This volume is based on the papers presented at the international conference Model-Based Reasoning in Science and Technology (MBR09_BRAZIL), held at the University of Campinas (UNICAMP), Campinas, Brazil, December 2009. The presentations given at the conference explored how scientific cognition, but several other kinds as well, use models, abduction, and explanatory reasoning to produce important or creative changes in theories and concepts. Some speakers addressed the problem of model-based reasoning in technology, and stressed the issue of science and technological innovation. (...) The various contributions of the book are written by interdisciplinary researchers who are active in the area of creative reasoning in logic, science, and technology: the most recent results and achievements about the topics above are illustrated in detail in the papers. The book is divided in three parts, which cover the following main areas: part I, abduction, problem solving, and practical reasoning; part II: formal and computational aspects of model based reasoning; part III, models, mental models, representations. (shrink)
http://dx.doi.org/10.5007/1808-1711.2009v13n3p283 Em uma série de seminários e conferências no Brasil em 2008, Jaakko Hintikka, em uma série de palestras no Brasil em 2008, defendeu que a “IF-lógica” (“independence friendly logic”) e a lógica paraconsistente são, em certo sentido, bastante similares. A partir do esboço de um novo sistema paraconsistente, ele afirma que várias potencialidades da IF-lógica podem ser reproduzidas na lógica paraconsistente. Uma das grandes dificuldades, deixada como um desafio, seria a formulação de condições de verdade para esta nova linguagem (...) paraconsistente de primeira ordem, com vistas a garantir uma maior inter-relação entre esta e a IF-lógica. Argumento que tais condições de verdade não somente sugerem uma abordagem inovadora em semântica de jogos para a paraconsistência, mas também que a partir deste ponto de vista as “Lógicas da Inconsistência Formal” podem modelar a lógica interna dos elencos socráticos. Pretendo discutir estes e outros pontos levantados por Hintikka, tomando-os como desafios e oportunidades para o paraconsistentismo e para a IF-lógica, bem como levantar algumas críticas sobre a visão de Hintikka sobre a paraconsistência. (shrink)
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.
Although a very recent topic in contemporary logic, the subject of combinations of logics has already shown its deep possibilities. Besides the pure philosophical interest offered by the possibility of defining mixed logic systems in which distinct operators obey logics of different nature, there are also several pragmatical and methodological reasons for considering combined logics. We survey methods for combining logics (integration of several logic systems into a homogeneous environment) as well as methods for decomposing logics, showing their interesting properties (...) and applications. (shrink)
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. (...) Main properties like soundness and completeness are shown to be preserved, comparison with bring is discussed, and some important classes of examples are analyzed with respect to the collapsing problem. (shrink)
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 (...) contexts evolve for the sake of argumentation intoone system containing both contexts.More technically, we show a new, dialogical, way tobuild paraconsistent systems for propositional andfirst-order logic with classical and intuitionisticfeatures (i.e. paraconsistency both with and withouttertium non-datur) and present theircorresponding tableaux. (shrink)
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}$$\scriptstyle \omega$, in particular, constitutes no more than a lower deductive bound to this hierarchy and differs considerably from its companions. A long standing problem in the literature (open for more than 35 years) is (...) to define the deductive limit to this hierarchy, that is, its greatest lower deductive bound. The calculus $ \mathcal {C}$min, stronger than $ \mathcal {C}$$\scriptstyle \omega$, is first presented as a step toward this limit. As an alternative to the bivaluation semantics of $ \mathcal {C}$min presented thereupon, possible-translations semantics are then introduced and suggested as the standard technique both to give this calculus a more reasonable semantics and to derive some interesting properties about it. Possible-translations semantics are then used to provide both a semantics and a decision procedure for $ \mathcal {C}$Lim, the real deductive limit of da Costa's hierarchy. Possible-translations semantics also make it possible to characterize a precise sense of duality: as an example, $ \mathcal {D}$min is proposed as the dual to $ \mathcal {C}$min. (shrink)
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.
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].
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 (...) particular many-valued formal systems. (shrink)
This publication refers to the proceedings of the Seventh Latin American on Mathematical Logic held in Campinas, SP, Brazil, from July 29 to August 2, 1985. The event, dedicated to the memory of Ayda I. Arruda, was sponsored as an official Meeting of the Association for Symbolic Logic. Walter Carnielli. -/- The Journal of Symbolic Logic Vol. 51, No. 4 (Dec., 1986), pp. 1093-1103.
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, (...) are introduced in this paper. (shrink)
