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Profile: Walter Carnielli (University of Campinas)
Profile: Walter Carnielli
  1.  8
    Walter A. Carnielli, João Marcos & Sandra De Amo (2000). Formal Inconsistency and Evolutionary Databases. Logic and Logical Philosophy 8 (2):115-152.
    This paper introduces new logical systems which axiomatize a formal representation of inconsistency (here taken to be equivalent to contradictoriness) in classical logic. We start from an intuitive semantical account of inconsistent data, fixing some basic requirements, and provide two distinct sound and complete axiomatics for such semantics, LFI1 and LFI2, as well as their first-order extensions, LFI1* and LFI2*, depending on which additional requirements are considered. These formal systems are examples of what we (...)
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  2.  30
    Walter A. Carnielli, Marcelo E. Coniglio & Itala M. L. D'Ottaviano (2009). New Dimensions on Translations Between Logics. Logica Universalis 3 (1):1-18.
    After a brief promenade on the several notions of translations that appear in the literature, we concentrate on three paradigms of translations between logics: ( conservative ) translations , transfers and contextual translations . Though independent, such approaches are here compared and assessed against questions about the meaning of a translation and about comparative strength and extensibility of a logic with respect to another.
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  3.  15
    Walter A. Carnielli & João Marcos (1999). Limits for Paraconsistent Calculi. Notre Dame Journal of Formal Logic 40 (3):375-390.
    This paper discusses how to define logics as deductive limits of sequences of other logics. The case of da Costa's hierarchy of increasingly weaker paraconsistent calculi, known as $ \mathcal {C}$n, 1 $ \leq$ n $ \leq$ $ \omega$, is carefully studied. The calculus $ \mathcal {C}$$\scriptstyle \omega$, in particular, constitutes no more than a lower deductive bound to this hierarchy and differs considerably from its companions. A long standing problem in the literature (open for more than 35 years) is (...)
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  4.  11
    A. M. Sette & Walter A. Carnielli (1995). Maximal Weakly-Intuitionistic Logics. Studia Logica 55 (1):181 - 203.
    This article introduces the three-valuedweakly-intuitionistic logicI 1 as a counterpart of theparaconsistent calculusP 1 studied in [11].I 1 is shown to be complete with respect to certainthree-valued matrices. We also show that in the sense that any proper extension ofI 1 collapses to classical logic.The second part shows thatI 1 is algebraizable in the sense of Block and Pigozzi (cf. [2]) in a way very similar to the algebraization ofP 1 given in [8].
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  5.  23
    Walter A. Carnielli (1987). Systematization of Finite Many-Valued Logics Through the Method of Tableaux. Journal of Symbolic Logic 52 (2):473-493.
    his paper presents a unified treatment of the propositional and first-order many-valued logics through the method of tableaux. It is shown that several important results on the proof theory and model theory of those logics can be obtained in a general way. We obtain, in this direction, abstract versions of the completeness theorem, model existence theorem (using a generalization of the classical analytic consistency properties), compactness theorem and Lowenheim-Skolem theorem. The paper is completely self-contained and includes examples of application to (...)
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  6.  15
    Cristina Sernadas, João Rasga & Walter A. Carnielli (2002). Modulated Fibring and the Collapsing Problem. Journal of Symbolic Logic 67 (4):1541-1569.
    Fibring is recognized as one of the main mechanisms in combining logics, with great signicance in the theory and applications of mathematical logic. However, an open challenge to bring is posed by the collapsing problem: even when no symbols are shared, certain combinations of logics simply collapse to one of them, indicating that bring imposes unwanted interconnections between the given logics. Modulated bring allows a ner control of the combination, solving the collapsing problem both at the semantic and deductive levels. (...)
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  7. Richard L. Epstein & Walter A. Carnielli (1989). Computability Computable Functions, Logic, and the Foundations of Mathematics. Monograph Collection (Matt - Pseudo).
    This book is dedicated to a classic presentation of the theory of computable functions in the context of the foundations of mathematics. Part I motivates the study of computability with discussions and readings about the crisis in the foundations of mathematics in the early 20th century, while presenting the basic ideas of whole number, function, proof, and real number. Part II starts with readings from Turing and Post leading to the formal theory of recursive functions. Part III presents sufficient formal (...)
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  8.  61
    Newton C. A. Costa & Walter A. Carnielli (1986). On Paraconsistent Deontic Logic. Philosophia 16 (3-4):293-305.
    This paper develops the first deontic logic in the context of paraconsistent logics.
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  9.  4
    Walter A. Carnielli & Marcelo E. Coniglio (1999). A Categorial Approach to the Combination of Logics. Manuscrito 22 (2):69-94.
    This paper investigates the general question of combination of logics from a categorial perspective.
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  10.  15
    Walter Alexandre Carnielli & Luiz Paulo Alcantara (1984). Paraconsistent Algebras. Studia Logica 43 (1-2):79 - 88.
    The prepositional calculiC n , 1 n introduced by N.C.A. da Costa constitute special kinds of paraconsistent logics. A question which remained open for some time concerned whether it was possible to obtain a Lindenbaum''s algebra forC n . C. Mortensen settled the problem, proving that no equivalence relation forC n . determines a non-trivial quotient algebra.The concept of da Costa algebra, which reflects most of the logical properties ofC n , as well as the concept of paraconsistent closure system, (...)
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  11. Walter A. Carnielli, Itala M. L. D'ottaviano & Brazilian Conference on Mathematical Logic (1999). Advances in Contemporary Logic and Computer Science Proceedings of the Eleventh Brazilian Conference on Mathematical Logic, May 6-10, 1996, Salvador, Bahia, Brazil. [REVIEW] Monograph Collection (Matt - Pseudo).
     
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  12. Walter Alexandre Carnielli & Mamede Lima-Marques (1992). Reasoning Under Inconsistent Knowledge. Journal of Applied Non-Classical Logics 2 (1):49-79.
     
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  13.  16
    Walter A. Carnielli (2004). Book Review: Yves Nievergelt, Foundations of Logic and Mathematics: Applications to Computer Science and Cryptography, Birkäuser Verlag, Boston, 2002, €90, Pp. 480, ISBN 0-8176-4249-8, Hardcover. Dimensions (in Inches): 1.00 × 9.96 × 7.36. [REVIEW] Studia Logica 78 (3):479-481.
    Book review r A. (2004). "Book review: Yves nievergelt, foundations of ...
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  14. Walter A. Carnielli & Itala Ml D'Ottaviano (1997). Translations Between Logical Systems: A Manifesto. Logique Et Analyse 157:67-81.
     
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  15.  18
    Sahid Rahman & Walter A. Carnielli (2000). The Dialogical Approach to Paraconsistency. Synthese 125 (1-2):201-232.
    Being a pragmatic and not a referential approach tosemantics, the dialogical formulation ofparaconsistency allows the following semantic idea tobe expressed within a semi-formal system: In anargumentation it sometimes makes sense to distinguishbetween the contradiction of one of the argumentationpartners with himself (internal contradiction) and thecontradiction between the partners (externalcontradiction). The idea is that externalcontradiction may involve different semantic contextsin which, say A and ¬A have been asserted.The dialogical approach suggests a way of studying thedynamic process of contradictions through which thetwo (...)
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  16.  4
    Walter A. Carnielli & Mamede Lima Marques (1991). Razão e irracionalidade na representação do conhecimento. Trans/Form/Ação 14:165-177.
    How is it possible that beginning from the negation of rational thoughts one comes to produce knowledge? This problem, besides its intrinsic interest, acquires a great relevance when the representation of a knowledge is settled, for example, on data and automatic reasoning. Many treatment ways have been tried, as in the case of the non-monotonic logics; logics that intend to formalize an idea of reasoning by default, etc. These attempts are incomplete and are subject to failure. A possible solution would (...)
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  17.  2
    Walter A. Carnielli (2004). Book Review: Yves Nievergelt, Birkäuser Verlag, Boston, 2002,€ 90, Pp. 480, ISBN 0-8176-4249-8, Hardcover. Dimensions (in Inches): 1.00× 9.96× 7.36. [REVIEW] Studia Logica 78 (3):479-481.
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  18.  2
    Walter Alexandre Carnielli & Carlos Augusto Di Prisco (1993). Some Results on Polarized Partion Relations of Higher Dimension. Mathematical Logic Quarterly 39 (1):461-474.
    Several types of polarized partition relations are considered. In particular we deal with partitions defined on cartesian products of more than two factors. MSC: 03E05.
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  19.  1
    Walter A. Carnielli (1987). The Problem Of Quantificational Completeness and the Characterization of All Perfect Quantifiers in 3‐Valued Logics. Mathematical Logic Quarterly 33 (1):19-29.
    This paper introduces the notions of perfect quantifiers in general many-valued logics and investigates the problem of quantificational completeness for such logics as well as the problem of characterizing all perfect quantifiers in 3-valued logics using techniques of combinatorial group theory.
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  20. Walter A. Carnielli & Luiz Carlos P. D. Pereira (eds.) (1995). Logic, Sets and Information: Proceedings of the Tenth Brazilian Conference on Mathematical Logic. Centro de Lógica, Epistemologia E História da Ciência, Unicamp.
    Proceedings of the Tenth Brazilian Conference on Mathematical Logic. Coleção CLE, volume 14, 1995. Centro De Lógica, Epistemologia e História da Ciência, Unicamp, Campinas, SP, Brazil.
     
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  21. Walter A. Carnielli, Marcelo E. Coniglio & Itala M. L. D'ottaviano (2002). Paraconsistency the Logical Way to the Inconsistent : Proceedings of the World Congress Held in São Paulo.
    This impressive compilation of the material presented at the Second World Congress on Paraconsistency held in Juquehy-Sao Sebastião, São Paulo, Brazil, represents an integrated discussion of all major topics in the area of paraconsistent logic---highlighting philosophical and historical aspects, major developments and real-world applications.
     
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  22. Walter A. Carnielli (1987). The Problem Of Quantificational Completeness and the Characterization of All Perfect Quantifiers in 3-Valued Logics. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (1):19-29.
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  23. Luiz Paulo de Alcantara & Walter Alexandre Carnielli (1981). Transfinite Induction on Ordinal Configurations. Mathematical Logic Quarterly 27 (31‐35):531-538.
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  24. Luiz Paulo de Alcantara & Walter Alexandre Carnielli (1981). Transfinite Induction on Ordinal Configurations. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 27 (31-35):531-538.
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