The relationships between various modal logics based on Belnap and Dunn’s paraconsistent four-valued logic FDE are investigated. It is shown that the paraconsistent modal logic \, which lacks a primitive possibility operator \, is definitionally equivalent with the logic \, which has both \ and \ as primitive modalities. Next, a tableau calculus for the paraconsistent modal logic KN4 introduced by L. Goble is defined and used to show that KN4 is definitionally equivalent with \ without the absurdity constant. Moreover, (...) a tableau calculus is defined for the modal bilattice logic MBL introduced and investigated by A. Jung, U. Rivieccio, and R. Jansana. MBL is a generalization of BK that in its Kripke semantics makes use of a four-valued accessibility relation. It is shown that MBL can be faithfully embedded into the bimodal logic \ over the non-modal vocabulary of MBL. On the way from \ to MBL, the Fischer Servi-style modal logic \ is defined as the set of all modal formulas valid under a modified standard translation into first-order FDE, and \ is shown to be characterized by the class of all models for \. Moreover, \ is axiomatized and this axiom system is proved to be strongly sound and complete with respect to the class of models for \. Moreover, the notion of definitional equivalence is suitably weakened, so as to show that \ and \ are weakly definitionally equivalent. (shrink)

We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t: F that read t is a justification for F. Justification Logic absorbs basic principles originating from both mainstream epistemology and the mathematical theory of proofs. It contributes to the studies of the well-known Justified True Belief vs. Knowledge problem. We state a general Correspondence Theorem showing that behind each epistemic modal logic, there is a (...) robust system of justifications. This renders a new, evidence-based foundation for epistemic logic. As a case study, we offer a resolution of the GoldmanRed Barns in Justification Logic. Furthermore, we formalize the well-known Gettier example and reveal hidden assumptions and redundancies in Gettier’s reasoning. (shrink)

Tracing how the logic of inoperativity works in the domains of language, law, history and humanity, 'Agamben and Politics' systematically introduces the fundamental concepts of Agamben's political thought and a critically interprets his insights in the wider context of contemporary philosophy.

Earlier algebraic semantics for Belnapian modal logics were defined in terms of twist-structures over modal algebras. In this paper we introduce the class of BK -lattices, show that this class coincides with the abstract closure of the class of twist-structures, and it forms a variety. We prove that the lattice of subvarieties of the variety of BK -lattices is dually isomorphic to the lattice of extensions of Belnapian modal logic BK . Finally, we describe invariants determining a twist-structure over a (...) modal algebra. (shrink)

This article examines a still contentious question: how conservative and liberal elements are combined in Boris N. Chicherin’s worldview and political doctrine. It considers several points of view...

Uncertainty can’t be understood without taking into account both properties of the problem situation and agent’s knowledge about it. The correspondence of knowledge and situation of decision-making is crucial for understanding the onto-epistemological nature of uncertainty. At the same time, this correspondence is the key topic in virtue epistemology, especially in its ‘non-classical’, regulatory, branch, related to works of R. Roberts and W.J. Wood. In this article, genetic consultation is chosen as an example of such a problematic situation since a (...) doctor and a patient explicitly deal with the uncertainty of genetic risks. The problems of communication and joint decision-making in the context of medical-genetic consultation are comprehensively described in bioethics. At the same time, its social dimension is limited to the direct interaction of two individual agents, that allows us to use it as a model for constructing the ethics of uncertainty. In this article, four forms of uncertainty are identified: descriptive, normative and radical uncertainties, and translation uncertainty. Referring to the approaches of virtue epistemology, the author brings each of these forms into conformity with the proposed regulatory principle. The regulations assume that generating or disseminating knowledge under conditions of uncertainty require taking into account the incompleteness of the presented model of reality in its four aspects. A modelled fragment of reality could change in a predictable (descriptive uncertainty) or unexpected (radical uncertainty) way. The goals and values of a model’s user can not be hierarchically ordered, and may also change in the future (normative uncertainty). User’s interpretations of the model may be diverse, and can never be strictly defined by the intentions of the model’s author (indeterminancy of translation, or uncertainty whether success of co-reference is achieved). (shrink)

We define a novel interpretation R of second order arithmetic into Explicit Mathematics. As a difference from standard D-interpretation, which was used before and was shown to interpret only subsystems proof-theoretically weaker than T 0 , our interpretation can reach the full strength of T 0 . The R-interpretation is an adaptation of Kleene's recursive realizability, and is applicable only to intuitionistic theories.

Here is an account of recent investigations into the two main concepts of negation developed in the constructive logic: the negation as reduction to absurdity, and the strong negation. These concepts are studied in the setting of paraconsistent logic.

The language of the basic logic of proofs extends the usual propositional language by forming sentences of the sort x is a proof of F for any sentence F. In this paper a complete axiomatization for the basic logic of proofs in Heyting Arithmetic HA was found.

Inspired by Hintikka’s ideas on constructivism, we are going to ‘effectivize’ the game-theoretic semantics for independence-friendly first-order logic, but in a somewhat different way than he did in the monograph ‘The Principles of Mathematics Revisited’. First we show that Nelson’s realizability interpretation—which extends the famous Kleene’s realizability interpretation by adding ‘strong negation’—restricted to the implication-free first-order formulas can be viewed as an effective version of GTS for FOL. Then we propose a realizability interpretation for IF-FOL, inspired by the so-called ‘trump (...) semantics’ which was discovered by Hodges, and show that this trump realizability interpretation can be viewed as an effective version of GTS for IF-FOL. Finally we prove that the trump realizability interpretation for IF-FOL appropriately generalises Nelson’s restricted realizability interpretation for the implication-free first-order formulas. (shrink)

Neuroscience has established several brain pathways that process visual information. Distinct neural circuits analyze body appearance and movement providing information about the person’s cognitive and emotional states. The activity of the pathways depends on the salience of visual stimuli for the organism in the given circumstances. Since ballet performances are not among the crucial events for the viewer’s organism, not all viewers perceive and interpret bodily signs that express the mental state of the dancer. Treatment of the dancer as close (...) other activates the neural circuits that elaborate emotions, this enables the viewer to feel the internal state of the dancer and enrich the interpretation of the scenic action. (shrink)

Let K be the least normal modal logic and BK its Belnapian version, which enriches K with ‘strong negation’. We carry out a systematic study of the lattice of logics containing BK based on: • introducing the classes of so-called explosive, complete and classical Belnapian modal logics; • assigning to every normal modal logic three special conservative extensions in these classes; • associating with every Belnapian modal logic its explosive, complete and classical counterparts. We investigate the relationships between special extensions (...) and counterparts, provide certain handy characterisations and suggest a useful decomposition of the lattice of logics containing BK. (shrink)

Byzantine intellectuals not only had direct access to Neoplatonic sources in the original language but also, at times, showed a particular interest in them. During the Early Byzantine period Platonism significantly contributed to the development of Christian doctrines and, paradoxically, remained a rival world view that was perceived by many Christian thinkers as a serious threat to their own intellectual identity. This problematic relationship was to become even more complex during the following centuries. Byzantine authors made numerous attempts to harmonize (...) Neoplatonic doctrines with Christianity as well as to criticize, refute and even condemn them. The papers assembled in this volume discuss a number of specific questions and concerns that drew the interest of Byzantine scholars in different periods towards Neoplatonic sources in an attempt to identify and explore the central issues in the reception of Neoplatonic texts during the Byzantine era. This is the first volume of the sub-series "Byzantinisches Archiv - Series Philosophica", which will be dedicated to the rapidly growing field of research in Byzantine philosophical texts. (shrink)

The present paper is devoted to computational aspects of propositional inconsistency-adaptive logics. In particular, we prove (relativized versions of) some principal results on computational complexity of derivability in such logics, namely in cases of CLuN r and CLuN m , i.e., CLuN supplied with the reliability strategy and the minimal abnormality strategy, respectively.

The word “encyclopedia” comes to us from the Greek or, more precisely, is the deformed transcription, through Latin, of a erase in which we recognize a word composed of two elements, enkyklios and paideia, found in Quintilian in the ancient editions of De institutione oratoria (I, 10, 1). The expression itself, enkyklios paideia, appears only later, in the Hellenistic Age, under Roman domination, beginning with Dionysius of Halicarnassus (around the first century B.C.), but the concept goes back to the Eleatics, (...) especially to Hippias of Elis who, if we can believe the account in Plato's Dialogues, taught this total knowledge, later known with the term enkyklopaideia. (shrink)

The paper aims to present a critical analysis of the phenomenon and notion of exceptionalism in bioethics. The authors demonstrate that exceptionalism pertains to phenomena that are not (yet) entirely familiar to us and could potentially bear risks regarding their regulation. After an overview of the state of the art, we briefly describe the origins and evolution of the concept, compared to exception and exclusion. In the second step, they look at the overall development debates on genetic exceptionalism, compared to (...) other bioethical debates on exceptionalism, before presenting a detailed analysis of a specific case of early regulation of genetic screening. In the last part, the authors explain the historical background behind the connection between exceptionalism and exclusion in these debates. Their main conclusion is that while the initial stage of the discussion is shaped by the concept of exceptionalism and awareness of risks of exclusion, the later development centers around exceptions that are needed in detailed regulatory procedures. (shrink)

We compare the logic HYPE recently suggested by H. Leitgeb as a basic propositional logic to deal with hyperintensional contexts and Heyting-Ockham logic introduced in the course of studying logical aspects of the well-founded semantics for logic programs with negation. The semantics of Heyting-Ockham logic makes use of the so-called Routley star negation. It is shown how the Routley star negation can be obtained from Dimiter Vakarelov’s theory of negation and that propositional HYPE coincides with the logic characterized by the (...) class of all involutive Routley star information frames. This result provides a much simplified semantics for HYPE and also a simplified axiomatization, which shows that HYPE is identical with the modal symmetric propositional calculus introduced by G. Moisil in 1942. Moreover, it is shown that HYPE can be faithfully embedded into a normal bi-modal logic based on classical logic. Against this background, we discuss the notion of hyperintensionality. (shrink)

The publication of The Use of Bodies, the final volume in Giorgio Agamben’s Homo Sacer series, makes it possible to take stock of Agamben’s project as a whole. Having started with a powerful critique of the biopolitical sovereignty as the essence of modern politics, Agamben concludes his project with an affirmative vision of inoperative politics of form-of-life, in which life is not negated or sacrificed to the privileged form it must attain, but rather remains inseparable from the form that does (...) nothing but express it. The article begins by reconstituting the non-relational logic that Agamben develops in order to render inoperative the existing apparatuses of ontology, ethics and politics. We then address the dimension of lifestyle as a new key domain of Agamben’s work, in which biopolitics may be recast in an affirmative key of form-of-life. While Agamben is better known for sceptical and scornful statements about contemporary liberal democracies, we shall argue that his affirmative biopolitics, characterized by destituent power, resonates with Claude Lefort’s understanding of democracy as structured around the ontological void and epistemic indeterminacy. In the conclusion we question the viability of this biopolitical democracy, focusing on Agamben’s example of the Nocturnal Council in Plato’s Laws. (shrink)

The article analyzes the philosophical concept of the “porous self” of J. Rivera. The originality of this concept in the post-phenomenological project is determined by the role of theological constructions that modify the primal experience of self-consciousness. This modification allows us to interpret the phenomenological description of the human self as different from the classical — “porous” temporality, i.e., correlating through “two entrances”—the internal and external—with eternity. Within this approach, the primary phenomenon of the constitution of the "porous" self becomes (...) the inner word, which in the appeal to eternity turns out to be the original self-awareness of the self as a temporality. The secondary phenomenon of the constitution of the “porous” self is not the mundane temporality of M. Heidegger, but Epektasis as an intense striving towards the end of time in General. The worldly temporality of the self, transformed by faith, is phenomenologically revealed as open to eternity in each of its moments. The third phenomenon of the temporality of the self is Memoria, whose interpretation reveals how the structure of the inner consciousness of time by E. Husserl can be framed ontologically and harmoniously integrated into the theological concept. The article shows how, based on this understanding of both the internal and external openness of the “porous” self for eternity, the integral structure of its temporality is formed. The temporality of the porous self is a modification of Husserl’s time diagrams and the intertwining of two streams of temporality at the same time from past to future and from future to past, which itself constitutes a phenomenal field of events of self. This understanding of temporality sets new perspectives for the phenomenological analysis of subjectivity. (shrink)

In their target article, Cohen and Marks (2025) argue that recognizing something as exceptional is a contextual matter. The authors consider the question of whether psychedelics are exceptional by...

Coercive subtyping offers a general approach to subtyping and inheritance by introducing a simple abbreviational mechanism to constructive type theories. In this paper, we study coercion completion in coercive subtyping and prove that the formal extension with coercive subtyping of a type theory such as Martin–Löf's type theory and UTT is a conservative extension. The importance of coherence conditions for the conservativity result is also discussed.

While Foucault’s work on biopolitics continues to inspire diverse studies in a variety of disciplines, it has largely been missing from the debates on the possibility of “affirmative biopolitics” which have been primarily influenced by the work of Agamben and Esposito. This article restores Foucault’s work to these debates, proposing that his final lecture course at the Collège de France in 1983–1984 developed a paradigm of affirmative biopolitics in the reading of the Cynic practice of truth-telling ( parrhesia). The Cynic (...) problematization of the relation between truth and life and their transvaluation of conventional truths by relocating them to the domain of bare life not only seeks to transform one’s life in accordance with the truth but also, through the confrontation with the existing conventions and norms, to transform the world as such. Cynic parrhesia is thus biopolitical, insofar as it reclaims the power of one’s life from the social order and its rationalities of government and applies it to oneself, investing one’s existence with truth. Since Foucault developed this reading of Cynicism in the context of his political engagement on behalf on East European dissidents, the article proceeds to analyse the resonances between parrhesia and Václav Havel’s idea of “living within the truth,” elaborating the biopolitical significance of both practices. We conclude by addressing the implications of our interpretation for Foucault scholarship and the wider debates on biopolitics. (shrink)

In 1933 Godel introduced a calculus of provability (also known as modal logic S4) and left open the question of its exact intended semantics. In this paper we give a solution to this problem. We find the logic LP of propositions and proofs and show that Godel's provability calculus is nothing but the forgetful projection of LP. This also achieves Godel's objective of defining intuitionistic propositional logic Int via classical proofs and provides a Brouwer-Heyting-Kolmogorov style provability semantics for Int which (...) resisted formalization since the early 1930s. LP may be regarded as a unified underlying structure for intuitionistic, modal logics, typed combinatory logic and λ-calculus. (shrink)

Pereboom and Caruso propose the quarantine model as an alternative to existing models of criminal justice. They appeal to the established public health practice of quarantining people, which is believed to be effective and morally justified, to explain why -in criminal justice- it is also morally acceptable to detain wrongdoers, without assuming the existence of a retrospective moral responsibility. Wrongdoers in their model are treated as carriers of dangerous diseases and as such should be preventively detained (or rehabilitated) until they (...) no longer pose a threat to society. Our main concern in this paper is that Pereboom and Caruso adopt an idiosyncratic meaning of quarantine regulations. We highlight a set of important disanalogies between their quarantine model and the quarantine regulations currently adopted in public health policies. More specifically, we argue that the similarities that Pereboom and Caruso propose to substantiate their analogy are not consistent—despite what they claim—with the regulations underlying quarantine as an epidemiological process. We also notice that certain quarantine procedures adopted in public health systems are inadequate to deal with criminal behaviors. On these grounds, we conclude that Pereboom and Caruso should not appeal to the quarantine analogy to substantiate their view, unless they address the issues and criticism we raise in this paper. (shrink)

This paper sheds light on the relationship between the logic of generalized truth values and the logic of bilattices. It suggests a definite solution to the problem of axiomatizing the truth and falsity consequence relations, \ and \ , considered in a language without implication and determined via the truth and falsity orderings on the trilattice SIXTEEN 3 . The solution is based on the fact that a certain algebra isomorphic to SIXTEEN 3 generates the variety of commutative and distributive (...) bilattices with conflation. (shrink)

We study unification problem and problem of admissibility for inference rules in minimal Johanssonsʼ logic J and positive intuitionistic logic IPC+. This paper proves that the problem of admissibility for inference rules with coefficients is decidable for the paraconsistent minimal Johanssonsʼ logic J and the positive intuitionistic logic IPC+. Using obtained technique we show also that the unification problem for these logics is also decidable: we offer algorithms which compute complete sets of unifiers for any unifiable formula. Checking just unifiability (...) of formulas with coefficients also works via verification of admissibility. (shrink)

Early normative studies of human behavior revealed a gap between the norms of practical rationality (what humans ought to do) and the actual human behavior (what they do). It has been suggested that, to close the gap between the descriptive and the normative, one has to revise norms of practical rationality according to the Quinean, engineering view of normativity. On this view, the norms must be designed such that they effectively account for behavior. I review recent studies of human perception (...) which pursued normative modeling and which found good agreement between the normative prescriptions and the actual behavior. I make the case that the goals and methods of this work have been incompatible with those of the engineering approach. I argue that norms of perception and action are observer-independent properties of biological agents; the norms are discovered using methods of natural sciences rather than the norms are designed to fit the observed behavior. (shrink)

N4-lattices provide algebraic semantics for the logic N4, the paraconsistent variant of Nelson's logic with strong negation. We obtain the representation of N4-lattices showing that the structure of an arbitrary N4-lattice is completely determined by a suitable implicative lattice with distinguished filter and ideal. We introduce also special filters on N4-lattices and prove that special filters are exactly kernels of homomorphisms. Criteria of embeddability and to be a homomorphic image are obtained for N4-lattices in terms of the above mentioned representation. (...) Finally, subdirectly irreducible N4-lattices are described. (shrink)

The article addresses Giorgio Agamben’s critical commentary on the global governance of the Covid-19 pandemic as a paradigm of his political thought. While Agamben’s comments have been criticized as exaggerated and conspiratorial, they arise from the conceptual constellation that he has developed starting from the first volume of his Homo Sacer series. At the centre of this constellation is the relation between the concepts of sovereign power and bare life, whose articulation in the figure of homo sacer Agamben traces from (...) the Antiquity to the present. We shall demonstrate that any such articulation is impossible due to the belonging of these concepts to different planes, respectively empirical and transcendental, which Agamben brings together in a problematic fashion. His account of the sovereign state of exception collapses a plurality of empirical states of exception into a zone of indistinction between different exceptional states and the normal state and then elevates this very indistinction to the transcendental condition of intelligibility of politics as such. Conversely, the notion of bare life, originally posited as the transcendental condition of possibility of positive forms of life, is recast as an empirical figure, whose sole form is the absence of form. We conclude that this problematic articulation should be abandoned for a theory that rather highlights the non-relation between sovereign power and bare life, which conditions the possibility of resistance and transformation that remains obscure in Agamben’s thought. (shrink)

This work treats the problem of axiomatizing the truth and falsity consequence relations, ⊨ t and ⊨ f, determined via truth and falsity orderings on the trilattice SIXTEEN 3 (Shramko and Wansing, 2005). The approach is based on a representation of SIXTEEN 3 as a twist-structure over the two-element Boolean algebra.

We outline an intuitionistic view of knowledge which maintains the original Brouwer–Heyting–Kolmogorov semantics for intuitionism and is consistent with the well-known approach that intuitionistic knowledge be regarded as the result of verification. We argue that on this view coreflectionA→KAis valid and the factivity of knowledge holds in the formKA→ ¬¬A‘known propositions cannot be false’.We show that the traditional form of factivityKA→Ais a distinctly classical principle which, liketertium non datur A∨ ¬A, does not hold intuitionistically, but, along with the whole of (...) classical epistemic logic, is intuitionistically valid in its double negation form ¬¬(KA¬A).Within the intuitionistic epistemic framework the knowability paradox is resolved in a constructive manner. We argue that this paradox is the result of an unwarranted classical reading of constructive principles and as such does not have the consequences for constructive foundations traditionally attributed it. (shrink)

We define a realizability interpretation of Aczel's Constructive Set Theory CZF into Explicit Mathematics. The final results are that CZF extended by Mahlo principles is realizable in corresponding extensions of T 0 , thus providing relative lower bounds for the proof-theoretic strength of the latter.

The article is devoted to the systematic study of the lattice εN4⊥ consisting of logics extending N4⊥. The logic N4⊥ is obtained from paraconsistent Nelson logic N4 by adding the new constant ⊥ and axioms ⊥ → p, p → ∼ ⊥. We study interrelations between εN4⊥ and the lattice of superintuitionistic logics. Distinguish in εN4⊥ basic subclasses of explosive logics, normal logics, logics of general form and study how they are relate.

The article takes Giorgio Agamben’s declaration of his optimism with regard to the possibilities of global political transformation as a point of departure for the inquiry into the affirmative aspects of Agamben’s political thought, frequently overshadowed by his more famous critical claims. We reconstitute three principles grounding Agamben’s optimism that pertain respectively to the total crisis of the contemporary biopolitical apparatuses, the possibility of a radically different form-of-life on the basis of their residue and the minimalist character of this transformation (...) that consists entirely in the subtraction of existence from these apparatuses. While the first two principles are unproblematic in the wider context of Agamben’s work, the third principle introduces the problematic of will that remains highly ambiguous in his philosophy. In the remainder of the article we address this ambiguity in an analysis of Agamben’s reading of Melville’s ‘Bartleby the Scrivener’ and conclude that Agamben’s optimism ultimately consists in the affirmation of absolute contingency, beyond both will and necessity. (shrink)

Coronavirus disease 2019 (COVID-19) first appeared in China in late 2019 and since then it has become a pandemic. Various countries, in accordance with their cultures, have adopted different approaches to deal with the spread of this disease. The dimensions of this disease and its global spread are such that it will certainly have enormous effects on various aspects of human life for many years. One of these issues is examining the approach of religious countries in dealing with this crisis. (...) The issue of science and religion is one of the main issues in the philosophy of religion. A historical event that human society is struggling with today is the COVID-19 crisis. The issues of religion and science were intertwined during the COVID-19 outbreak, contrary to what some thought. This shows that the opposition between religion and science is not real but aims to attack religion without a valid reason. Given the importance of the subject, this article addresses two aspects of people’s exposure to religion during the COVID-19 period. On the one hand, the researchers’ field observations indicate that group of citizens has turned towards religious teachings since the beginning of the COVID-19 crisis. On the other hand, another group of citizens have distanced themselves from religiosity, raising the duality of science and religion.Contribution: This article describes the dual attitude of citizens towards religiosity due to the occurrence of COVID-19, which has not been previously considered in research. (shrink)