We define in precise terms the basic properties that an ‘ideal propositional paraconsistent logic’ is expected to have, and investigate the relations between them. This leads to a precise characterization of ideal propositional paraconsistent logics. We show that every three-valued paraconsistent logic which is contained in classical logic, and has a proper implication connective, is ideal. Then we show that for every n > 2 there exists an extensive family of ideal n -valued logics, each one of which is not (...) equivalent to any k -valued logic with k < n. (shrink)

This paper aims to empirically explore the state of practical applications of paraconsistent logics. To this end, we performed an exploratory literature review, analysing papers published between the years 2015 and 2018. Paraconsistent formalisms based on annotated logics are practically the sole type of approach we found to be applied in engineering applications. The engineering problems solved by paraconsistent approaches were mainly in the fields of signal and image processing and decision support. The results of our exploratory review indicate that (...) recent developments in the theory of paraconsistency have not yet been adopted for applications. (shrink)

This paper develops an inference system for natural language within the ‘Natural Logic’ paradigm as advocated by van Benthem, Sánchez and others. The system that we propose is based on the Lambek calculus and works directly on the Curry-Howard counterparts for syntactic representations of natural language, with no intermediate translation to logical formulae. The Lambek -based system we propose extends the system by Fyodorov et~al., which is based on the Ajdukiewicz/Bar-Hillel calculus Bar Hillel,. This enables the system to deal with (...) new kinds of inferences, involving relative clauses, non-constituent coordination, and meaning postulates that involve complex expressions. Basing the system on the Lambek calculus leads to problems with non-normalized proof terms, which are treated by using normalization axioms. (shrink)

Canonical Propositional Gentzen-type systems are systems which in addition to the standard axioms and structural rules have only pure logical rules with the sub-formula property, in which exactly one occurrence of a connective is introduced in the conclusion, and no other occurrence of any connective is mentioned anywhere else. In this paper we considerably generalize the notion of a “canonical system” to first-order languages and beyond. We extend the Propositional coherence criterion for the non-triviality of such systems to rules with (...) unary quantifiers and show that it remains constructive. Then we provide semantics for such canonical systems using 2-valued non-deterministic matrices extended to languages with quantifiers, and prove that the following properties are equivalent for a canonical system G: (1) G admits Cut-Elimination, (2) G is coherent, and (3) G has a characteristic 2-valued non-deterministic matrix. (shrink)

An (n, k)-ary quantifier is a generalized logical connective, binding k variables and connecting n formulas. Canonical systems with (n, k)-ary quantifiers form a natural class of Gentzen-type systems which in addition to the standard axioms and structural rules have only logical rules in which exactly one occurrence of a quantifier is introduced. The semantics for these systems is provided using two-valued non-deterministic matrices, a generalization of the classical matrix. In this paper we use a constructive syntactic criterion of coherence (...) to characterize strong cutelimination in such systems. We show that the following properties of a canonical system G with arbitrary (n, k)-ary quantifiers are equivalent: (i) G is coherent, (ii) G admits strong cut-elimination, and (iii) G has a strongly characteristic two-valued generalized non-deterministic matrix. (shrink)

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)

Paraconsistent logics are logics that, in contrast to classical and intuitionistic logic, do not trivialize inconsistent theories. In this paper we take a paraconsistent view on two famous modal logics: B and S5. We use for this a well-known general method for turning modal logics to paraconsistent logics by defining a new negation as $\neg \varphi =_{Def} \sim \Box \varphi$. We show that while that makes both B and S5 members of the well-studied family of paraconsistent C-systems, they differ from (...) most other C-systems in having the important replacement property. We further show that B is a very robust C-system in the sense that almost any axiom which has been considered in the context of C-systems is either already a theorem of B or its addition to B leads to a logic that is no longer paraconsistent. There is exactly one notable exception, and the result of adding this exception to B leads to the other logic studied here, S5. (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)

Les Prolegomenes a la Philosophie de Platon sont un manuel d'ecole neoplatonicien. Il s'inspire d'un modele dont Proclus a du etre l'auteur, mais l'origine de ce texte est presque surement alexandrine et doit dater de la premiere moitie du Vle siecle. Cette oeuvre est essentielle pour comprendre comment etait diffuse l'enseignement platonicien, et pour mieux saisir le mouvement des idees de l'Antiquite finissante. Dans une importante introduction, L. O. Westerink a retrace l'histoire de l'ecole d'Alexandrie et celle du genre litteraire (...) de ces introductions a Platon et a Aristote. (shrink)

Purpose. To examine the existential anthropology of G. Marcel and E. Minkowski, in order to demonstrate the necessity of distinguishing the universal-spiritual, as human in human being, apart from the individual-existential in him, and to reveal the hierarchical correlation of biosocial, existential and spiritual spheres in personality. Theoretical basis. Within existential philosophy the author differentiates two separate traditions and proceeds from the insufficiency of the distinction of existential sphere, proposed by phenomenological tradition, showing the necessity of its correlation with the (...) spiritual sphere as a sphere of humanity, proposed by non-phenomenological tradition of G. Marcel and E. Minkowski. Originality. The author presents the anthropological conception of G. Marcel and E. Minkowski, in which human personality is understood as unity of individual-existential and universal-spiritual, which requires a special trans-empirical field of culture, which contains senses, images and symbols of humanity. Also, the author presents the recent developments of existential thinkers in distinguishing existential and spiritual dimensions, both not reducible to the physical and social dimensions. Conclusions. In both existential traditions, the specifically human was founded as a trans-biological and trans-social phenomenon, which appears as indefinable and non-predetermined. But in first tradition, humanity is understood as an existence, as a unique individuality, "project", variant of humanity, equivalent to other variants, and universal is understood as a community of human condition in the world. While in the second tradition, the universal is understood as spiritual. Thus, horizontal level of our private existence, as the process of movement from birth to death, is supplemented by vertical of human, universal ideals and images. Humanity appears as a task, on the way to which human being transcends beyond the limits of his individual "self" to the "super-individual", through inclusion into spiritual community, into universal culture. (shrink)

Modern scholars have been concerned with the hostility shown to Alexander by the Hellenistic schools of philosophy. Two literary portraits have been distinguished, the Peripatetic and the Stoic, the former deriving from Theophrastus' book on Callisthenes, or starting with this work the Peripatetics worked out a theory of and applied it to Alexander, in order to belittle his achievements. It was a case of giving sophisticated expression to the kind of crude resentment expressed by Demades.

The locus classicus for Plutarch's own views on his methods is in the Alexander He has begun by asking for the indulgence of his readers if they do not find all the exploits of Alexander and Caesar recounted by the biographer or if they discover him not reporting some famous incident in detail (); and he goes on to compare his own search for evidence which will indicate the kind of soul, with the activity of the painter, who, in order (...) to create a likeness, concentrates on the eyes and pays little attention to the other parts. Commentators and critics have been right to take this as a key text for the purpose of understanding Plutarch's attitude towards his biographical work; nevertheless there are other passages in the Lives where we can at least glimpse his attitude to his subject, and we can only see the Alexander-remarks in correct perspective if we take these other passages into account. I propose therefore, starting with the Alexander, to see how far these critical remarks apply to Plutarch's theory and practice elsewhere in the Lives. (shrink)

According to the Ars Amatoria the notorious rape took place on the occasion of a primitive dramatic entertainment staged in a theatre, in which the seats and furnishings were also primitive. There is no time for a description of the arts of the performers—a tibicen and a ludius—before the Romans, impatient for action, receive their signal from Romulus. Nor is there any mention of a god in whose honour the entertainment had been provided.

Catalog of the collection of the Madamkhand Museum of Art, named after the wife of Batzhargalyn Batbai︠a︡r, businessman and member of the Mongolian Khural.

This paper explores the relationship between eugenics, disability, and dehumanization, with a focus on forms of eugenics beyond Nazi eugenics.

Tuberculosis (TB) is a potentially fatal infectious disease that, in Aotearoa New Zealand (NZ), inequitably affects Asian, Pacific, Middle Eastern, Latin American, and African (MELAA), and Māori people. Medical research involving genome sequencing of TB samples enables more nuanced understanding of disease strains and their transmission. This could inform highly specific health interventions. However, the collection and management of TB isolate samples for research are currently informed by monocultural biomedical models often lacking key ethical considerations. Drawing on a qualitative kaupapa (...) Māori–consistent study, this paper reports on preliminary discussions with groups of Māori, Pacific, and Afghan people in NZ, whose communities have been harmed by TB and TB stigma. Participants’ discussions highlight key concerns and meanings that ought to inform the development of guidelines and a more robust consultative process for the governance of how TB isolate samples are collected and used both retrospectively and in future research. We argue for ethical processes to be culturally nuanced and community-generated, flexible and meaningful, and situated in relation to the physical and symbolic effects of TB. We discuss the significance of Indigenous data sovereignty, rights, and kāwanatanga (governorship) in shaping a multicultural data sovereignty model. (shrink)

De Interpretatione is among Aristotle's most influential and widely read writings; C. W. A. Whitaker presents the first systematic study of this work, and offers a radical new view of its aims, its structure, and its place in Aristotle's system. He shows that De Interpretatione is not a disjointed essay on ill-connected subjects, as traditionally thought, but a highly organized and systematic treatise on logic, argument, and dialectic.