In this note, an error in the axiomatization of Ivlev’s modal system Sa+ which we inadvertedly reproduced in our paper “Finite non-deterministic semantics for some modal systems”, is fixed. Additionally, some axioms proposed in were slightly modified. All the technical results in which depend on the previous axiomatization were also fixed. Finally, the discussion about decidability of the level valuation semantics initiated in is taken up. The error in Ivlev’s axiomatization was originally pointed out by H. Omori and D. Skurt (...) in the paper “More modal semantics without possible worlds”, where an alternative solution was proposed. (shrink)

In this paper, logics are conceived as two-sorted first-order structures, and we argue that this broad definition encompasses a wide class of logics with theoretical interest as well as interest from the point of view of applications. The language, concepts and methods of model theory can thus be used to describe the relationship between logics through morphisms of structures called transfers. This leads to a formal framework for studying several properties of abstract logics and their attributes such as consequence operator, (...) syntactical structure, and internal transformations. In particular, we treat Belief Revision Systems (BRS) as our main example, defining the Wide Belief Revision Systems (WBRS''s). This generalization allows us to define BRS''s in an abstract setting for classical and non-standard logics. We also show how the concept of translation between logics can be obtained as a particular case of transfers. (shrink)

The ``Many Sides of Logic'' is a volume containing a selection of the papers delivered at three simultaneous events held between 11-17 May 2008 in Paraty, RJ, Brazil, continuing a tradition of three decades of Brazilian and Latin-American meetings and celebrating the 30th anniversary of an institution congenital with the mature interest for logic, epistemology and history of sciences in Brazil: CLE 30 - 30th Anniversary of the Centre for Logic, Epistemology and the History of Science at the State University (...) of Campinas (UNICAMP) XV EBL -15th Brazilian Logic Conference XIV SLALM - 14th Latin-American Symposium on Mathematical Logic Several renowned logicians, philosophers and mathematicians gathered in colonial Paraty, a historic village on the Brazilian coast founded in the 17th Century and surrounded by the luscious Atlantic rain forest to deliver lectures and talks celebrating the many sides of logic: the philosophical, the mathematical, the computational, the historical, and the multiple facets therein. The topics of the joint conferences, well represented here, included philosophical and mathematical Logic and applications with emphasis on model theory and proof theory, set theory, non-classical logics and applications, history and philosophy of logic, philosophy of the formal sciences and issues on the foundations of mathematics. The events have been preceded by a Logic School planned for students and young researchers held at the UNICAMP campus in Campinas, SP. (shrink)

Proceedings of the II World Congress on Paraconsistency held in Juquey, SP, Brazil, from May 12-19, 2000.

This paper introduces the logic _Q__L__E__T_ _F_, a quantified extension of the logic of evidence and truth _L__E__T_ _F_, together with a corresponding sound and complete first-order non-deterministic valuation semantics. _L__E__T_ _F_ is a paraconsistent and paracomplete sentential logic that extends the logic of first-degree entailment (_FDE_) with a classicality operator ∘ and a non-classicality operator ∙, dual to each other: while ∘_A_ entails that _A_ behaves classically, ∙_A_ follows from _A_’s violating some classically valid inferences. The semantics of _Q__L__E__T_ (...) _F_ combines structures that interpret negated predicates in terms of anti-extensions with first-order non-deterministic valuations, and completeness is obtained through a generalization of Henkin’s method. By providing sound and complete semantics for first-order extensions of _FDE_, _K3_, and _LP_, we show how these tools, which we call here the method of _anti-extensions + valuations_, can be naturally applied to a number of non-classical logics. (shrink)

Fibring has been shown to be useful for combining logics endowed withtruth-functional semantics. However, the techniques used so far are unableto cope with fibring of logics endowed with non-truth-functional semanticsas, for example, paraconsistent logics. The first main contribution of thepaper is the development of a suitable abstract notion of logic, that mayalso encompass systems with non-truth-functional connectives, and wherefibring can still be dealt with. Furthermore, it is shown that thisextended notion of fibring preserves completeness under certain reasonableconditions. This completeness transfer (...) result, the second main contributionof the paper, generalizes the one established in Zanardo et al. (2001) butis obtained using new techniques that explore the properties of a suitablemeta-logic (conditional equational logic) where the (possibly)non-truth-functional valuations are specified. The modal paraconsistentlogic of da Costa and Carnielli (1988) is studied in the context of this novel notionof fibring and its completeness is so established. (shrink)

In 1940 Dugundji proved that no system between S1 and S5 can be characterized by finite matrices. Dugundji’s result forced the development of alternative semantics, in particular Kripke’s relational semantics. The success of this semantics allowed the creation of a huge family of modal systems. With few adaptations, this semantics can characterize almost the totality of the modal systems developed in the last five decades. This semantics however has some limits. Two results of incompleteness showed that not every modal logic (...) can be characterized by Kripke frames. Besides, the creation of non-classical modal logics puts the problem of characterization of finite matrices very far away from the original scope of Dugundji’s result. In this sense, we will show how to update Dugundji’s result in order to make precise the scope and the limits of many-valued matrices as semantic of modal systems. A brief comparison with the useful Chagrov and Zakharyaschev’s criterion of tabularity for modal logics is provided. (shrink)

Trying to overcome Dugundji’s result on uncharacterisability of modal logics by finite logical matrices, Kearns and Ivlev proposed, independently, a characterisation of some modal systems by means of four-valued multivalued truth-functions , as an alternative to Kripke semantics. This constitutes an antecedent of the non-deterministic matrices introduced by Avron and Lev . In this paper we propose a reconstruction of Kearns’s and Ivlev’s results in a uniform way, obtaining an extension to another modal systems. The first part of the paper (...) is devoted to four-valued Nmatrices, including Kearns’s and Ivlev’s. Besides proving with full details Kearns’s results for T, S4 and S5, we also obtain a characterisation of the system B by four-valued Nmatrices with level valuations. Concerning Ivlev’s results, two new modal systems are introduced and char.. (shrink)

Two systems of belief change based on paraconsistent logics are introduced in this article by means of AGM-like postulates. The first one, AGMp, is defined over any paraconsistent logic which extends classical logic such that the law of excluded middle holds w.r.t. the paraconsistent negation. The second one, AGMo , is specifically designed for paraconsistent logics known as Logics of Formal Inconsistency (LFIs), which have a formal consistency operator that allows to recover all the classical inferences. Besides the three usual (...) operations over belief sets, namely expansion, contraction and revision (which is obtained from contraction by the Levi identity), the underlying paraconsistent logic allows us to define additional operations involving (non-explosive) contradictions. Thus, it is defined external revision (which is obtained from contraction by the reverse Levi identity), consolidation and semi-revision, all of them over belief sets. It is worth noting that the latter operations, introduced by S. Hansson, involve the temporary acceptance of contradictory beliefs, and so they were originally defined only for belief bases. Unlike to previous proposals in the literature, only defined for specific paraconsistent logics, the present approach can be applied to a general class of paraconsistent logics which are supraclassical, thus preserving the spirit of AGM. Moreover, representation theorems w.r.t. constructions based on selection functions are obtained for all the operations. (shrink)

In this paper we introduce non-normal modal extensions of the sub-classical logics CLoN, CluN and CLaN, in the same way that S0.5 0 extends classical logic. The first modal system is both paraconsistent and paracomplete, while the second one is paraconsistent and the third is paracomplete. Despite being non-normal, these systems are sound and complete for a suitable Kripke semantics. We also show that these systems are appropriate for interpreting □ as “is provable in classical logic”. This allows us to (...) recover the theorems of propositional classical logic within three sub-classical modal systems. (shrink)

In this paper two systems of AGM-like Paraconsistent Belief Revision are overviewed, both defined over Logics of Formal Inconsistency (LFIs) due to the possibility of defining a formal consistency operator within these logics. The AGM° system is strongly based on this operator and internalize the notion of formal consistency in the explicit constructions and postulates. Alternatively, the AGMp system uses the AGM-compliance of LFIs and thus assumes a wider notion of paraconsistency - not necessarily related to the notion of formal (...) consistency. (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.

In 1988, J. Ivlev proposed some (non-normal) modal systems which are semantically characterized by four-valued non-deterministic matrices in the sense of A. Avron and I. Lev. Swap structures are multialgebras (a.k.a. hyperalgebras) of a special kind, which were introduced in 2016 by W. Carnielli and M. Coniglio in order to give a non-deterministic semantical account for several paraconsistent logics known as logics of formal inconsistency, which are not algebraizable by means of the standard techniques. Each swap structure induces naturally (...) a non-deterministic matrix. The aim of this paper is to obtain a swap structures semantics for some Ivlev-like modal systems proposed in 2015 by M. Coniglio, L. Fariñas del Cerro and N. Peron. Completeness results will be stated by means of the notion of Lindenbaum–Tarski swap structures, which constitute a natural generalization to multialgebras of the concept of Lindenbaum–Tarski algebras. (shrink)

Society Semantics, introduced by W. Carnielli and M. Lima-Marques, is a method for obtaining new logics from the combination of agents of a given logic. The goal of this paper is to present several generalizations of this method, as well as to show some applications to many-valued logics. After a reformulation of Society Semantics in a wider setting, we develop in detail two examples of application of the new formalism, characterizing a hierarchy of paraconsistent logics called Pn and a hierarchy (...) of paracomplete logics In. We also propose three further generalizations, obtaining Society Semantics for several many-valued logics, including a hierarchy of logics called In Pk which are both paraconsistent and paracomplete. (shrink)

This paper reviews the central points and presents some recent developments of the epistemic approach to paraconsistency in terms of the preservation of evidence. Two formal systems are surveyed, the basic logic of evidence (BLE) and the logic of evidence and truth (LET J ), designed to deal, respectively, with evidence and with evidence and truth. While BLE is equivalent to Nelson’s logic N4, it has been conceived for a different purpose. Adequate valuation semantics that provide decidability are given for (...) both BLE and LET J . The meanings of the connectives of BLE and LET J , from the point of view of preservation of evidence, is explained with the aid of an inferential semantics. A formalization of the notion of evidence for BLE as proposed by M. Fitting is also reviewed here. As a novel result, the paper shows that LET J is semantically characterized through the so-called Fidel structures. Some opportunities for further research are also discussed. (shrink)

A graph-theoretic account of logics is explored based on the general notion of m-graph (that is, a graph where each edge can have a finite sequence of nodes as source). Signatures, interpretation structures and deduction systems are seen as m-graphs. After defining a category freely generated by a m-graph, formulas and expressions in general can be seen as morphisms. Moreover, derivations involving rule instantiation are also morphisms. Soundness and completeness theorems are proved. As a consequence of the generality of the (...) approach our results apply to very different logics encompassing, among others, substructural logics as well as logics with nondeterministic semantics, and subsume all logics endowed with an algebraic semantics. (shrink)

In this interview, Jean-Luc Marion recalls the intellectual world of Paris in 1970s, reflecting on how his engagement with the ubiquitous “death of God” question led to the sketches of God without Being first presented at this 1979 Colloquium, and discusses the criticism it provoked not only from Heideggerians but also from Thomists. He discusses the reception history of phenomenology in France the reasons for the particular power it gained among thinkers of his generation. Finally, he recounts how his work (...) has led from the 1979 Colloquium through the “Theological Turn” and up to his forthcoming D’ ailleurs, la révélation, which he briefly previews here. Marion closes with words on originality, criticism, and the particular challenges of the contemporary world that await philosophical thinking today. (shrink)

Tetravalent modal logic (TML) was introduced by Font and Rius in 2000. It is an expansion of the Belnap-Dunn four-valued logic FOUR, a logical system that is well-known for the many applications found in several fields. Besides, TML is the logic that preserves degrees of truth with respect to Monteiro’s tetravalent modal algebras. Among other things, Font and Rius showed that TML has a strongly adequate sequent system, but unfortunately this system does not enjoy the cut-elimination property. However, in a (...) previous work we presented a sequent system for TML with the cut-elimination property. Besides, in this same work, it was also presented a sound and complete natural deduction system for this logic. In the present article we continue with the study of TML under a proof-theoretic perspective. In the first place, we show that the natural deduction system that we introduced before admits a normalization theorem. In the second place, taking advantage of the contrapositive implication for the tetravalent modal algebras introduced by A. V. Figallo and P. Landini, we define a decidable tableau system adequate to check validity in the logic TML. Finally, we provide a sound and complete tableau system for TML in the original language. These two tableau systems constitute new (proof-theoretic) decision procedures for checking validity in the variety of tetravalent modal algebras. (shrink)

In this paper the class of Fidel-structures for the paraconsistent logic mbC is studied from the point of view of Model Theory and Category Theory. The basic point is that Fidel-structures for mbC (or mbC-structures) can be seen as first-order structures over the signature of Boolean algebras expanded by two binary predicate symbols N (for negation) and O (for the consistency connective) satisfying certain Horn sentences. This perspective allows us to consider notions and results from Model Theory in order to (...) analyze the class of mbC-structures. Thus, substructures, union of chains, direct products, direct limits, congruences and quotient structures can be analyzed under this perspective. In particular, a Birkhoff-like representation theorem for mbC-structures as subdirect poducts in terms of subdirectly irreducible mbC-structures is obtained by adapting a general result for first-order structures due to Caicedo. Moreover, a characterization of all the subdirectly irreducible mbC-structures is also given. An alternative decomposition theorem is obtained by using the notions of weak substructure and weak isomorphism considered by Fidel for Cn-structures. (shrink)

In this paper the propositional logic LTop is introduced, as an extension of classical propositional logic by adding a paraconsistent negation. This logic has a very natural interpretation in terms of topological models. The logic LTop is nothing more than an alternative presentation of modal logic S4, but in the language of a paraconsistent logic. Moreover, LTop is a logic of formal inconsistency in which the consistency and inconsistency operators have a nice topological interpretation. This constitutes a new proof of (...) S4 as being "the logic of topological spaces", but now under the perspective of paraconsistency. (shrink)

In this paper we develop the elementary theory of modules in the category Sh of sheaves over right-sided idempotent quantales. The main ingredient is the construction of a logic sound for Sh . As an application we prove that in Sh , a finitely generated projective module is free , a result that is relevant to the study of representation of non-commutative C ∗ -algebras.

After introducing the new field of cultural evolution, we review a growing body of empirical evidence suggesting that culture shapes what people attend to, perceive and remember as well as how they think, feel and reason. Focusing on perception, spatial navigation, mentalizing, thinking styles, reasoning (epistemic norms) and language, we discuss not only important variation in these domains, but emphasize that most researchers (including philosophers) and research participants are psychologically peculiar within a global and historical context. This rising tide of (...) evidence recommends caution in relying on one’s intuitions or even in generalizing from reliable psychological findings to the species, Homo sapiens. Our evolutionary approach suggests that humans have evolved a suite of reliably developing cognitive abilities that adapt our minds, information-processing abilities and emotions ontogenetically to the diverse culturally-constructed worlds we confront. (shrink)

With increased visibility of trans people comes increased philosophical interest in gendered language. This chapter aims to look at the research on gendered language in analytic philosophy of language so far, which has focused on two concerns: (1) determining how to define gender terms like ‘man’ and ‘woman’ such that they are trans inclusive and (2) if, or to what extent, we should use gendered language at all. We argue that the literature has focused too heavily on how gendered language (...) can harm trans people, and has not considered how trans people use gendered language to create meaning and joy for ourselves. Pulling from the literature in sociolinguistics, we look at examples of how trans people use language to make their lives better by gaining recognition, playing with gendered language, finding joy in gendered language, and taking control of definitional power, concluding that debates about gendered language need to consider not only how such language harms trans people but also how trans people use it for our own liberation. (shrink)

This research explores the contextual approach within Christian-Jewish religious education, addressing a notable gap in existing literature and offering fresh insights into the application of the Contextual Teaching and Learning (CTL) model within Christian contexts. Through a qualitative literature study employing a three-step methodology, including an in-depth analysis of Deuteronomy 11:19–20, this study reveals that this biblical text provides both educational guidance and theological significance, serving as a foundational support for the CTL model in Christian-Jewish religious education. The integration of (...) digital media into biblical sources holds promise for future research, while the central challenge lies in harmonising life experiences and empirical phenomena with biblical reflections to seamlessly integrate inquiry processes and pedagogical phases, with potential avenues for further exploration in scripture models endorsing CTL. This research provides valuable insights for educators, parents and policymakers in Indonesia and beyond, advancing educational research in contextualised teaching models within religious education.Contribution: This article demonstrates that the CTL model in the digital era has the potential to revolutionise religious education and profoundly impact learners, making it a significant scientific contribution in the context of Christian-Jewish religious education. (shrink)

Wittgenstein's work remains, undeniably, now, that off one of those few philosophers who will be read by all future generations.

How educators and students process and respond to emotions can either enhance or impede the development of the whole child. Social and emotional learning (SEL) refers to the processes of developing social and emotional competencies, which depend on individuals’ capacity to recognize, understand, and manage emotions (i.e., emotional intelligence or EI). Consensus across disciplines about the importance of EI highlights the need to advance the science of how to teach SEL. RULER, an evidence-based approach to teaching EI, provides an educational (...) framework that encompasses a set of practices for comprehensive SEL integration across a school or district. In this article, we describe RULER, explain how it teaches EI, and summarize evidence of its effectiveness. (shrink)

Is God's foreknowledge compatible with human freedom? One of the most attractive attempts to reconcile the two is the Ockhamistic view, which subscribes not only to human freedom and divine omniscience, but retains our most fundamental intuitions concerning God and time: that the past is immutable, that God exists and acts in time, and that there is no backward causation. In order to achieve all that, Ockhamists distinguish ‘hard facts’ about the past which cannot possibly be altered from ‘soft facts’ (...) about the past which are alterable, and argue that God's prior beliefs about human actions are soft facts about the past. (shrink)

In their “social contextual view” of emotional mimicry, authors Hess and Fischer (2022) put forward emotional mimicry as a social regulator, considering it a social act, bound to certain affiliative contexts or goals. In this commentary, we argue that the core function of mimicry is to ease predicting conspecifics’ behaviours and the environment, and that as a consequence, this often smoothens social interactions. Accordingly, we make three main points. First, we argue that there is no good reason to believe that (...) the mimicry of negative expressions is fundamentally different than the mimicry of positive or ambiguous or autonomic expressions. Second, we give examples of empirical evidence that mimicry is not always a social act. Third, we show that mimicry has primary benefits for the mimicker. As such, we will briefly summarise and elaborate on the relevant findings in these respects, and propose a comparative, multi-method and ecologically valid approach which can explain the multifaceted character of the phenomenon. (shrink)

Older adults report high emotional well-being, but age-comparative studies of emotion regulation strategies have not identified systematic age differences. We propose that emotion regulation tactics may be more promising. Emotion regulation tactics involve strategy implementation in a specific situation, and have features shared across strategies involving positive or negative elements (objects/thoughts) in the environment that may be approached or receded from in the regulation attempt (i.e., a valence dimension about the environmental element, and a direction dimension indicating movement toward or (...) away from it). Across several studies, older adults used more positive-approaching than negative-receding tactics. Positive-approaching tactics may also be more effective at regulating mood. We consider implications for aging, as well as group differences in emotion regulation behavior generally. (shrink)

In this concluding reflection, the editors of this special issue reflect on the significance that Heidegger has had for French philosophy, precisely because of the creative and critical engagement of many of the original thinkers demonstrated above. It is not insignificant that Christian thinkers were drawn to Heidegger, seeing promise in his expansion of philosophical questioning, above all an enrichment of the idea of truth. However it is equally important to recognize that Heidegger’s native Christian roots were stripped of their (...) animating spirit, the question of God and the revelation of the Hebraic scriptures. It is thus notable that the criticisms from this conference originating from the side of faith frequently appeal to the Scriptures as they argue that there are truths which Heidegger himself simply does not seem to see. (shrink)

Organized by Richard Kearney and Joseph S. O’Leary, the 1979 Colloquium Heidegger et la question de Dieu was of critical importance for the development of phenomenology of religion in France. This special issue introduces the event and its ensuing publication to the English-speaking world. The editors’ historical and thematic contextualizing essay is followed by contributions from six leading philosophers. Richard Kearney sets the stage by updating his original foreword, while Jean-Yves Lacoste presents the central moments in the history of Heidegger’s (...) complicated relationship to Christian thinking. Paul Ricoeur’s “Introductory Note” delivers a well-known challenge to Heidegger in a piece whose brevity belies its impact. Finally, three participants of the 1979 Colloquium, Joseph S. O’Leary, Jean Greisch, and Jean-Luc Marion, reflect back on the significance of this event and its role in developing their own groundbreaking work. The special issue closes with a brief reflection on where we find ourselves in philosophy today. (shrink)

In 2001, Le Bars proved that there exists an existential monadic second-order sentence such that the probability that it is true on [Formula: see text] does not converge and conjectured that, for EMSO sentences with two first-order variables, the zero–one law holds. In this paper, we prove that the conjecture fails for [Formula: see text], and give new examples of sentences with fewer variables without convergence.

Animal ethicists have recently debated the ethical questions raised by disenhancing animals to improve their welfare. Here, we focus on the particular case of breeding hens for commercial egg-laying systems to become blind, in order to benefit their welfare. Many people find breeding blind hens intuitively repellent, yet ‘welfare-only’ positions appear to be committed to endorsing this possibility if it produces welfare gains. We call this the ‘Blind Hens’ Challenge’. In this paper, we argue that there are both empirical and (...) theoretical reasons why even those adopting ‘welfare-only’ views should be concerned about breeding blind hens. But we also argue that alternative views, which (for example) claim that it is important to respect the telos or rights of an animal, do not offer a more convincing solution to questions raised by the possibility of disenhancing animals for their own benefit. (shrink)