroyuki, editor, and Yamakawa, Takeshi, editor

Published
2008
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24. Anti-exceptionalism, truth and the BA-plan

Author

Eduardo Alejandro Barrio, Federico Matías Pailos, and Joaquín Santiago Toranzo Calderón

Subjects
Discrete mathematics, Philosophy of language, Philosophy, Exceptionalism, Development (topology), Hierarchy (mathematics), Classical logic, General Social Sciences, Truth predicate, Scientific theory, Logical theory, Mathematics
Abstract

Anti-exceptionalism about logic states that logical theories have no special epistemological status. Such theories are continuous with scientific theories. Contemporary anti-exceptionalists include the semantic paradoxes as a part of the elements to accept a logical theory. Exploring the Buenos Aires Plan, the recent development of the metainferential hierarchy of $${\mathbf {ST}}$$ -logics shows that there are multiple options to deal with such paradoxes. There is a whole $${\mathbf {ST}}$$ -based hierarchy, of which $${\mathbf {LP}}$$ and $${\mathbf {ST}}$$ themselves are only the first steps. This means that the logics in this hierarchy are also options to analyze the inferential patterns allowed in a language that contains its own truth predicate. This paper explores these responses analyzing some reasons to go beyond the first steps. We show that $${\mathbf {LP}}$$ , $${\mathbf {ST}}$$ and the logics of the $${\mathbf {ST}}$$ -hierarchy offer different diagnoses for the same evidence: the inferences and metainferences the agents endorse in the presence of the truth-predicate. But even if the data are not enough to adopt one of these logics, there are other elements to evaluate the revision of classical logic. Which is the best explanation for the logical principles to deal with semantic paradoxes? How close should we be to classical logic? And mainly, how could a logic obey the validities it contains (just like classical logic)? From an anti-exceptionalist perspective, we argue that $${\mathbf {ST}}$$ -metainferential logics in general—and $${\mathbf {STT}}_{\omega }$$ in particular—are the best available options to explain the inferential principles involved with the notion of truth.

Published
2021
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27. From Chaos to Undefinedness

Author

Broy, Manfred, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Futatsugi, Kokichi, editor, Jouannaud, Jean-Pierre, editor, and Meseguer, José, editor

Published
2006
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28. Psychological Validity of Schematic Proofs

Author

Jamnik, Mateja, Bundy, Alan, Goos, Gerhard, editor, Hartmanis, Juris, editor, van Leeuwen, Jan, editor, Carbonell, Jaime G., editor, Siekmann, Jörg, editor, Hutter, Dieter, editor, and Stephan, Werner, editor

Published
2005
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29. A Formal Access Control Model for XML Databases

Author

Gabillon, Alban, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Jonker, Willem, editor, and Petković, Milan, editor

Published
2005
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32. Detecting Outliers via Logical Theories and Its Data Complexity

Author

Angiulli, Fabrizio, Greco, Gianluigi, Palopoli, Luigi, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Carbonell, Jaime G., editor, Siekmann, Jörg, editor, Suzuki, Einoshin, editor, and Arikawa, Setsuo, editor

Published
2004
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34. On the Epistemology of Game-Theoretical Semantics

Author

Hintikka, Jaakko, Hendricks, Vincent F., editor, Symons, John, editor, Hintikka, Jaakko, editor, Van Dalen, Dirk, editor, Kuipers, Theo A. F., editor, Seidenfeld, Teddy, editor, Suppes, Patrick, editor, Woleński, Jan, editor, Czarnecki, Tadeusz, editor, Kijania-Placek, Katarzyna, editor, Placek, Tomasz, editor, and Rojszczak, Artur, editor

Published
2003
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37. MetaPRL – A Modular Logical Environment

Author

Hickey, Jason, Nogin, Aleksey, Constable, Robert L., Aydemir, Brian E., Barzilay, Eli, Bryukhov, Yegor, Eaton, Richard, Granicz, Adam, Kopylov, Alexei, Kreitz, Christoph, Krupski, Vladimir N., Lorigo, Lori, Schmitt, Stephan, Witty, Carl, Yu, Xin, Goos, Gerhard, editor, Hartmanis, Juris, editor, van Leeuwen, Jan, editor, Basin, David, editor, and Wolff, Burkhart, editor

Published
2003
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38. Obrar en consecuencia. La lógica de la experiencia de John Dewey

Author

Arenas Llopis, Luis and Arenas Llopis, Luis

Abstract

Despite the scant echo of Dewey’s contributions in the field of Logic, the development of Logic during the second half of the twentieth century and during the twenty-first century can be considered a confirmation of Dewey’s ideas about the role of logic in relation to knowledge. Logic, in the precise sense that Dewey gives the term, has been the constant concern of Dewey’s philosophy and is the pinnacle that crowns his project of a naturalization of philosophy. In the case of Logic, Dewey’s project tries to show how logical forms arise in the operation of investigating and are in charge of controlling the investigation so that it can produce warranted assertability. Two consequences follow from this approach, that is, the empirical character of logical principles and hence its naturalization and a radical reformulation of the classic problem of truth., A pesar del escaso eco que las contribuciones de Dewey parecen haber logrado en el campo de la lógica, la ampliación que ha sufrido la disciplina lógica en la segunda mitad del siglo XX y en lo que llevamos del siglo XXI puede considerarse en muchos sentidos una confirmación de las ideas de Dewey en torno al papel de la lógica en el conjunto del saber. La lógica, en el preciso sentido que Dewey otorga al término, ha sido la preocupación constante del recorrido intelectual de Dewey y es la cima que corona su proyecto de una naturalización de la filosofía. En el caso de la lógica, ese proyecto pasa por mostrar en qué sentido las formas lógicas surgen en la operación de investigar y se ocupan de controlar la investigación para que esta pueda producir aserciones garantizadas. Lo que tendrá como consecuencia asumir el carácter empírico de los principios lógicos y una reformulación radical del problema clásico de la verdad.

Published
2022

40. Sets

Author

Searcóid, Mícheál Ó and Searcóid, Mícheál Ó

Published
2002
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41. Sequent Schema for Derived Rules

Author

Nogin, Aleksey, Hickey, Jason, Goos, Gerhard, editor, Hartmanis, Juris, editor, van Leeuwen, Jan, editor, Carreño, Victor A., editor, Muñoz, César A., editor, and Tahar, Sofiène, editor

Published
2002
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42. CVC: A Cooperating Validity Checker

Author

Stump, Aaron, Barrett, Clark W., Dill, David L., Goos, Gerhard, editor, Hartmanis, Juris, editor, van Leeuwen, Jan, editor, Brinksma, Ed, editor, and Larsen, Kim Guldstrand, editor

Published
2002
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43. Semiconcept Graphs with Variables

Author

Klinger, Julia, Goos, G., editor, Hartmanis, J., editor, van Leeuwen, J., editor, Carbonell, Jaime G., editor, Siekmann, Jörg, editor, Priss, Uta, editor, Corbett, Dan, editor, and Angelova, Galia, editor

Published
2002
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44. O rozstrzygalności teologii

Author

Adam Olszewski

Subjects
Glossary, Point (typography), Philosophy, General Medicine, General Chemistry, Impossibility, Paragraph, Epistemology, Logical theory, Decidability
Abstract

The paper takes a synthetic, not an analytical approach to the title issue. From the methodological point of view, it is an attempt to apply logical notions such as consequence, proof, rule and decidability to theology as a whole. In the first part (to the paragraph 3.1) the theology is considered as a logical theory and the drawbacks of such an approach are pointed out, including the impossibility of a sensible consideration of the decidability of such a theology. The second part weakens the logical notion of decidability and narrows down the notion of theology for which the weakened decidability can be applied. The whole discussion poses a lot of problems concerning theology, which probably theologians should solve. The work is quite controversial for both sides: theologians andlogicians. To make it easier for theologians to read the paper, a glossary of loosely worded terms of logical terms has been added.

Published
2021
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46. Twenty Years of Rewriting Logic

Author

Meseguer, José, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, and Ölveczky, Peter Csaba, editor

Published
2010
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