“Trends in Logic XVI: Consistency, Contradiction, Paraconsistency, and Reasoning - 40 years of CLE” is being organized by the Centre for Logic, Epistemology and the History of Science at the State University of Campinas (CLEUnicamp) from September 12th to 15th, 2016, with the auspices of the Brazilian Logic Society, Studia Logica and the Polish Academy of Sciences. The conference is intended to celebrate the 40th anniversary of CLE, and is centered around the areas of logic, epistemology, philosophy and history of (...) science, while bringing together scholars in the fields of philosophy, logic, mathematics, computer science and other disciplines who have contributed significantly to what Studia Logica is today and to what CLE has achieved in its four decades of existence. It intends to celebrate CLE’s strong influence in Brazil and Latin America and the tradition of investigating formal methods inspired by, and devoted to, philosophical views, as well as philosophical problems approached by means of formal methods. The title of the event commemorates one of the three main areas of CLE, what has been called the “Brazilian school of paraconsistency”, combining such a pluralist view about logic and reasoning. (shrink)

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 dub Logics of Formal Inconsistency (LFI) (...) and form part of a much larger family of similar logics. We also show that there are translations from classical and paraconsistent first-order logics into LFI1* and LFI2*, and back. Hence, despite their status as subsystems of classical logic, LFI1* and LFI2* can codify any classical or paraconsistent reasoning. (shrink)

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)

The main objective o f this descriptive paper is to present the general notion of translation between logical systems as studied by the GTAL research group, as well as its main results, questions, problems and indagations. Logical systems here are defined in the most general sense, as sets endowed with consequence relations; translations between logical systems are characterized as maps which preserve consequence relations (that is, as continuous functions between those sets). In this sense, logics together with translations form a (...) bicomplete category of which topological spaces with topological continuous functions constitute a full subcategory. We also describe other uses of translations in providing new semantics for non-classical logics and in investigating duality between them. An important subclass of translations, the conservative translations, which strongly preserve consequence relations, is introduced and studied. Some specific new examples of translations involving modal logics, many-valued logics, para- consistent logics, intuitionistic and classical logics are also described. (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.

We propose in this paper a family of algebraic models of ZFC based on the three-valued paraconsistent logic LPT0, a linguistic variant of da Costa and D’Ottaviano’s logic J3. The semantics is given by twist structures defined over complete Boolean agebras. The Boolean-valued models of ZFC are adapted to twist-valued models of an expansion of ZFC by adding a paraconsistent negation. This allows for inconsistent sets w satisfying ‘not (w = w)’, where ‘not’ stands for the paraconsistent negation. Finally, our (...) framework is adapted to provide a class of twist-valued models generalizing Löwe and Tarafder’s model based on logic (PS 3,∗), showing that they are paraconsistent models of ZFC. The present approach offers more options for investigating independence results in paraconsistent set theory. (shrink)

In this paper we propose a very general de nition of combination of logics by means of the concept of sheaves of logics. We first discuss some properties of this general definition and list some problems, as well as connections to related work. As applications of our abstract setting, we show that the notion of possible-translations semantics, introduced in previous papers by the first author, can be described in categorial terms. Possible-translations semantics constitute illustrative cases, since they provide a new (...) semantical account for abstract logical systems, particularly for many-valued and paraconsistent logics. (shrink)

Attempts to comprehend the traumatic significance of Hiroshima in order to construct a new theory of history.

Fish has always been adept at revising his position to incorporate what he’s learned from his critics while repaying the favor by assigning them a position they never took. The latter practice naturally helps conceal the borrowings, but as Fish’s position evolves it becomes progressively difficult to determine who is the author of his essays. I am, of course, gratified to see how much Fish has learned from me. It is salutary to find that Fish is finally just a humble (...) historian working with others at “recovering a system of thought and feeling” that will enable us to establish the historical context of Milton’s most probable intentions and realizing, as many historians of literature don’t, that we can only do so by bringing concepts provided by literary theory—form, function, artistic purpose, and so forth—to bear on the mass of historical materials at our disposal.3 It is also gratifying to see that Fish has discovered the law of context and now realizes that there are no local matters. Had he discovered that earlier, we’d have been spared Aunt Tilly and the discussion of Mr. Collins—as well as the general notion extrapolated from those examples that anything a sizable group decides to do will fly since nothing else constraints interpretation. We’d also have been spared the concepts of reading and affective criticism presented in Fish’s early work and the unchecked linguistic hijinks used to sustain those readings. I derive my deepest pleasure, however, from finding that Fish has finally discovered the conflict of interpretations proper and its primacy—“the resistance offered by one interpretively produced shape to the production of another” —though I must sadly abridge this progress report by noting that he finds himself powerless to do anything with this recognition. That is as it must be, for the most interesting thing about Fish’s borrowings is where he stops—and why he has to. Having let me write the first 5 ½ pages of his reply, he suddenly stops taking dictation so that he can simply reassert, in all its abstract glory, his tried-and-true resolution of all interpretive controversy by community interest. Had he read further, he would have discovered that a good deal more emerges if one attempts to preserve and deal with the conflict of interpretations rather than to do away with it. He would even have discovered my epistemology and would have learned the main lesson—that his position is not an alternative to mine but an early moment it contains and sublates in a larger context.Have taught Fish so much, I found myself, instead, poorly repaid by the position he foists upon me. Constantly caught up in an effort to reiterate the dichotomy on which his entire theorizing depends, Fish’s fixed need is to rework all disputes into an opposition between the party of independent fact-disinterested reason and the party of interest so that he might triumphantly resolve all difficulties by once again discovering the simple fact of interests. Lest this strategy hide behind a common misconception, our debate is not a case where distinct frameworks are simply misreading one another, as they must, but one where one framework must deliberately and seriously misread others since it has no other way to sustain itself. If the account Fish gives of my argument is the way things must look from his framework, all that this fact signifies is the paucity of his framework and its inability to achieve even minimal descriptive adequacy. 3. But even here things are a good deal more complex than Fish imagines. For a good statement of the logic and problems of historical interpretation, see Robert Marsh, “Historical Interpretation and the History of Criticism,” in Literary Criticism and Historical Understanding, ed. Philip Damon , pp. 1-24. (shrink)

There is no doubt that soybean is the most important crop for Argentina, with a planted surface that rose 11,000,000 hectares and a production of around 35,000,000 metric tons. During the 1990s, there was a significant agriculture transformation in the country, motorize by the adoption of transgenic crops (soy-bean, maize, and cotton) under the no-tillage system. The expansion of this model has been spread not only in the Pampas but also in very rich areas with high biodiversity, opening a new (...) agricultural border to important eco-regions like the Yungas, Great Chaco, and the Mesopotamian Forest. Transgenic cropping is a powerful technology. This produced relevant transformations over the environment and society where it is allowed. Migration, concentration of agribusiness, and loss of food sovereignty are some of the social results. Landscape transformation in the rural sector is evident, and the appearance of tolerance weeds to glyphosate is a reality. Nutrient depletion, soil-structure degradation, potential desertification, and loss of species are other consequences on the environmental level. (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)

This paper briefly outlines some advancements in paraconsistent logics for modelling knowledge representation and reasoning. Emphasis is given on the so-called Logics of Formal Inconsistency (LFIs), a class of paraconsistent logics that formally internalize the very concept(s) of consistency and inconsistency. A couple of specialized systems based on the LFIs will be reviewed, including belief revision and probabilistic reasoning. Potential applications of those systems in the AI area of KRR are tackled by illustrating some examples that emphasizes the importance of (...) a fine-tuned treatment of consistency in modelling reputation systems, preferences, argumentation, and evidence. (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)

Interpretation is an institutional activity and that may be the most significant fact about it; we are, indeed, a profession, and as such we train students to think about literature in certain ways. Membership in the community is determined by how well one masters the rules of the game. These inescapable facts may be the source of our greatest problems—or their hidden solution. Stanley Fish champions the latter alternative, arguing, in his most recent book, that “the interpretive community” is the (...) ultimate principle of authority in criticism and is capable of resolving all the problems of interpretation.1 If we want to know what reading is, how texts achieve determinate meaning, what constitutes validity in interpretation, or how to resolve the “conflict of interpretations,” we must, Fish argues, focus on the community itself, for it is here alone that these matters are determined.Though he has had more than his share of professional attention, having developed this argument makes Fish’s work worthy of further consideration. He quite simply presents the best picture we are likely to get of the “mind” of the profession, and, in treating him at length here, I am primarily concerned with his representative status. His great achievement is to have articulated the assumptions and beliefs underlying the practices that are favored in our profession: the tacit theoretical position composed of ideas and commonplaces that are so deeply held and constantly in use that they “prestructure” both our dealings with literature and our debates over those dealings. While remaining for the most part “unconscious,” these ideas nevertheless function as self-evident and unassailable truths. If we are to move, as I think we must, toward experiencing a crisis in our discipline, we first have to know where we are. And for that, Fish is invaluable because he has set out to become the official spokesman and efender of the profession. Walter A. Davis, associate professor of English at the Ohio State University, is the author of The Act of Interpretation: A Critique of Literary Reason. The present essay is from a recently completed work on contemporary criticism. He is currently writing a book on modern American drama. (shrink)

First Published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

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 (...) be to formulate a logic of the irrational, which offers a model for reasoning permitting to support contradictions as well as to produce knowledge from such situations. An intuition underlying the foundation of such a logic consists of the da Costa's paraconsistent logics presenting however, a different deduction theory and a whole distinct semantics, called here "the semantics of possible translations". The present proposing, following our argumentation, intends to enlight all this question, by a whole satisfactory logical point of view, being practically applicable and philosophically acceptable.Como é possível que a partir da negação do racional se possa obter conhecimento adicional? Esse problema, além de seu interesse intrínseco, adquire uma relevância adicional quando o encontramos na representação do conhecimento em bases de dados e raciocínio automático, por exemplo. Nesse caso, diversas tentativas de tratamento têm sido propostas, como as lógicas não-monotônicas, as lógicas que tentam formalizar a ideia do raciocínio por falha . Tais tentativas de solução, porém, são falhas e incompletas; proponho que uma solução possível seria formular uma lógica do irracional, que oferecesse um modelo para o raciocínio permitindo não só suportar contradições, como conseguir obter conhecimento, a partir de tais situações. A intuição subjacente à formulação de tal lógica são as lógicas paraconsistentes de da Costa, mas com uma teoria da dedução diferente e uma semântica completamente distinta . Tal proposta, como pretendo argumentar, fornece um enfoque para a questão que é ao mesmo tempo completamente satisfatório, aplicável do ponto de vista prático e aceitável do ponto de vista filosófico. (shrink)

There are two foundational, but not fully developed, ideas in paraconsistency, namely, the duality between paraconsistent and intuitionistic paradigms, and the introduction of logical operators that express meta-logical notions in the object language. The aim of this paper is to show how these two ideas can be adequately accomplished by the Logics of Formal Inconsistency (LFIs) and by the Logics of Formal Undeterminedness (LFUs). LFIs recover the validity of the principle of explosion in a paraconsistent scenario, while LFUs recover the (...) validity of the principle of excluded middle in a paracomplete scenario. We introduce definitions of duality between inference rules and connectives that allow comparing rules and connectives that belong to different logics. Two formal systems are studied, the logics mbC and mbD, that display the duality between paraconsistency and paracompleteness as a duality between inference rules added to a common core– in the case studied here, this common core is classical positive propositional logic (CPL + ). The logics mbC and mbD are equipped with recovery operators that restore classical logic for, respectively, consistent and determined propositions. These two logics are then combined obtaining a pair of logics of formal inconsistency and undeterminedness (LFIUs), namely, mbCD and mbCDE. The logic mbCDE exhibits some nice duality properties. Besides, it is simultaneously paraconsistent and paracomplete, and able to recover the principles of excluded middle and explosion at once. The last sections offer an algebraic account for such logics by adapting the swap-structures semantics framework of the LFIs the LFUs. This semantics highlights some subtle aspects of these logics, and allows us to prove decidability by means of finite non-deterministic matrices. (shrink)