Maximality is a desirable property of paraconsistent logics, motivated by the aspiration to tolerate inconsistencies, but at the same time retain from classical logic as much as possible. In this paper we introduce the strongest possible notion of maximal paraconsistency, and investigate it in the context of logics that are based on deterministic or non-deterministic three-valued matrices. We show that all reasonable paraconsistent logics based on three-valued deterministic matrices are maximal in our strong sense. This applies to practically all three-valued (...) paraconsistent logics that have been considered in the literature, including a large family of logics which were developed by da Costa's school. Then we show that in contrast, paraconsistent logics based on three-valued properly nondeterministic matrices are not maximal, except for a few special cases (which are fully characterized). However, these non-deterministic matrices are useful for representing in a clear and concise way the vast variety of the (deterministic) three-valued maximally paraconsistent matrices. The corresponding weaker notion of maximality, called premaximal paraconsistency, captures the "core" of maximal paraconsistency of all possible paraconsistent determinizations of a non-deterministic matrix, thus representing what is really essential for their maximal paraconsistency. (shrink)

The notion of bilattice was introduced by Ginsberg, and further examined by Fitting, as a general framework for many applications. In the present paper we develop proof systems, which correspond to bilattices in an essential way. For this goal we introduce the notion of logical bilattices. We also show how they can be used for efficient inferences from possibly inconsistent data. For this we incorporate certain ideas of Kifer and Lozinskii, which happen to suit well the context of our work. (...) The outcome are paraconsistent logics with a lot of desirable properties.1. (shrink)

Paradefinite logics are logics that can be used for handling contradictory or partial information. As such, paradefinite logics should be both paraconsistent and paracomplete. In this paper we consider the simplest semantic framework for introducing paradefinite logics. It consists of the four-valued matrices that expand the minimal matrix which is characteristic for first degree entailments: Dunn–Belnap matrix. We survey and study the expressive power and proof theory of the most important logics that can be developed in this framework.

We introduce a general approach for representing and reasoning with argumentation-based systems. In our framework arguments are represented by Gentzen-style sequents, attacks between arguments are represented by sequent elimination rules, and deductions are made according to Dung-style skeptical or credulous semantics. This framework accommodates different languages and logics in which arguments may be represented, allows for a flexible and simple way of expressing and identifying arguments, supports a variety of attack relations, and is faithful to standard methods of drawing conclusions (...) by argumentation frameworks. Altogether, we show that argumentation theory may benefit from incorporating proof theoretical techniques and that different non-classical formalisms may be used for backing up intended argumentation semantics. (shrink)

In this paper we provide a proof theoretical investigation of logical argumentation, where arguments are represented by sequents, conflicts between arguments are represented by sequent elimination rules, and deductions are made by dynamic proof systems extending standard sequent calculi. The idea is to imitate argumentative movements in which certain claims are introduced or withdrawn in the presence of counter-claims. This is done by a dynamic evaluation of sequences of sequents, in which the latter are considered ‘derived’ or ‘not derived’ according (...) to the content of the sequence. We show that decisive conclusions of such a process correspond to well-accepted consequences of the underlying argumentation framework. The outcome is therefore a general and modular proof-theoretical approach for paraconsistent and non-monotonic reasoning with argumentation systems. (shrink)

Reasoning with the maximally consistent subsets of the premises is a well-known approach for handling contradictory information. In this paper we consider several variations of this kind of reasoning, for each one we introduce two complementary computational methods that are based on logical argumentation theory. The difference between the two approaches is in their ways of making consequences: one approach is of a declarative nature and is related to Dung-style semantics for abstract argumentation, while the other approach has a more (...) proof-theoretical flavor, extending Gentzen-style sequent calculi. The outcome of this work is a new perspective on reasoning with MCS, which shows a strong link between the latter and argumentation systems, and which can be generalized to some related formalisms. As a by-product of this we obtain soundness and completeness results for the dynamic proof systems with respect to several of Dung’s semantics. In a broader context, we believe that this work helps to better understand and evaluate the role of logic-based instantiations of argumentation frameworks. (shrink)

We introduce a family of preferential logics that are useful for handling information with different levels of uncertainty. The corresponding consequence relations are nonmonotonic, paraconsistent, adaptive, and rational. It is also shown that the formalisms in this family can be embedded in corresponding four-valued logics with at most three uncertainty levels, and that reasoning with these logics can be simulated by algorithms for processing circumscriptive theories, such as DLS and SCAN.

In this article, we present an argumentative approach to normative reasoning. Special attention is paid to deontic conflicts, contrary-to-duty and specificity cases, which are modelled by means of argumentative attacks. For this, we adopt a recently proposed framework for logical argumentation in which arguments are generated by a sequent calculus of a given base logic of Argument & Computation ), and use standard deontic logic as our base logic. Argumentative attacks are realized by elimination rules that allow to discharge specific (...) sequents. We demonstrate the usefulness of our approach by means of various well-known benchmark examples, and show that this approach is rich enough to capture a variety of paradigms for handling conflicting norms such as reasoning with maximally consistent sets, prioritized norms and deontic formalisms based on I/O logic. (shrink)

This book is a collection of contributions honouring Arnon Avron’s seminal work on the semantics and proof theory of non-classical logics. It includes presentations of advanced work by some of the most esteemed scholars working on semantic and proof-theoretical aspects of computer science logic. Topics in this book include frameworks for paraconsistent reasoning, foundations of relevance logics, analysis and characterizations of modal logics and fuzzy logics, hypersequent calculi and their properties, non-deterministic semantics, algebraic structures for many-valued logics, and representations of (...) the mechanization of mathematics. Avron’s foundational and pioneering contributions have been widely acknowledged and adopted by the scientific community. His research interests are very broad, spanning over proof theory, automated reasoning, non-classical logics, foundations of mathematics, and applications of logic in computer science and artificial intelligence. This is clearly reflected by the diversity of topics discussed in the chapters included in this book, all of which directly relate to Avron’s past and present works. This book is of interest to computer scientists and scholars of formal logic. (shrink)

In this paper we introduce hypersequent-based frameworks for the modelling of defeasible reasoning by means of logic-based argumentation and the induced entailment relations. These structures are an extension of sequent-based argumentation frameworks, in which arguments and the attack relations among them are expressed not only by Gentzen-style sequents, but by more general expressions, called hypersequents. This generalization allows us to overcome some of the known weaknesses of logical argumentation frameworks and to prove several desirable properties of the entailments that are (...) induced by the extended frameworks. It also allows us to incorporate as the deductive base of our formalism some well-known logics, which lack cut-free sequent calculi, and so are not adequate for standard sequent-based argumentation. We show that hypersequent-based argumentation yields robust defeasible variants of these logics, with many desirable properties. (shrink)

In the ongoing research of the functions of consciousness, special emphasis has been put on integration of information: the ability to combine different signals into a coherent, unified one. Several theories of consciousness hold that this ability depends on – or at least goes hand in hand with – conscious processing. Yet some empirical findings have suggested otherwise, claiming that integration of information could take place even without awareness. Trying to reconcile this apparent contradiction, the “windows of integration” hypothesis claims (...) that conscious access enables signal processing over large integration windows. The hypothesis applies to integration windows defined either temporally, spatially, or semantically. In this review, we explain the hypothesis and re-examine it in light of new studies published since it was suggested. In line with the hypothesis, these studies provide compelling evidence for unconscious integration, but also demonstrate its limits with respect to time, space, and semantic distance. The review further highlights open questions that still need to be pursued to demonstrate the applicability of the WOI hypothesis as a guiding principle for understanding the depth and scope of unconscious processes. (shrink)

We present a four-valued approach for recovering consistent data from inconsistent set of assertions. For a common family of knowledge-bases we also provide an e cient algorithm for doing so automaticly. This method is particularly useful for making model-based diagnoses.

The work of Arnon Avron and Ofer Arieli has shown a deep relationship between the theory of bilattices and the Belnap-Dunn logic \. This correspondence has been interpreted as evidence that \ is “the” logic of bilattices, a consideration reinforced by the work of Yaroslav Shramko and Heinrich Wansing in which \ is shown to be similarly entrenched with respect to the theories of trilattices and, more generally, multilattices. In this paper, we export Melvin Fitting’s “cut-down” connectives—propositional connectives (...) that “cut down” available evidence—to the case of multilattices and show that two related first degree systems—Harry Deutsch’s four-valued \ and Richard Angell’s \—emerge just as elegantly and are as intimately connected to the theories of bilattices and trilattices as the Belnap-Dunn logic. (shrink)

Sometimes, the availability of more evidence for a conclusion provides a reason to believe in its falsity. This counter-intuitive phenomenon is related to the idea of higher-order evidence, which has attracted broad interest in recent epistemological literature. Occasionally, providing more evidence for something weakens the case in its favor, by casting doubt on the probative value of other evidence of the same sort or on the fact-finder’s cognitive performance. We analyze this phenomenon, discuss its rationality, and outline possible application to (...) evidence law and to the law in general. It is suggested, inter alia, that such higher-order evidence may explain how judicial experience-based expertise in fact-finding is possible despite the absence of a feedback mechanism; and that fact-finders’ self-doubt regarding their own competence in making ‘beyond-reasonable doubt’ judgments might be reasonable and should not be ignored. (shrink)

This article seeks to contribute to the challenge of presenting the silenced voices of excluded groups in society by means of a philosophic community of inquiry composed primarily of children and young adults. It proposes a theoretical model named ‘enabling identity’ that presents the stages whereby, under the guiding role played by the community of philosophic inquiry, the hegemonic meta-narrative of the mainstream society makes room for the identity of members of marginalised groups. The model is based on the recognition (...) of diverse narratives within a web of communal narratives that does not favour the meta-narrative. It reports on the experiences of moderators and students from weak and excluded sectors of society in two countries whose participation in communities of philosophical inquiry gave them not only a “voice” but also a presence and identity. (shrink)

This volume offers a critical analysis of one the most ambitious editorial projects of late Victorian Britain: the edition of the fifty substantial volumes of the Sacred Books of the East. The series was edited and conceptualized by Friedrich Max Müller, a world-famous German-born philologist, orientalist, and religious scholar. Müller and his influential Oxford colleagues secured financial support from the India Office of the British Empire and from Oxford University Press. Arie L. Molendijk documents how the series has become a (...) landmark in the development of the humanities-especially the study of religion and language-in the second half of the nineteenth century. The edition also contributed significantly to the Western perception of the 'religious' or even 'mystic' East, which was textually represented in English translations. The series was a token of the rise of 'big science' and textualized the East, by selecting their 'sacred books' and bringing them under the power of western scholarship. (shrink)

This new book argues that at the core of legal philosophy’s principal debates there is essentially one issue judicial impartiality. Keeping this issue to the forefront,Raban’s approach sheds much light on many difficult and seemingly perplexing jurisprudential debates. Modern Legal Theory and Judicial Impartiality.

This paper grew as a continuation of [Sh462] but in the present form it can serve as a motivation for it as well. We deal with the same notions, all defined in 1.1, and use just one simple lemma from there whose statement and proof we repeat as 2.1. Originally entangledness was introduced, in [BoSh210] for example, in order to get narrow boolean algebras and examples of the nonmultiplicativity of c.c-ness. These applications became marginal when other methods were found and (...) successfully applied (especially Todorčevic walks) but after the pcf constructions which made their début in [Sh-g] and were continued in [Sh462] it seems that this notion gained independence.Generally we aim at characterizing the existence of strong and weak entangled orders in cardinal arithmetic terms. In [Sh462, §6] necessary conditions were shown for strong entangledness which in a previous version was erroneously proved to be equivalent to plain entangledness. In §1 we give a forcing counterexample to this equivalence and in §2 we get those results for entangledness (certainly the most interesting case). A new construction of an entangled order ends this section. In §3 we get weaker results for positively entangledness, especially when supplemented with the existence of a separating point (Definition 2.2). An antipodal case is defined in 3.10 and completely characterized in 3.11. Lastly we outline in 3.12 a forcing example showing that these two subcases of positive entangledness comprise no dichotomy. The work was done during the fall of 1994 and the winter of 1995. The second author proved Theorems 1.2, 2.14, the result that is mentioned in Remark 2.11 and what appears in this version as Theorem 2.10(a) with the further assumptionden(I)θ< μ. The first author is responsible for waving off this assumption (actually by showing that it holds in the general case), for Theorems 2.12 and 2.13 in Section 2 and for the work which is presented in Section 3. (shrink)

Longer-term developments shape the present and endogenous futures of institutions and practices of science and technology in society and their governance. Understanding the patterns allows diagnosis and soft intervention, often linked to scenario exercises. The book collects six articles offering key examples of this perspective, addressing ongoing issues in the governance of science and technology, including nanotechnology and responsible research and innovation. And adds two more articles that address background philosophical issues.

The main aim of this paper is to revisit the curve fitting problem using the reliability of inductive inference as a primary criterion for the ‘fittest' curve. Viewed from this perspective, it is argued that a crucial concern with the current framework for addressing the curve fitting problem is, on the one hand, the undue influence of the mathematical approximation perspective, and on the other, the insufficient attention paid to the statistical modeling aspects of the problem. Using goodness-of-fit as the (...) primary criterion for ‘best', the mathematical approximation perspective undermines the reliability of inference objective by giving rise to selection rules which pay insufficient attention to ‘accounting for the regularities in the data'. A more appropriate framework is offered by the error-statistical approach, where (i) statistical adequacy provides the criterion for assessing when a curve captures the regularities in the data adequately, and (ii) the relevant error probabilities can be used to assess the reliability of inductive inference. Broadly speaking, the fittest curve (statistically adequate) is not determined by the smallness if its residuals, tempered by simplicity or other pragmatic criteria, but by the nonsystematic (e.g. white noise) nature of its residuals. The advocated error-statistical arguments are illustrated by comparing the Kepler and Ptolemaic models on empirical grounds. ‡I am grateful to Deborah Mayo and Clark Glymour for many valuable suggestions and comments on an earlier draft of the paper; estimating the Ptolemaic model was the result of Glymour's prompting and encouragement. †To contact the author, please write to: Department of Economics, Virginia Tech 3019 Pamplin Hall (0316), Blacksburg, VA 24061; e-mail: [email protected]. (shrink)

Ariès traces Western man's attitudes toward mortality from the early medieval conception of death as the familiar collective destiny of the human race to the modern tendency, so pronounced in industrial societies, to hide death as if it were an embarrassing family secret.

Seventeenth-century optics naturalizes the eye while estranging the mind from objects. A mere screen, on which rests a blurry array of light stains, the eye no longer furnishes the observer with genuine re-presentations of visible objects. The intellect is thus compelled to decipher flat images of no inherent epistemic value, accidental effects of a purely causal process, as vague, reversed reflections of wholly independent objects. Reflecting on and trespassing the boundaries between natural and artificial, orderly and disorderly, this optical paradox (...) is a Baroque phenomenon; and it is the origin of Descartes’ celebrated doubt---whether we know anything at all. (shrink)

Liberal democracy suffers from an internal contradiction stemming from its ideological roots and rending it from within. On the one hand its goal is to generate a system of laws and rules that maximize individual rights and liberties; on the other hand, some of its fundamental assumptions pertaining to the Subject restrict the political and social agent's existential experience to a limited threshold of speech and action. The central assumption of this article is that the main meeting point of the (...) critics of modernity, Apel and Habermas primarily, and the post-structuralists, Foucault and Deleuze, in regard to the Subject, rehabilitates liberal discourse and creates an opening for a political theory that maximizes the freedom of the individual as a structured, anti-essentialist Subject. I will show that the expansion of the concept of the self in the two streams sheds new light on the concepts of political control and liberty, and in this way extends the normative discussion of all aspects of the political agent's status in a modern democracy. (shrink)

The Purūravac-cakkiravartti-katai, “The Story of Emperor Purūravas,” is a pre-modern Tamil folk telling of the ancient Urvaśī-Purūravas legend. The classical narrative of King Purūravas of the Lunar Dynasty tells about his love affair with the celestial nymph Urvaśī, their tragic separation, and final reunion. The PCK follows the classical narrative closely, but interposes a long account of other exploits of Purūravas, which do not appear in any of the Sanskrit tellings of the story. In this supplement, which I call “The (...) Tamil Life of Purūravas,” Purūravas faces a tragic chain of unavoidable events, but eventually restores his former status through meditation and devotion. A comparative examination of the two parts of the text, that is, the classical narrative and the Tamil Life, shows that the latter generates an inverted mirror image of the fundamental notions implied in the classical narrative. The outcome of this structure is a shift in the ideological tendencies of the narrative toward a local ethos and popular religious notions. The PCK is thus shown to be a field of cultural negotiations, in which opposing ideologies contend for superiority, and its structure can be regarded as a transformative mechanism applied by local and popular cultural forms to enable appropriation of classical narrative traditions. (shrink)

According to international scientific medical consensus, death is a biological, unidirectional, ontological state of an organism, the event that separates the process of dying from the process of disintegration. Death is not merely a social contrivance or a normative concept; it is a scientific reality. Using this paradigm, the international consensus is that, regardless of context, death is operationally defined as “the permanent loss of the capacity for consciousness and all brainstem function. This may result from permanent cessation of circulation (...) or catastrophic brain injury. In the context of death determination, ‘permanent’ refers to loss of function that cannot resume spontaneously and will not be restored through intervention.” The word “permanent” replaces “irreversible” (used in the United States’ 1980 Uniform Declaration of Death Act) in this new definition, arguably invented to allow donation after circulatory determination of death (DCDD) while still complying with the dead donor rule. I will show that this invention fails, for at least four reasons. (shrink)