We address the problem of combining intuitionistic and S4 modal logic in a non-collapsing way inspired by the recent works in combining intuitionistic and classical logic. The combined language includes the shared constructors of both logics namely conjunction, disjunction and falsum as well as the intuitionistic implication, the classical implication and the necessity modality.We present a Gentzen calculus for the combined logic defined over a Gentzen calculus for the host S4 modal logic. The semantics is provided by Kripke structures. The (...) calculus is proved to be sound and complete with respect to this semantics. We also show that the combined logic is a conservative extension of each component. Finally we establish that the Gentzen calculus for the combined logic enjoys cut elimination. (shrink)

The main objective of this paper is to define a logic for reasoning about distributed time-stamped claims. Such a logic is interesting for theoretical reasons, i.e. as a logic per se, but also because it has a number of practical applications, in particular when one needs to reason about a huge amount of pieces of evidence collected from different sources, where some of the pieces of evidence may be contradictory and some sources are considered to be more trustworthy than others. (...) We introduce the time-stamped claim logic including a sound and complete sequent calculus. In order to show how time-stamped claim logic can be used in practice, we consider a concrete cyber-attribution case study. (shrink)

Sufficient conditions for first-order-based sequent calculi to admit cut elimination by a Schütte–Tait style cut elimination proof are established. The worst case complexity of the cut elimination is analysed. The obtained upper bound is parameterized by a quantity related to the calculus. The conditions are general enough to be satisfied by a wide class of sequent calculi encompassing, among others, some sequent calculi presentations for the first order and the propositional versions of classical and intuitionistic logic, classical and intuitionistic modal (...) logic S4, and classical and intuitionistic linear logic and some of its fragments. Moreover the conditions are such that there is an algorithm for checking if they are satisfied by a sequent calculus. (shrink)

Satisfaction systems and reductions between them are presented as an appropriate context for analyzing the satisfiability and the validity problems. The notion of reduction is generalized in order to cope with the meet-combination of logics. Reductions between satisfaction systems induce reductions between the respective satisfiability problems and (under mild conditions) also between their validity problems. Sufficient conditions are provided for relating satisfiability problems to validity problems. Reflection results for decidability in the presence of reductions are established. The validity problem in (...) the meet-combination is proved to be decidable whenever the validity problem for the components are decidable. Several examples are discussed, namely, involving modal and intuitionistic logics, as well as the meet-combination of modal logic and intuitionistic logic. (shrink)

We give an axiomatization of first‐order logic enriched with the almost‐everywhere quantifier over finitely additive measures. Using an adapted version of the consistency property adequate for dealing with this generalized quantifier, we show that such a logic is both strongly complete and enjoys Craig interpolation, relying on a (countable) model existence theorem. We also discuss possible extensions of these results to the almost‐everywhere quantifier over countably additive measures.

The novel notion of importing logics is introduced, subsuming as special cases several kinds of asymmetric combination mechanisms, like temporalization [8, 9], modalization [7] and exogenous enrichment [13, 5, 12, 4, 1]. The graph-theoretic approach proposed in [15] is used, but formulas are identified with irreducible paths in the signature multi-graph instead of equivalence classes of such paths, facilitating proofs involving inductions on formulas. Importing is proved to be strongly conservative. Conservative results follow as corollaries for temporalization, modalization and exogenous (...) enrichment. (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)

A new technique is presented for proving that a consequence system enjoys Craig interpolation or Maehara interpolation based on the fact that these properties hold in another consequence system. This technique is based on the existence of a back and forth translation satisfying some properties between the consequence systems. Some examples of translations satisfying those properties are described. Namely a translation between the global/local consequence systems induced by fragments of linear logic, a Kolmogorov-Gentzen-Gödel style translation, and a new translation between (...) the global consequence systems induced by full Lambek calculus and linear logic, mixing features of a Kiriyama-Ono style translation with features of a Kolmogorov-Gentzen-Gödel style translation. These translations establish a strong relationship between the logics involved and are used to obtain new results about whether Craig interpolation and Maehara interpolation hold in that logics . (shrink)

Arrow and turnstile interpolations are investigated in UCL [introduced by Sernadas et al. ], a logic that is a complete extension of classical propositional logic for reasoning about connectives that only behave as expected with a given probability. Arrow interpolation is shown to hold in general and turnstile interpolation is established under some provisos.

Fusion is a well-known form of combining normal modal logics endowed with a Hilbert calculi and a Kripke semantics. Herein, fusion is studied over logic systems using sequent calculi labelled with truth values and with a semantics based on a two-sorted algebra allowing, in particular, the representation of general Kripke structures. A wide variety of logics, including non-classical logics like, for instance, modal logics and intuitionistic logic can be presented by logic systems of this kind. A categorical approach of fusion (...) is defined in the context of these logic systems. Preservation of soundness and completeness by fusion is studied. Soundness is preserved without further requirements, completeness is preserved under mild assumptions. (shrink)

We extend meet-combination of logics for capturing the consequences that are common to both logics. With this purpose in mind we define meet-combination of consequence systems. This notion has the advantage of accommodating different ways of presenting the semantics and the deductive calculi. We consider consequence systems generated by a matrix semantics and consequence systems generated by Hilbert calculi. The meet-combination of consequence systems generated by matrix semantics is the consequence system generated by their product. On the other hand, the (...) meet-combination of consequence systems generated by Hilbert calculi is the consequence system generated by their interconnection. We investigate preservation of several properties. Capitalizing on these results we show that interconnection provides an axiomatization for the product. Illustrations are given for intuitionistic and modal logics, Łukasiewicz logic and some paraconsistent logics. (shrink)

Cut elimination is shown, in a constructive way, to hold in sequent calculi labelled with truth values for a wide class of normal modal logics, supporting global and local reasoning and allowing a general frame semantics. The complexity of cut elimination is studied in terms of the increase of logical depth of the derivations. A hyperexponential worst case bound is established. The subformula property and a similar property for the label terms are shown to be satisfied by that class of (...) modal sequent calculi. Modal logics presented by these calculi are proven to be globally and locally consistent. (shrink)

Linear temporal logic with Since and Until modalities is expressively equivalent, over the class of complete linear orders, to a fragment of first-order logic known as FOMLO. It turns out that LTL, under some basic assumptions, is expressively complete if and only if it has the property, called separation, that every formula is equivalent to a Boolean combination of formulas that each refer only to the past, present or future. Herein we present simple algorithms and their implementations to perform separation (...) of the LTL with Since and Until, over discrete and complete linear orders, and translation from FOMLO formulas into equivalent temporal logic formulas. We additionally show that the separation of a certain fragment of LTL results in at most a double exponential size growth. (shrink)

We introduce a general recipe for presenting non-classical logics in a modular and uniform way as labelled deduction systems. Our recipe is based on a labelling mechanism where labels are general entities that are present, in one way or another, in all logics, namely truth-values. More specifically, the main idea underlying our approach is the use of algebras of truth-values, whose operators reflect the semantics we have in mind, as the labelling algebras of our labelled deduction systems. The “truth-values as (...) labels” approach allows us to give generalized systems for multiple-valued logics within the same formalism: since we can take multiple-valued logics as meaning not only finitely or infinitely many-valued logics but also power-set logics, i.e. logics for which the denotation of a formula can be seen as a set of worlds, our recipe allows us to capture also logics such as modal, intuitionistic and relevance logics, thus providing a first step towards the fibring of these logics with many-valued ones. (shrink)

The essential structure of proofs is proposed as the basis for a measure of complexity of formulas in FOL. The motivating idea was the recognition that distinct theorems can have the same derivation modulo some non essential details. Hence the difficulty in proving them is identical and so their complexity should be the same. We propose a notion of complexity of formulas capturing this property. With this purpose, we introduce the notions of schema calculus, schema derivation and description complexity of (...) a schema formula. Based on these concepts we prove general robustness results that relate the complexity of introducing a logical constructor with the complexity of the component schema formulas as well as the complexity of a schema formula across different schema calculi. (shrink)

O trabalho que aqui se propões tem por objetivo analisar as obras de Immanuel Kant buscando sintetizar suas contribuições para a compreensão da filosofia enquanto atitude filosófica, num diálogo com as pedagogias ativas, bem como refletir sobre os métodos para o seu ensino. A pesquisa partirá de um viés bibliográfico a fim de trazer os conceitos de autonomia e esclarecimento para uma reflexão sobre os métodos adequados para o despertar de uma consciência filosófica. Embora distante de sua finalidade, a educação (...) deve manter-se em constante busca por melhorias, pelo desenvolvimento da humanidade em todas as suas esferas. (shrink)

This paper addresses the problems of justifying and explaining beliefs about facts in the context of civil trials. The first section contains some remarks about the nature of adjudicative fact-finding and highlights the communicative features of deciding about facts in judicial context. In Sect. 2, some difficulties and the incompleteness presented by Bayesian and coherentist frameworks, which are taken as methods suitable to solve the above-mentioned problems, are pointed out. In the third section, the purely epistemic approach to the justification (...) and the explanation of beliefs about facts is abandoned and focus is given to the dialectical nature of civil procedure, where the parties and, particularly, the judge have to make their reasoning clear enough to allow a fruitful and efficient debate about facts. For this purpose, a communication/argumentation system is put forward, consisting of fourteen intertwined rules of discourse. The system embodies the fundamental epistemic principle according to which belief is updated given new evidence, is tailored for abductive inferences and is structured on fundamental concepts of civil procedural law. The fourth section presents an empirical application of the system to a real case. (shrink)

In classical logic, a contradiction allows one to derive every other sentence of the underlying language; paraconsistent logics came relatively recently to subvert this explosive principle, by allowing for the subsistence of contradictory yet non-trivial theories. Therefore our surprise to find Wittgenstein, already at the 1930s, in comments and lectures delivered on the foundations of mathematics, as well as in other writings, counseling a certain tolerance on what concerns the presence of contradictions in a mathematical system. ‘Contradiction. Why just this (...) spectre? This is really very suspicious.’ In the last decades, several authors have been digging into Wittgenstein’s rather non-standard standpoint on what concerns the interpretation and import of contradiction in logic and mathematics, and many other authors have been investigating the possibility of taking Wittgenstein seriously as one of the early forerunners of paraconsistency. While many advances have been made on the first front, the second set of investigations has led almost exclusively to negative results: no, no operational proposal about the construction of a logic in which contradictions are made inoffensive can be read from Wittgenstein’s philosophical work; in fact, it appears that the most one can find there is the exhortation for mathematicians to alter their attitude with respect to contradictions and to consistency proofs. The play is done, and one looks for a resume of the opera. This paper fills that blank, as a thorough investigation of the possible relations between Wittgenstein and paraconsistency. • DOI:10.5007/1808-1711.2010v14n1p135. (shrink)

This article presents some results of a research on computational strategies for the visualization of sign classification structures and sign processes. The focus of this research is the various classifications of signs described by Peirce. Two models are presented. One of them concerns specifically the 10-fold classification as described in the 1903 Syllabus (MS 540, EP 2: 289–299), while the other deals with the deep structure of Peirce’s various trichotomic classifications. The first is 10cubes, an interactive 3-D model of Peirce’s (...) 10-fold classification, as described in the Syllabus. The second is 3N3, a computer program that builds equivalent diagrams for any n-trichotomic classification of signs. We are specially interested in how a graphic design methodology, associated with computer graphic resources and techniques, can contribute to the construction of interactive models that serve as tools for the investigation of C. S. Peirce’s theory of signs. (shrink)

We present here a digital scenario to simulate the emergence of self-organized symbol-based communication among artificial creatures inhabiting a virtual world of predatory events. In order to design the environment and creatures, we seek theoretical and empirical constraints from C.S.Peirce Semiotics and an ethological case study of communication among animals. Our results show that the creatures, assuming the role of sign users and learners, behave collectively as a complex system, where self-organization of communicative interactions plays a major role in the (...) emergence of symbol-based communication. We also strive for a careful use of the theoretical concepts involved, including the concepts of symbol, communication, and emergence, and we use a multi-level model as a basis for the interpretation of inter-level relationships in the semiotic processes we are studying. (shrink)

Este texto introduz a tradução do discurso de intitulado "Sobre os números transfinitos" ("Über transfinite Zahlen"), proferido por Henri Poincaré em 27 de abril de 1909, na Universidade de Göttingen. Após uma breve apresentação do pensamento do autor acerca dos fundamentos da aritmética, procura-se citar os aspectos mais relevantes da chamada crise dos fundamentos da matemática, para então introduzir a reformulação do conceito de predicatividade aventada no referido discurso sobre números transfinitos, contribuição compreendida como um recurso teórico necessário para a (...) superação dos paradoxos relativos à teoria dos conjuntos. Com isso, pretende-se evidenciar o papel central do texto publicado nesta edição para o desenvolvimento da concepção matemática de Henri Poincaré. This article provides an introduction to the translation of the lecture entitled "On transfinite numbers" ("Über transfinite Zahlen"), given by Henri Poincaré at the University of Göttingen on April 27, 1909. Following a short presentation of Poincaré's views on the foundations of arithmetic, it identifies the aspects of the so-called crisis of the foundations of mathematics that are most relevant for understanding his reconstruction of the concept of predicativity, which is intended to be a theoretical resource that may overcome the paradoxes of set theory. In doing so, the article highlights the central role of this text in the process of maturation of Poincaré's views on the foundations of mathematics. (shrink)

In this paper, I intend to dispute Marc Hauser’s thesis, sustained in Wild Minds. What animals Really Think, that we must abandon the question of whether animals have a feeling of themselves, replacing it for an objective and scientific analysis capable of disclosing the extraordinary similitude between different mental procedures animals undergo when they face common challenges.

Uma seção da Gramática Especulativa de C.S.Peirce – Dez classes de signos – recebeu, a partir de 1903, um importante tratamento diagramático. Neste artigo, são apresentados e discutidos dois diagramas desenvolvidos por Peirce para as dez classes, incluindo esboços desses modelos.

This paper proposes that we read a late work of Georg Lukács, The Ontology of Social Being, as an indispensable contribution to ontological investigation in general and particularly to the understanding of social reality. As the ontology of Lukács tends not to be familiar even to those who have foregrounded ontological issues in recent decades, it seems to be extremely fruitful to bring it into discussion. Comparing the analysis of Lukács with the ontology of critical realism, we argue that it (...) is not only possible to identify obvious convergences but also to shed light on many questions that still demand a proper treatment from an ontological perspective. (shrink)

The transference of preservation results between importing and unconstrained fibring is investigated. For that purpose, a new formulation of fibring, called biporting, is introduced, and importing is shown to be subsumed by biporting. In consequence, particular cases of importing, like temporalization, modalization and globalization are subsumed by fibring. Capitalizing on these results, the preservation of the finite model property by fibring is transferred to importing and then carried over to globalization.

Zones of social abandonment are emerging everywhere in Brazil’s big cities—places like Vita, where the unwanted, the mentally ill, the sick, and the homeless are left to die. This haunting, unforgettable story centers on a young woman named Catarina, increasingly paralyzed and said to be mad, living out her time at Vita. Anthropologist João Biehl leads a detective-like journey to know Catarina; to unravel the cryptic, poetic words that are part of the “dictionary” she is compiling; and to trace (...) the complex network of family, medicine, state, and economy in which her abandonment and pathology took form. An instant classic, _Vita_ has been widely acclaimed for its bold fieldwork, theoretical innovation, and literary force. Reflecting on how Catarina’s life story continues, this updated edition offers the reader a powerful new afterword and gripping new photographs following Biehl and Eskerod’s return to Vita. Anthropology at its finest, _Vita_ is essential reading for anyone who is grappling with how to understand the conditions of life, thought, and ethics in the contemporary world. (shrink)

Zones of social abandonment are emerging everywhere in Brazil’s big cities—places like Vita, where the unwanted, the mentally ill, the sick, and the homeless are left to die. This haunting, unforgettable story centers on a young woman named Catarina, increasingly paralyzed and said to be mad, living out her time at Vita. Anthropologist João Biehl leads a detective-like journey to know Catarina; to unravel the cryptic, poetic words that are part of the “dictionary” she is compiling; and to trace (...) the complex network of family, medicine, state, and economy in which her abandonment and pathology took form. As Biehl painstakingly relates Catarina’s words to a vanished world and elucidates her condition, we learn of subjectivities unmade and remade under economic pressures, pharmaceuticals as moral technologies, a public common sense that lets the unsound and unproductive die, and anthropology’s unique power to work through these juxtaposed fields. _Vita’s_ methodological innovations, bold fieldwork, and rigorous social theory make it an essential reading for anyone who is grappling with how to understand the conditions of life, thought and ethics in the contemporary world. (shrink)

This innovative volume is an extended intellectual conversation about the ways personal lives are being undone and remade today. Examining the ethnography of the modern subject, this preeminent group of scholars probes the continuity and diversity of modes of personhood across a range of Western and non-Western societies. Contributors consider what happens to individual subjectivity when stable or imagined environments such as nations and communities are transformed or displaced by free trade economics, terrorism, and war; how new information and medical (...) technologies reshape the relation one has to oneself; and which forms of subjectivity and life possibilities are produced against a world in pieces. The transdisciplinary conversation includes anthropologists, historians of science, psychologists, a literary critic, a philosopher, physicians, and an economist. The authors touch on how we think and write about contingency, human agency, and ethics today. (shrink)

The Second Vatican Council was built within a solidly constituted tradition in the Catholic Church. All councils were held within the traditional and legal parameters of the Church. The question about the condition of possibility of a renewal Council under this tradition shows relevant. The Vatican II is the result of a negotiation between renewal and preservation. Pope John XXIII personally coordinated the construction of the legitimacy of the new event, following steps which may be rescued during the preparatory stages (...) of the great assembly. The reading of this process from sociological parameters may elucidate its plausibility within the tradition and the Church's bureaucratic organization. Pope John started ably a church renewal process, opening a new phase in the long Catholic tradition. Under his Pope condition, he knew how to seed the idea of a revamping event in the name of a divine inspiration and with the set of bishops’ participation of the Church. (shrink)

Ao longo da história, a relação entre a filosofia e a política tem-se revelado espinhosa, denunciando a dificuldade em se conceptualizar sobre o que é por natureza antagónico à cristalização, porque particular e pluralista. Na esfera da opinião, o filósofo deve restringir-se a analisar, criticar, rever e aperfeiçoar os valores políticos coevos, a explicar aos seus conterrâneos o universo de acepções sociais partilhadas, consciente de que a sua concepção fundamenta uma via entre as muitas poss...

: In this paper, we intend to discuss if and in what sense semiosis (meaning process, cf. C. S. Peirce) can be regarded as an "emergent" process in semiotic systems. It is not our problem here to answer when or how semiosis emerged in nature. As a prerequisite for the very formulation of these problems, we are rather interested in discussing the conditions which should be fulfilled for semiosis to be characterized as an emergent process. The first step in this (...) work is to summarize a systematic analysis of the variety of emergence theories and concepts, elaborated by Achim Stephan. Along the summary of this analysis, we pose fundamental questions that have to be answered in order to ascribe a precise meaning to the term "emergence" in the context of an understanding of semiosis. After discussing a model for explaining emergence based on Salthe's hierarchical structuralism, which considers three levels at a time in a semiotic system, we present some tentative answers to those questions. (shrink)

Against the view that symbol-based semiosis is a human cognitive uniqueness, we have argued that non-human primates such as African vervet monkeys possess symbolic competence, as formally defined by Charles S. Peirce. Here I develop this argument by showing that the equivocal role ascribed to symbols by “folk semiotics” stems from an incomplete application of the Peircean logical framework for the classification of signs, which describes three kinds of symbols: rheme, dicent and argument. In an attempt to advance in the (...) classifying semiotic processes, Peirce proposed several typologies, with different degrees of refinement. Around 1903, he developed a division into ten classes. According to this typology, symbols can be further analysed in three subclasses (rheme, dicent, argument). I proceed to demonstrate that vervet monkeys employ dicent symbols. There are remarkable implications of this argument since ‘symbolic species theory’ fails to explore the vast Peircean semiotic philosophy to frame questions regarding the emergence and evolution of symbolic processes. (shrink)