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)

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)

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)

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)

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)

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)

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

First published in 1969, this was a new assessment of Freud’s most creative years and the formative period in psychoanalysis and was the first book to attempt a systematic presentation of Freud’s early ideas, relating them to his later work and to contemporary psychoanalysis. During the years 1888-1898 Freud published 15 papers and one book. In addition many of his ideas were formulated in a series of letters and drafts that he wrote to Dr Wilhelm Fliess. This material provided new (...) insights into the nature of Freud’s creative genius and gave new meaning to his published works. Psychoanalysis: The First Ten Years reviews these early papers, drafts and letters, and describes tentative formulations that, in spite of their value, were not developed further because of lack of time or a shift in interest. As Dr Stewart observes, ‘the study of this aspect of Freud’s work is perhaps the most exciting. Freud’s creativity in these years was remarkable. The ideas he _discarded_ in this short period of time would, for a less gifted person, have been a full life’s work of which he could have been proud.’ There is a good deal of historical and literary interest in his account of Freud’s relationships with Fliess, Breuer and others, but the core of the book is the critical assessment and systematic presentation of Freud’s early major insights, which dramatically reveal a creative genius in the process of discovery. (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)

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)

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.

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 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.