Logic, sets and information: proceedings of the tenth brazilian conference on mathematical logic
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Logic, sets and information: proceedings of the tenth Brazilian Conference in Mathematical Logic (digital)
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“In the last fifteen years nine Brazilian Conferences in Logic have been organized, beginning in 1977 with the conference which took place at the State University of Campinas (UNICAMP), Sao Paulo. Since the foundation of the Brazilian Logic Society in 1979 these meetings have been organized by the Society, and have been supported by the Centre for Logic, Epistemology and the History of Science (CLE) of UNICAMP. The present volume contains a selection, chosen by anonymous referees, of the papers presented at the Tenth Brazilian Logic Conference, which took place in Itatiaia, Rio do Janeiro, in May 1993, and which was organized by the Society in collaboration with CLE-UNICAMP, sponsored by CNPq, FAPERJ and FAPESP, under the direction of an organizing committee consisting of Walter Alexandre Carnielli (UNICAMP), Jose Alexandre D. Guerzoni (UNICAMP), Luiz Carlos P.D. Pereira (UFRJ) and Vera Vidal (UFRJ). These papers do not focus on any single theme, but rather reflect the wide variety of areas in which research in logic is being carried out in Brazil. This preface should not be considered as a kind of abstract of the fourteen papers; it does not summarize them. Its general aim is just to indicate some of the questions and results taken up in the papers.
Six of the papers discuss themes and questions related to pure and applied non-classical logic.
In A natural deduction presentation for intuitionistic modal logics, Mario Benevides proposes a natural deduction formulation for intuitionistic modal logic where, besides necessity we also have the possibility operator "O". The modal operators are defined as higher level operators. The author shows how to systematically formalize intuitionistic versions of important and traditional modal logics, such as, K, T, S4, S5, D, D4 and D5. Benevides also discusses the possibility of providing what he calls an "intuitionistic interpretation" for the modal operators.
In Is there a logic behind fuzziness?, Walter Carnielli and J.C. Cifuentcs Vasquez address some basic questions in the foundationsof fuzzy logic and fuzzy set-theory. Their specific aim is to characterize the syntax and semantics of fuzzy logics obtained from abstract classes of fuzzy sets.
Figueiredo and Hauesler in Another approach to Abramsky's proofs-as-processes for multiplicative linear logic define a calculus where the relationship between proofs-as-processes and proof-nets can be adequatedly emphasized. As in the case of proof-nets, inputs and outputs are not predetermined in the new calculus. The authors also discuss a kind of Curry-Howard Isomorphism between the new calculus and proof-nets.
In The problem of persistence in a system of many-valued intcnsional logic, Cosme Massi and Elias Alves discuss the question of persistence for an extension of Montague's system IL for intensional logic, to a three-valued extensional system called IL3. The Persisence Theorem for IL shows that if we are restricted to a specific class of formulas of IL, the system is complete in the non-generalized sense of completeness. After a brief presentation of the system IL3, the authors prove an analogue of the Persistence Theorem for IL3.
Epistemic inconsistency is the theme of Pequeno and Buchsbaum's The logic of epistemic inconsistency, Epistemic inconsistency reflects the position that reasoning can be carried out on contradictory views of the same situation. Pequeno and Buchsbaum propose a syntax and a semantics suitable for the study of reasoning in these contexts of epistemic inconsistency. The authors also address the relation between reasoning on epistemic inconsistent contexts and nonmonotonic reasoning.
The sixth paper on non-classical logics is Zaverucha and da Silva's An extension of Poolers logical framework for default reasoning to multiple agents. In this paper, Poole's approach to.single-agent defeasible reasoning is extended to multiple-agent defeasible reasoning. The authors take computational applications into consideration and show that the new framework allows the definition of several logics for multiple-agent defeasible reasoning.
An interesting discussion about the relation between interpolation and modularity is taken up by Paulo Veloso in On some logical properties related to modularity and interpolation. Modularity is a central property in logical approaches to formal program and specification development. It guarantees composability of implementations via preservation of conservativeness. Veloso's main purpose is to show that some logical properties can be regarded as versions of interpolation, ensuring preservation of conservativeness.
In Cauchy completeness of Stone spaces in boolean algebras, J,C, Cifuentes Vasquez shows that the uniformizability of the Stone space topology of a Boolean algebra directly implies the Cauchy-completeness of the resulting uniform space. Vasquez also shows that, since this uniform space is totally bounded, the compactness property is a directly consequence of Cauchy-completeness. General applications of these results to algebra and model theory are also discussed.
The aim of R. Bianconi in Some model theory for the reals with analytic functionsis to discuss some open problems for the model theory of expansions of reals through the addition of analytic functions. These open problems arc related to model (and strong) completeness and quantifier elimination for these structures.
Carlos Lungarzo in some logical issues in AL addresses two questions concerning logical aspects of the syntax and semantics of expert systems. The first question is related to the possibility of the application of a probabilistic criterion in our choices between contradictory statements in expert systems' databases. The second question deals with the possibility of a generalization of well-founded semantics to this probabilistic approach. His general aim is to argue for a use of probabilistic interpretation as an alternative approach to the use of non-classical logics in the treatment of some important features of expert systems.
In A general definition of the informational content of signals, Jairo da Silva investigates the problem of providing a formal theory of the notion of "semantic content" of messages. He proposes a general definition of the informational content of outputs of commumcational channels whose inputs are taken from discrete information sources. Da Silva also argues that his theory may have interesting applications in philosophy, specifically in the treatment of epistemological problems.
Set-theoretical questions are raised in two papers. In Dense linear orderings and weak forms of choice Carlos Gonzales proves some results on the relative consistency and independence of the statement "any infinite set can be densely linearly ordered". Decio Krause's paper The theories of quasi-sets and ZFC are equiconsistent tackles the question of the equiconsistency of quasi-set theories with ZFC.
And last, but certainly not least, we have a paper by Itala D'Ottaviano The intellectual development of A jidres Raggio. This is a very necessary homage to a figure whose work and personality were of such decisive importance for the development of research in logic in South America in general, and especially in Brazil, and for this reason it is most appropriate that this volume is dedicated to his memory.
We would like to thank the following colleagues who kindly agreed to colaborate as referees: E.H. Alves, A. Avron, P. Bcsnard, G. Bierman, P. Borowik, N.C.A. da Costa, F. Doria, K. Dosen, M. Fitting, F. Miraglia, D.F. Pincus, P.H. Rodenburg, A.M. Sette and A.F.I. Urquhart.
The publication of this volume was made possible by financial support from FAPESP (Fundaqao de Amparo a Pcsquisa do Estado de Sao Paulo), and from CLE of UNICAMP.”
Walter A. Carnielli
Luiz Carlos P.D. Pereira (editors)
Volume 14 – 1995
ISSN: 0103-3147 First edition 1995
Index for catalogue record
1. Symbolic logic and mathematics 511.3
OBS. The majority of the papers address topics in non-classical logics, both pure and applied, a field in which Brazilian logicians have already anchieved widespread recognition. Among the topics discussed are intuitionistic modalities, foundations of fuzzy set theory, the relationship between proofs-as-processes and proof nets, intencional logic, reasoning under contradictions, defeasible reasoning, questions about interpolation and modularity, etc.
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