Some aspects of vagueness as presented in Shapiro’s book Vagueness in Context [23] are analyzed from the point of fuzzy logic. Presented are some generalizations of Shapiro’s formal apparatus.

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)

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.

Masarykovy a Brentanovy snahy o překonání Humova skepticismu prostřednictvím počtu pravděpodobnosti lze chápat jako svého druhu "třetí cestu" mezi kantovským apriorismem a kapitulací před subtilními Humovými argumenty. U Masaryka je ono snažení součástí jeho projektu nové induktivní logiky, která (v návaznosti na Leibnize) by měla být logickým základem pro "umění vynalézat" (ars inveniendi). Masaryk akceptuje Humovu koncepci analytických soudů, ale zároveň inklinuje i ke koncepci Adolfa Ficka, v souladu s níž mají věty počtu pravděpodobnosti charakter syntetických soudů a priori; kromě (...) toho odkazuje pozoruhodným způsobem k Bernoulliho zákonu velkých čísel. Masarykovy úvahy vedou k závěru, že zákon velkých čísel zaručuje shodu mezi apriorními tvrzeními počtu pravděpodobnosti a empirickou skutečností, což podle Masaryka vyvrací "tresť" Humova skepticismu, spočívající v tvrzení, že rozum a zkušenost se vylučují. Vzhledem k tomu, že hlavním objektem Humovy kritiky byl pojem kauzality, je však nutno konstatovat, že Masarykovo snažení bylo neúspěšné, neboť žádná aplikace počtu pravděpodobnosti, jenž se zabývá náhodnými jevy, nemůže vést k založení kauzálního zákona (pokud tento zákon zahrnuje také tezi uniformity kauzální determinace). (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)

Ästhetik und Humanität sind in Arendts Werk eng miteinander verknüpft: Die Ausbildung einer ästhetischen (Denk-)Haltung impliziert eine Cultura Animi, die das Denken für den öffentlichen Raum vorbereitet. Wesentlich an der Kultivierung des Geistes ist die Ausbildung des Geschmacks. Überraschender Weise liest Arendt die Kritik der Urteilskraft als Referenztheorie und findet dort Kants 'wahre' politische Theorie vor: Der Geschmack als Inbegriff der Humanitas avanciert bei ihr zur conditio sine qua non des Politischen. Er ermöglicht es, Menschen qua ästhetischer Haltung als 'Zweck-in-sich-selbst' (...) zu betrachten. Jennifer Pavliks Studie legt in eindringlicher Weise dar, wie Hannah Arendts Werk das Ästhetische als Inbegriff des Politischen versteht. (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.

An experiment was performed to investigate the effects of practice and spacing on retention of Japanese–English vocabulary paired associates. The relative benefit of spacing increased with increased practice and with longer retention intervals. Data were fitted with an activation‐based memory model, which proposes that each time an item is practiced it receives an increment of strength but that these increments decay as a power function of time. The rate of decay for each presentation depended on the activation at the time (...) of the presentation. This mechanism limits long‐term benefits from further practice at higher levels of activation and produces the spacing effect and its observed interactions with practice and retention interval. The model was compared with another model of the spacing effect (Raaijmakers, 2003) and was fit to some results from the literature on spacing and memory. (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)

This paper empirically examines how consumers react when a company marks a product with a gay label. The company under scrutiny is one of the largest video game developers in the world, and the labeled product is a popular video game character. We use a regression discontinuity design to exploit the quasi-experimental setting. The main finding was significant drop in demand for this character and a return to previous levels after approximately 3 months. Possible mechanisms and dynamics were explored by (...) analyzing demand for other characters and by surveying consumers. The results are consistent after performing robustness checks based on grid search, subsampling, and placebo tests. (shrink)

Despite an increasing role of machine learning in science, there is a lack of results on limits of empirical exploration aided by machine learning. In this paper, we construct one such limit by proving undecidability of learnability of state spaces of physical systems. We characterize state spaces as binary hypothesis classes of the computable Probably Approximately Correct learning framework. This leads to identifying the first limit for learnability of state spaces in the agnostic setting. Further, using the fact that finiteness (...) of the combinatorial dimension of hypothesis classes is undecidable, we derive undecidability for learnability of state spaces as well. Throughout the paper, we try to connect our formal results with modern neural networks. This allows us to bring the limits close to the current practice and make a first step in connecting scientific exploration aided by machine learning with results from learning theory. (shrink)

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.

In fuzzy predicate logic, assignment of truth values may be partial, i.e. the truth value of a formula in an interpretation may be undefined . A logic is supersound if each provable formula is true in each interpretation in which the truth value of is defined. It is shown that among the logics given by continuous t-norms, Gödel logic is the only one that is supersound; all others are not supersound. This supports the view that the usual restriction of semantics (...) to safe interpretations is very natural. (shrink)

Each closed (i.e. variable free) formula of interpretability logic is equivalent in ILF to a closed formula of the provability logic G, thus to a Boolean combination of formulas of the form n.

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)

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.

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)

This paper addresses the ontological status of the body in the context of bodily practices in body-oriented disciplines, such as sport training, dance, and physiotherapy. Following Descartes’, Huss...

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)

Important works of Mostowski and Rasiowa dealing with many-valued logic are analyzed from the point of view of contemporary mathematical fuzzy logic.

Poté, co je ve studii podán obraz Humovy osobnosti na pozadí jeho doby, jsou v ní rozvíjeny následující teze: I. Smyslem a cílem veškerého Humova filosofování (zejména jeho popření ontologického statusu kategorií substance a kauzality a jeho teorie mravních citů) je připravit půdu pro skeptickou destrukci veškerých tvrzení týkajících se existence a přirozenosti Boží a pro zdůvodnění pojetí, v souladu s nímž může člověk žít mravně bezúhonným životem i bez jakékoliv opory v náboženském transcendentnu. II. Všechny silně nekonsistentní momenty Humovy (...) filosofie jsou sjednoceny (obvykle perfidně utajovaným) účelem, jímž je vyvrátit náboženství z kořene; právě z onoho vrcholného bodu "syntézy" lze uchopit jejich smysl a - zároveň také jinak neuchopitelnou jednotu Humovy filosofie. III. Popření ontologického statutu kategorie substance traktované v kontextu řešení problematiky teleologického důkazu Boží existence, rezultuje u Huma (takřka s železnou logikou) v anticipační nástin fundamentálních myšlenek evolučního přístupu a teorie samoorganizace, které s velkou pravděpodobností přímo ovlivnily pojetí Charlese Darwina. (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)

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)

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)

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)

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)

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)

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)

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)