The one-variable fragment of a first-order logic may be viewed as an “S5-like” modal logic, where the universal and existential quantifiers are replaced by box and diamond modalities, respectively. Axiomatizations of these modal logics have been obtained for special cases—notably, the modal counterparts $\mathrm {S5}$ and $\mathrm {MIPC}$ of the one-variable fragments of first-order classical logic and first-order intuitionistic logic, respectively—but a general approach, extending beyond first-order intermediate logics, has been lacking. To this end, a sufficient criterion is given in (...) this paper for the one-variable fragment of a semantically defined first-order logic—spanning families of intermediate, substructural, many-valued, and modal logics—to admit a certain natural axiomatization. More precisely, an axiomatization is obtained for the one-variable fragment of any first-order logic based on a variety of algebraic structures with a lattice reduct that has the superamalgamation property, using a generalized version of a functional representation theorem for monadic Heyting algebras due to Bezhanishvili and Harding. An alternative proof-theoretic strategy for obtaining such axiomatization results is also developed for first-order substructural logics that have a cut-free sequent calculus and admit a certain interpolation property. (shrink)

On the Notion "Type of Language" Petr Sgall It is well known that the high frequency of terminological vagueness and confusion has been a serious obstacle ...

Structural completeness properties are investigated for a range of popular t-norm based fuzzy logics—including Łukasiewicz Logic, Gödel Logic, Product Logic, and Hájek's Basic Logic—and their fragments. General methods are defined and used to establish these properties or exhibit their failure, solving a number of open problems.

Despite their flaws, large language models (LLMs) deserve a fair chance to prove their mettle against human experts, who are often plagued with biases, conflicts of interest, and other frailties. For epistemically unprivileged laypeople struggling to access expert knowledge, the accessibility advantages of LLMs could prove crucial. While complaints about LLMs' inconsistencies and arguments for human superiority are often justified (for now), they distract from the urgent need to prepare for the likely scenario of LLMs' continued ascent. Experimentation with both (...) the capabilities and institutional architecture of LLMs is necessary. Neither tech-bashing nor excessive gatekeeping will suffice. As LLMs are here to stay and they keep improving, it is high time we started thinking about how to navigate the impending wave of their proliferation. (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)

It is shown that the low basis theorem is meaningful and provable in I∑ 1 and that the priority-free solution to Post's problem formalizes in this theory.

We give a brief introduction to the axiomatization of temporal logics. Branching continuations are shortly presented thereafter and the possibility of their clear syntactical axiomatization in a Hilbert-style system is investigated as last. Some basic preliminary observations and suggestions, how such axiomatization could start, are presented.

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.

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 article identifies the assumption of responsibility as a basic need of human beings and applies the concept specifically to older people with dementia or Alzheimer's disease. It suggests a two‐level concept of responsibility, based on the approach of discourse ethicist Karl‐Otto Apel, as a promising approach to recognizing human diversity while at the same time respecting people's equal rights to participate in discourse. This concept can serve as a theoretical starting point for the construction of individually adapted types of (...) responsibility. Furthermore, the article describes practical ideas (primarily the practice of doll therapy) that can enable people with dementia or Alzheimer's disease to assume responsibility. Direct communication and a reflective, sensitive consideration of each individual case are identified as important prerequisites for the inclusion of elderly people with dementia. (shrink)

An arithmetical interpretation of dynamic propositional logic (DPL) is a mapping f satisfying the following: (1) f associates with each formula A of DPL a sentence f(A) of Peano arithmetic (PA) and with each program α a formula f(α) of PA with one free variable describing formally a supertheory of PA; (2) f commutes with logical connectives; (3) f([α] A) is the sentence saying that f(A) is provable in the theory f(α); (4) for each axiom A of DPL, f(A) is (...) provable in PA (and consequently, for each A provable in DPL, f(A) is provable in PA). The arithmetical completeness theorem is proved saying that a formula A of DPL is provable in DPL iff for each arithmetical interpretation f, f(A) is provable in PA. Various modifications of this result are considered. (shrink)

Vague language and corresponding models of inference and information processing is an important and challenging topic as witnessed by a number of recent monographs and collections of essays devoted to the topic. This volume collects fifteen papers, the majority of which originated with talks presented at the conference "Logical Models of Reasoning with Vague Information ", September 14-17, 2009, in Čejkovice, that initiated a EUROCORES/LogICCC project with the same title. At least two features set the current volume apart from other (...) texts: first, the interdisciplinary nature of the topic is nicely reflected by the wide range of interests of the authors, who include philosophers, linguists, logicians, as well as mathematicians and computer scientists. Secondly, all the papers are accompanied by comments written by other authors and a few outside experts. These comments and corresponding replies by the authors document the very lively ongoing debate on adequate models of vague language. (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)

We show that the modal prepositional logicILM (interpretability logic with Montagna's principle), which has been shown sound and complete as the interpretability logic of Peano arithmetic PA (by Berarducci and Savrukov), is sound and complete as the logic ofπ 1-conservativity over eachbE 1-sound axiomatized theory containingI⌆ 1 (PA with induction restricted tobE 1-formulas). Furthermore, we extend this result to a systemILMR obtained fromILM by adding witness comparisons in the style of Guaspari's and Solovay's logicR (this will be done in a (...) separate continuation of the present paper). (shrink)

Results on arithmetical complexity of important sets of formulas of several fuzzy predicate logics are surveyed and some new results are proven.

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 article is focused on the notions of health and illness, as they appear in the context of philosophical reflections on finitude and contingency of human existence. Criticizing Heidegger's approach to health and illness which is based on the Aristotelian concept of privation, the author tries to find an alternative to the privative concept of illness with the help of Schelling's treatise on human freedom which explicates Evil not as a privation of Good, but as a sort of illness that (...) has its own phenomenal positivity. Even Schelling's philosophical investigation of the nature of Evil, however, doesn't seem to provide a solid ground for a non-privative and non-normative approach to pathological phenomena. Only when Schelling's treatise on human freedom is de-contextualized and radicalized in a way suggested, for instance, by Deleuze in his Difference and Repetition, does it seem possible to elucidate pathological, and especially psychopathological phenomena, as they show themselves from themselves, and not from the perspective given by the normative ideal of health. (shrink)

This text presents an assessment of the literary work of Karel Čapek from a perspective that has not yet been discussed. It focuses on analysing Čapek’s works from the viewpoint of their possible inspiration by bioethical issues. Čapek’s philosophy and the powerful ethical charge of his texts tend to be associated with his interest in pragmatism, a subject to which he, however, took an individual and critical approach. One of the most important categories of his way of thinking is life. (...) In his prose works and plays we therefore see motifs that may be associated with the thematic definition of bioethics. These are questions concerning the value and quality of human life, issues concerning the dehumanizing impact of science and technology, as well as reflections upon the moral dimension of man’s relationship to nature and also to the relationship between people and animals. Čapek’s work may therefore provide inspiration from the perspective of the history of the gradual formation of the bioethical point of view. (shrink)

Článek rekapituluje ideová východiska Alfreda Schütze, který se na půdě metodologie společenských věd snaží o syntézu příspěvků Edmunda Husserla a Maxe Webera. Přestože v raném období Schütz blízce následuje Husserlův fenomenologický přístup, projevuje se již zde v první řadě důraz na empirický charakter zkoumání, který navazuje na weberovskou linii argumentace a staví se i proti názorům dalšího ze Schützových velkých učitelů, Ludwiga von Misese. Článek postupně analyzuje klíčové znaky Schützovy vlastní metody a ukazuje klíčové postavení, které hraje při našem vědeckém (...) i každodenním rozumění světu, v němž žijeme, typizace a anonymizace. Z fenomenologických východisek se tak dostáváme k problematice Weberových ideálních typů a v závěru i na půdu Rakouské ekonomie reprezentované von Misesem, jehož některá neudržitelná východiska se Schütz snaží modifikovat. (shrink)

Fuzzy logic is understood as a logic with a comparative and truth-functional notion of truth. Arithmetical complexity of sets of tautologies and satisfiable sentences as well of sets of provable formulas of the most important systems of fuzzy predicate logic is determined or at least estimated.

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)

This text is an attempt to reflect on some of the morally relevant issues raised by the current pandemic crisis. The specificity of this situation is also defined by comparison with the AIDS pandemic. The topicality of the current crisis is an obstacle to a more systematic analysis and formulation of more coherent conclusions. This is the reason why the text outlines those aspects that can now be formulated as possible starting points for discourse on the moral dimension of the (...) pandemic. These mainly include the problem of responsibility (individual, social and professional) at a time of escalating risk situation. Other problems are briefly outlined according to the basic areas of bioethics – human bioethics, environmental ethics, and animal ethics. (shrink)

The paper discusses one of the central problems of contemporary formal semantics — counterexamples to the predictions of the theory of binding (due to N. Chomsky). In particular, the author addresses cases of the so-called coreferential readings of reflexive pronouns which are standardly predicted to receive only the bound reading. The author examines theories of T. Reinhart and I. Heim and suggests an extension ofthe latter theory in order to enable it to account for the aforementioned readings of reflexive pronouns.

‘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 (persons with (...) severe cognitive disabilities or those struggling with addictions) 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)