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Results for criterions:- Topic: Logic
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Results n° 1 to 8 of 96 matches
| Title |
M. van Atten, P. Boldini, M. Bourdeau, G. Heinzmann (eds), One Hundred Years of Intuitionism (1907-2007), The Cerisy conference, Bâle, Boston, Berlin, Birkhäuser, Publications des archives Henri Poincaré, 2008, 422 pages. |
| Author |
POGGIOLESI Francesca |
| Keywords |
None |
| Topics |
Book review, Epistemology, Logic |
| Abstract |
Book review |
| Number |
186, Summer 2009 |
| Language |
 French | Read the article
Read the article
| Title |
Projective operations on relatinal constraints |
| Author |
BURIGANA Luigi |
| Keywords |
Constraint, Expressive power, Projection, Relation |
| Topics |
Lattices, Logic, Psychology |
| Abstract |
Given a set of variables and a set of values, by a (relational) constraint we mean any set of functions from the former to the latter. Two special operations on constraints are considered, called existential and universal projections, because of their similarity with existential and universal quantifiers in a predicate calculus. The expressive power of both operations is explored, i.e., the general properties of the variety of constraints which may be produced starting from some initial constraint and applying those operations one or more times. A few comments are added concerning the expressive power of a larger system, comprising projective and Boolean operations (i.e., complementation, union and intersection) on constraints. |
| Number |
181, Spring 2008 |
| Language |
 English | Read the article
| Title |
Dialectical boundaries |
| Author |
DUGOWSON Stéphane |
| Keywords |
Category, Fuzzy, Graph, Lattice, Pretopology, Topology |
| Topics |
Graphs, Lattices, Logic, Topology |
| Abstract |
The aim of this paper is to propose, under the generic term of dialectical boundaries, a generalization of the concept of boundary, better suited to discrete spaces than the classical topological one. We shall consider first the case of crisp spaces then, after recalling the recent works about the formalization of fuzzy boundaries, we propose a partial typology of the various definitions that they contain, based on the concepts of fuzzy dialectical spaces and of spaces with fuzzy boundaries. |
| Number |
177, Spring 2007 |
| Language |
French | Read the article
| Title |
Gabriel Cramer's probabilistic logic |
| Author |
MARTIN Thierry |
| Keywords |
Cramer Gabriel, Encyclopaedia, Probabilistic logic, Probability of testimony |
| Topics |
History of sciences, Logic, Probabilities |
| Abstract |
Around 1745, the algebrist Gabriel Cramer gave a course of lectures on Logic, which was unpublished until to-day and of which an important part was dedicated to probable knowledge. The article «Probability» from the Diderot-D'Alembert's Encyclopaedia originates from these lectures. In this paper, we intend to disclose the representation of the probabilistic logic developed in this text, and we show in what way: 1°) this text highly testifies to the development of the probabilistic thought in the first half of the XVIIIth century and to the difficulties met by its formalization, 2°) it reveals a clearness and an exactness which the abstract given by the Encyclopaedia failed to account for. |
| Number |
176, Winter 2006, special issue: Contribution to the history of probabilities. Tribute issue to Bernard Bru |
| Language |
French | Read the article
| Title |
Critical analysis of variable (semiotic and formal viewpoints) [second part] |
| Author |
DESCLES Jean-Pierre, CHEONG Kye-Seop |
| Keywords |
Algebra, Combinatory logic, Function, Quantification, Semiotics, Variable |
| Topics |
Combinatorics, Linguistics, Logic, Semiology |
| Abstract |
For B. Russell «The variable is perhaps the most distinctively mathematical of all notions ; it is certainly also one of the most difficult to understand» (The Principles of Mathematics, 1903). The aim of this paper is to highlight the meaning of variable in different fields of Mathematics: the expression of equations in Algebra with indeterminate entities; the analytical expression of functions in Analysis; the expression of quantification in Logic. We give a historical survey of this notion from Viète and Descartes to Frege's representations of a concept, viewed as a non numerical function, yielding to the modern theory of quantification in first order languages. On one hand, the Peirce's theory of signs, and on the other hand, with Church's functional types, l-calculus «with bound variables» and Curry's combinatory logic «without bound variables», are very useful tools for investigating different kinds of variables in Mathematics, in Logic and in theoretical Computer Sciences. For instance, it was showed that «bound variables» were not semiotic tools necessary to formulate quantification (in Frege's sense) in «classical» Logic. Indeed, a simple quantifier is an operator which applies to a predicate by building a proposition; restricted quantifiers are derived from simple quantifiers by formal combinations with logical connectors (conditional or conjunction operators). We propose to take into account and to formalize, inside the framework of Combinatory Logic with types, (i) the «old logical notions» of «extension / intension»; (ii) determination operations from Port Royal's Logic; (iii) the distinction from the anthropology and cognitive psychology between «typical» and «atypical» instances of a concept, which brings us to define new quantifiers, called «star quantifiers», conceived as determination operators acting on terms. These quantifiers are more adequate than the fregean quantifiers, for a natural languages processing. Thus, we are able to give a conceptual distinction between the meanings of «Whatever» and «Indeterminate», implicitly used in Gentzen's Natural Deduction; thanks to this distinction, we can clarify an apparent «paradox» emerging with the universal quantifier introduction rule. |
| Number |
174, Summer 2006 |
| Language |
French | Read the article
| Title |
J.-H. Lambert, "Phénoménologie", trad. G. Fanfalone, Paris, Vrin, 2002, 221 p. |
| Author |
MARTIN Thierry |
| Keywords |
None |
| Topics |
Book review, Epistemology, History of Mathematics, Logic, Probabilities |
| Abstract |
Book review |
| Number |
174, Summer 2006 |
| Language |
French | Read the article
| Title |
Critical Analysis of Variable (Semiotic and Formal Viewpoints) [First part] |
| Author |
DESCLES Jean-Pierre, CHEONG Kye-Seop |
| Keywords |
Algebra, Combinatory logic, Correlation, Function, Quantification, Semiotics, Variable |
| Topics |
Algebra, Linguistics, Logic, Modelling, Semiology |
| Abstract |
For B. Russell «The variable is perhaps the most distinctively mathematical of all notions ; it is certainly also one of the most difficult to understand» (The Principles of Mathematics, 1903). The aim of this paper is to highlight the meaning of variable in different fields of Mathematics: the expression of equations in Algebra with indeterminate entities; the analytical expression of functions in Analysis; the expression of quantification in Logic. We give a historical survey of this notion from Viète and Descartes to Frege's representations of a concept, viewed as a non numerical function, yielding to the modern theory of quantification in first order languages. On one hand, the Peirce's theory of signs, and on the other hand, with Church's functional types, ?-calculus «with bound variables» and Curry's combinatory logic «without bound variables», are very useful tools for investigating different kinds of variables in Mathematics, in Logic and in theoretical Computer Sciences. For instance, it was showed that «bound variables» were not semiotic tools necessary to formulate quantification (in Frege's sense) in «classical» Logic. Indeed, a simple quantifier is an operator which applies to a predicate by building a proposition; restricted quantifiers are derived from simple quantifiers by formal combinations with logical connectors (conditional or conjunction operators). We propose to take into account and to formalize, inside the framework of Combinatory Logic with types, (i) the «old logical notions» of «extension / intension»; (ii) determination operations from Port Royal's Logic; (iii) the distinction from the anthropology and cognitive psychology between «typical» and «atypical» instances of a concept, which brings us to define new quantifiers, called «star quantifiers», conceived as determination operators acting on terms. These quantifiers are more adequate than the fregean quantifiers, for a natural languages processing. Thus, we are able to give a conceptual distinction between the meanings of «Whatever» and «Indeterminate», implicitly used in Gentzen's Natural Deduction; thanks to this distinction, we can clarify an apparent «paradox» emerging with the universal quantifier introduction rule. |
| Number |
173, Spring 2006 |
| Language |
French | Read the article
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