Dave Ripley has recently argued against the plausibility of multiset consequence relations and of contraction-free approaches to paradox. For Ripley, who endorses a nontransitive theory, the best arguments that buttress transitivity also push for contraction—whence it is wiser for the substructural logician to go nontransitive from the start. One of Ripley’s allegations is especially insidious, since it assumes the form of a trivialisation result: it is shown that if a multiset consequence relation can be associated to a closure operator in (...) the expected way, then it necessarily contracts. We counter Ripley’s objection by presenting an approach to multiset consequence that escapes this trap. This approach is multiple-conclusioned in a heterodox way, for multiple succedents are given a conjunctive, rather than a disjunctive reading. Finally, we address a further objection by French and Ripley to the effect that the informational interpretation of sequents in linear logic does not motivate cut. (shrink)

In the last few decades many formal systems of fuzzy logics have been developed. Since the main differences between fuzzy and classical logics lie at the propositional level, the fuzzy predicate logics have developed more slowly (compared to the propositional ones). In this text we aim to promote interest in fuzzy predicate logics by contributing to the model theory of fuzzy predicate logics. First, we generalize the completeness theorem, then we use it to get results on conservative extensions of theories (...) and on witnessed models. (shrink)

This monograph presents a general theory of weakly implicative logics, a family covering a vast number of non-classical logics studied in the literature, concentrating mainly on the abstract study of the relationship between logics and their algebraic semantics. It can also serve as an introduction to algebraic logic, both propositional and first-order, with special attention paid to the role of implication, lattice and residuated connectives, and generalized disjunctions. Based on their recent work, the authors develop a powerful uniform framework for (...) the study of non-classical logics. In a self-contained and didactic style, starting from very elementary notions, they build a general theory with a substantial number of abstract results. The theory is then applied to obtain numerous results for prominent families of logics and their algebraic counterparts, in particular for superintuitionistic, modal, substructural, fuzzy, and relevant logics. The book may be of interest to a wide audience, especially students and scholars in the fields of mathematics, philosophy, computer science, or related areas, looking for an introduction to a general theory of non-classical logics and their algebraic semantics. (shrink)

This is the continuation of the paper :417–446, 2010). We continue the abstract study of non-classical logics based on the kind of generalized implication connectives they possess and we focus on semilinear logics, i.e. those that are complete with respect to the class of models where the implication defines a linear order. We obtain general characterizations of semilinearity in terms of the intersection-prime extension property, the syntactical semilinearity metarule and the class of finitely subdirectly irreducible models. Moreover, we consider extensions (...) of the language with lattice connectives and generalized disjunctions, study their interplay with implication and obtain axiomatizations and further descriptions of semilinear logics in terms of disjunctions and the proof by cases property. (shrink)

Large language models (LLMs) represent the currently most relevant incarnation of artificial intelligence with respect to the future fate of democratic governance. Considering their potential, this paper seeks to answer a pressing question: Could LLMs outperform humans as expert advisors to democratic assemblies? While bearing the promise of enhanced expertise availability and accessibility, they also present challenges of hallucinations, misalignment, or value imposition. Weighing LLMs’ benefits and drawbacks compared to their human counterparts, I argue for their careful integration to augment (...) democracy’s ability to address complex policy issues. The paper posits that time-tested democratic procedures like deliberation and aggregation by voting provide safeguards effective against both human and machine advisor imperfections. Additional protective measures include custom LLM training for the advisory role, boosting representatives’ competencies in query formulation, or implementation of adversarial proceedings in which LLM advisors could debate each other and provide dissenting opinions. These could further mitigate the risks that LLMs present in advisory roles and empower human decision-makers toward increased autonomy and quality of their collective choices. My conceptual exploration offers a roadmap for the co-evolution of AI and democratic institutions, setting the stage for an empirical research agenda to finetune the implementation specifics. (shrink)

Drawing on current debates at the frontiers of economics, psychology, and political philosophy, this book explores the challenges that arise for liberal democracies from a confrontation between modern technologies and the bounds of human rationality. With the ongoing transition of democracy's underlying information economy into the digital space, threats of disinformation and runaway political polarization have been gaining prominence. Employing the economic approach informed by behavioral sciences' findings, the book's chief concern is how these challenges can be addressed while preserving (...) a commitment to democratic values and maximizing the epistemic benefits of democratic decision-making. The book has two key strands: it provides a systematic argument for building a behaviorally informed theory of democracy; and explores how scientific knowledge on quirks and bounds of human rationality can inform the design of resilient democratic institutions. Drawing these together, the book explores the centrality of the rationality assumption in the methodological debates surrounding behavioral sciences as exemplified by the dispute between neoclassical and behavioral economics; the role of rationality in democratic social choice; behaviorally informed paternalism as a response to the challenge of irrationality; and non-paternalistic avenues to increase the resilience of the democratic institutions towards political irrationality This book is invaluable reading for anyone interested in behavioral economics and sciences, political philosophy and the future of democracy. (shrink)

Rational Pavelka logic extends Lukasiewicz infinitely valued logic by adding truth constants r̄ for rationals in [0, 1]. We show that this is a conservative extension. We note that this shows that provability degree can be defined in Lukasiewicz logic. We also give a counterexample to a soundness theorem of Belluce and Chang published in 1963.

Substructural logics extending the full Lambek calculus FL have largely benefited from a systematical algebraic approach based on the study of their algebraic counterparts: residuated lattices. Recently, a nonassociative generalization of FL has been studied by Galatos and Ono as the logic of lattice-ordered residuated unital groupoids. This paper is based on an alternative Hilbert-style presentation for SL which is almost MP -based. This presentation is then used to obtain, in a uniform way applicable to most substructural logics, a form (...) of local deduction theorem, description of filter generation, and proper forms of generalized disjunctions. A special stress is put on semilinear substructural logics. Axiomatizations of the weakest semilinear logic over SL and other prominent substructural logics are provided and their completeness with respect to chains defined over the real unit interval is proved. (shrink)

In contrast to Anglophone debates on personal identity initially formed by John Locke’s investigation of personal identity in the sense of personal continuity or persistence through time, the Continental tradition focuses on what constitutes ipseity in the sense of individuality or uniqueness of the human being “constituted” by its continuous transformation through changing experience. In this study, I claim that contemporary phenomenological research in France—especially the “phenomenology of the event” as represented by Henri Maldiney and Claude Romano—contributes to this Continental (...) discussion in a significant way: it formulates the conditions of personal uniqueness or distinctiveness with regard to other persons, conditions not to be found in Heidegger’s existential conception of selfhood in Being and Time. More precisely, Maldiney and Romano allow us to answer the principal questions of this study: In what does the personal uniqueness consist? What exactly individualizes the first-person selfhood disclosed in Dasein’s relation to death? In my three-stage analysis, I first deal with Heidegger’s conception of selfhood in Being and Time and its limits with respect to the question of personal uniqueness. Next, I analyse Maldiney’s conception of “eventful selfhood” in which he “completes” Heidegger’s conception of selfhood by describing Dasein’s openness to ontical, and yet fully authentic events. Finally, I develop the argumentation by presenting Romano’s even more radical conception of the “happening subjectivity”, which allows us to return to the second major feature of personal identity: personal persistence. Nonetheless, I conclude that the connection between personal uniqueness and persistence is not sufficiently examined in the phenomenology of the event, which opens the path towards another related inquiry into the following problem: What is the proper subjective dimension or the “underlying thing” in the background of personal persistence which somehow resists events? (shrink)

We generalise the Blok–Jónsson account of structural consequence relations, later developed by Galatos, Tsinakis and other authors, in such a way as to naturally accommodate multiset consequence. While Blok and Jónsson admit, in place of sheer formulas, a wider range of syntactic units to be manipulated in deductions (including sequents or equations), these objects are invariablyaggregatedvia set-theoretical union. Our approach is more general in that nonidempotent forms of premiss and conclusion aggregation, including multiset sum and fuzzy set union, are considered. (...) In their abstract form, thus,deductive relationsare defined as additional compatible preorderings over certain partially ordered monoids. We investigate these relations using categorical methods and provide analogues of the main results obtained in the general theory of consequence relations. Then we focus on the driving example of multiset deductive relations, providing variations of the methods of matrix semantics and Hilbert systems in Abstract Algebraic Logic. (shrink)

Transfer theorems are central results in abstract algebraic logic that allow to generalize properties of the lattice of theories of a logic to any algebraic model and its lattice of filters. Their proofs sometimes require the existence of a natural extension of the logic to a bigger set of variables. Constructions of such extensions have been proposed in particular settings in the literature. In this paper we show that these constructions need not always work and propose a wider setting in (...) which they can still be used. (shrink)

Formal systems of fuzzy logic are well-established logical systems and respected members of the broad family of the so-called substructural logics closely related to the famous logic BCK. The study of fragments of logical systems is an important issue of research in any class of non-classical logics. Here we study the fragments of nine prominent fuzzy logics to all sublanguages containing implication. However, the results achieved in the paper for those nine logics are usually corollaries of theorems with much wider (...) scope of applicability. In particular, we show how many of these fragments are really distinct and we find axiomatic systems for most of them. In fact, we construct strongly separable axiomatic systems for eight of our nine logics. We also fully answer the question for which of the studied fragments the corresponding class of algebras forms a variety. Finally, we solve the problem how to axiomatize predicate versions of logics without the lattice disjunction. (shrink)

This article reviews recent findings indicating some common brain processes during dissociative states and dreaming with the aim to outline a perspective that neural chaotic states during dreaming can be closely related to dissociative states that may manifest in dreams scenery. These data are in agreement with various clinical findings that dissociated states can be projected into the “dream scenery” in REM sleep periods and dreams may represent their specific interactions that may uncover unusual psychological potential of creativity in psychotherapy, (...) art and scientific discoveries. (shrink)

Uniform infinite bases are defined for the single-conclusion and multiple-conclusion admissible rules of the implication–negation fragments of intuitionistic logic and its consistent axiomatic extensions . A Kripke semantics characterization is given for the structurally complete implication–negation fragments of intermediate logics, and it is shown that the admissible rules of this fragment of form a PSPACE-complete set and have no finite basis.

Shows how different forms of skepticism can lead to remarkably different moral and political implications.

Can one extend crisp Peano arithmetic PA by a possibly many-valued predicate Tr(x) saying “xis true” and satisfying the “dequotation schema”for all sentences φ? This problem is investigated in the frame of Łukasiewicz infinitely valued logic.

The paper deals with the problem of divine causation in relation to created agents in general and human rational agents in particular. Beyond creation and conservation, Aquinas specifies divine contribution to created agents’ operation as application in the role of the first cause and the operation of the principal cause employing an instrumental cause. It is especially the latter which is open to varying interpretation and which might be potentially threatening to human freedom. There are different readings of what it (...) is for the secondary agent to “act through the power of the principal cause”. Either the divine cause causes only the existence of the effect of the secondary cause, or it also causes the cause to operate in the sense that it determines its outcome. The latter seems to contradict human freedom. Both readings of Aquinas were developed in the latter half of the sixteenth century within scholastic philosophy and theology. (shrink)

This paper is a contribution to Mathematical fuzzy logic, in particular to the algebraic study of t-norm based fuzzy logics. In the general framework of propositional core and Δ-core fuzzy logics we consider three properties of completeness with respect to any semantics of linearly ordered algebras. Useful algebraic characterizations of these completeness properties are obtained and their relations are studied. Moreover, we concentrate on five kinds of distinguished semantics for these logics–namely the class of algebras defined over the real unit (...) interval, the rational unit interval, the hyperreals , the strict hyperreals and finite chains, respectively–and we survey the known completeness methods and results for prominent logics. We also obtain new interesting relations between the real, rational and hyperreal semantics, and good characterizations for the completeness with respect to the semantics of finite chains. Finally, all completeness properties and distinguished semantics are also considered for the first-order versions of the logics where a number of new results are proved. (shrink)

Procedural justifications of democracy emphasize inclusiveness and respect and by doing so come into conflict with instrumental justifications that depend on voters’ competence. This conflict raises questions about jury theorems and makes their standing in democratic theory contested. We show that a type of no-regret learning called meta-induction can help to satisfy the competence assumption without excluding voters or diverse opinion leaders on an a priori basis. Meta-induction assigns weights to opinion leaders based on their past predictive performance to determine (...) the level of their inclusion in recommendations for voters. The weighting minimizes the difference between the performance of meta-induction and the best opinion leader in hindsight. The difference represents the regret of meta-induction whose minimization ensures that the recommendations are optimal in supporting voters’ competence. Meta-induction has optimal truth-tracking properties that support voters’ competence even if it is targeted by mis/disinformation and should be considered a tool for supporting democracy in hyper-plurality. (shrink)

An important task for every major philosopher is to offer us an understanding of the nature of mind. The essays in this volume discuss different aspects of the philosophical theories of mind put forward in the century and a half that followed Descartes' Meditations of 1641. These years, often referred to as the 'early-modern' period, are probably unparalleled for originality and diversity in conceiving the mind. The volume not only includes two essays on Descartes' own thinking, but there are also (...) examinations of what Spinoza, Malebranche, Locke, Berkeley, Reid, the Cambridge Platonists, and others, have to say about the nature of mind. The aim of the volume is to represent some of the best contemporary research and reflection on mind in early-modern philosophy. The contributors, who teach at a range of universities in mainland Europe, Great Britain and North America, are Margaret Atherton, Miran BozoviÄ, Petr GlombìÄek, Boris Hennig, James Hill, Nicholas Jolley, Jan Palkoska, G. A. J. Rogers, and Anthony Savile. All the essays appear here for the first time. (shrink)

Many democratic countries have failed to stand up to the challenge presented by the COVID-19 pandemic. I argue that the collective response to the pandemic has been incapacitated by an ‘epistemic crisis’, (i.e., a breakdown in the social division of epistemic labor) that led to a failure of citizens’ beliefs to converge towards a shared perception of the situation. Neither a paucity of relevant expert knowledge nor democratic citizens’ irrationality is required for the crisis to emerge. In particular, I highlight (...) three obstacles capable of preventing relevant expert testimony from gaining democratic legitimacy necessary for an effective policy response: 1) the proper domain of expertise is uncertain; 2) regular citizens’ meta-expertise – (i.e., ability to discriminate among the putative experts based on their relative epistemic merit) – is not efficacious enough to trigger truth-convergence of the public opinion; 3) the prominent sources of third-party meta-expertise lack credibility due to their conflicts of interest. Since the first two problems appear irresolvable, I propose that the search for a path towards preclusion of future epistemic crises concentrates on upgrading the institutional fundament for meta-expertise provision. Social epistemology plays a vital role in this search, but its close cooperation with other disciplines is a must. (shrink)

A very simple many-valued predicate calculus is presented; a completeness theorem is proved and the arithmetical complexity of some notions concerning provability is determined.

Witnessed models of fuzzy predicate logic are models in which each quantified formula is witnessed, i.e. the truth value of a universally quantified formula is the minimum of the values of its instances and similarly for existential quantification. Systematic theory of known fuzzy logics endowed with this semantics is developed with special attention paid to problems of arithmetical complexity of sets of tautologies and of satisfiable formulas.

The paper proposes a synthesis between human scientists and artificial representation learning models as a way of augmenting epistemic warrants of realist theories against various anti-realist attempts. Towards this end, the paper fleshes out unconceived alternatives not as a critique of scientific realism but rather a reinforcement, as it rejects the retrospective interpretations of scientific progress, which brought about the problem of alternatives in the first place. By utilising adversarial machine learning, the synthesis explores possibility spaces of available evidence for (...) unconceived alternatives providing modal knowledge of what is possible therein. As a result, the epistemic warrant of synthesised realist theories should emerge bolstered as the underdetermination by available evidence gets reduced. While shifting the realist commitment away from theoretical artefacts towards modalities of the possibility spaces, the synthesis comes out as a kind of perspectival modelling. (shrink)

Can one extend crisp Peano arithmetic PA by a possibly many-valued predicate Tr(x) saying "x is true" and satisfying the "dequotation schema" $\varphi \equiv \text{Tr}(\bar{\varphi})$ for all sentences φ? This problem is investigated in the frame of Lukasiewicz infinitely valued logic.

A simple complete axiomatic system is presented for the many-valued propositional logic based on the conjunction interpreted as product, the coresponding implication (Goguen's implication) and the corresponding negation (Gödel's negation). Algebraic proof methods are used. The meaning for fuzzy logic (in the narrow sense) is shortly discussed.

We explored differences in the course of physiological functions and in the subjective evaluations in response to listening to a 7-min recording of the sound of a chainsaw and to the sounds of a forest. A Biofeedback 2000x-pert apparatus was used for continual recording of the following physiological functions in 50 examined persons: abdominal and thoracic respiration and their amplitude and frequency, electrodermal activity, finger skin temperature, heart rate and heart rate variability. The group of 25 subjects listening to the (...) sound of a chainsaw exhibited significantly lower values of blood volume pulse amplitude, lower values in peak alpha frequency HRV and higher values in peak high-frequency HRV. In the time interval from 80 s to 209 s, in which the two groups showed the greatest differences, lower values of blood volume pulse were also recorded while listening to the sound of a chainsaw. Listening to the sound of a chainsaw is associated with a greater feeling of fatigue and higher tension, while listening to the sounds of a forest is even considered to elicit feelings of improved learning abilities. The assumption that listening to the sound of a chainsaw results in higher defense arousal was confirmed. The greater variability which is exhibited by a majority of physiological functions while listening to the forest sounds may also be an innovative finding. It seems that there are two types of arousal following from correlations between physiological functions and subjective assessment. Low values of blood volume pulse amplitude are especially important from the health perspective. They correspond to the amount of vasoconstriction which occurs in the endothelial dysfunction related to increased mortality, incidence of myocardial infarction, leg atherosclerosis and topically to COVID-19. (shrink)

While the assumption that the sociopolitical and economic situation affects adolescents’ well-being, encompassing life satisfaction and a positive sense of self, is plausible, few studies have confirmed such macrosocial influences. The case of the Czech Republic offers an example of a society transitioning from totalitarian government to western democracy. Our study provides statistical description of Czech adolescents’ well-being over the past 30 years in association with the subjective perception of everyday problems. These daily hassles represent experiences and conditions of daily (...) living that have been appraised as salient and harmful or threatening to adolescents’ well-being. We analyzed four samples of adolescents aged 14–17 years surveyed at four time points over the last three decades—1992, 2001, 2011, and 2019, total N = 4,005. The results show that life satisfaction, self-esteem, and self-reported daily hassles changed only marginally from 1992 to 2019 with small differences related to the post-revolution 1992 cohort. Adolescents reported increasing problems in school, relationships with parents, sports, and leisure time over the study period. A model linking daily hassles and self-esteem to life satisfaction across four cohorts showed that daily hassles strongly predicted life satisfaction except in the post-revolution cohort of 1992 when life satisfaction was also the lowest. The effect was slightly higher in females. Across the cohorts, gender differences in life satisfaction changed from males being more satisfied in 1992 to females being more satisfaction in 2019. Limitations stemming from sampling differences across cohorts are discussed. (shrink)

‘The Russian Orthodox Church’s Basic Teaching on Human Dignity, Freedom and Rights’ has been a constant source of controversy since its release in 2008. While most scholars debated the document for its political implications, little attention has been paid to its anthropological consequences, particularly those deriving from linking a dignified life with the ethical use of freedom. The article highlights that if the sole criteria for living a dignified life is freedom then the most vulnerable categories in society can claim (...) only basic dignity. Engaging constructively with the work of Romanian theologian Dumitru Stăniloae, it will be argued that the source of human dignity is not a specific capacity, but the recapitulation of all human beings in Christ’s death and resurrection. The dignity that belongs to Christ is transferred through recapitulation to all humans irrespective of their abilities or sins. In fact, what changes with the use of freedom is not the dignity of the person, but our ability to perceive that dignity. (shrink)

Humans are remarkably adaptable, and therefore a successful species. There are many speculative answers to the question of why this is so. One of them represents the cultural intelligence hypothesis, which consid-ers cultural learning skills as the key to human success. This work aims to present the hypothesis of cultural intelligence as a viable alternative to more conventional approaches within the debate about the origin of human intelligence, such as the hypothesis of general and improvisational intelligence. Theirmutual comparison shows that (...) cultural intelligence hypothesis must necessarily work with flexible social learning strategies to describe cultural transmission, thus losing part of its explanatory power. As the theory of metacognitive strategies of social learning by cognitive psychologist Cecilia Heyes shows, there is a way to combine the flexibility of human reasoning with the “stupid” process of cultural selection. (shrink)

This paper is a contribution to the study of the rôle of disjunction inAlgebraic Logic. Several kinds of (generalized) disjunctions, usually defined using a suitable variant of the proof by cases property, were introduced and extensively studied in the literature mainly in the context of finitary logics. The goals of this paper are to extend these results to all logics, to systematize the multitude of notions of disjunction (both those already considered in the literature and those introduced in this paper), (...) and to show several interesting applications allowed by the presence of a suitable disjunction in a given logic. (shrink)