Fuzzy Logic

Kamp and Fine presented an influential argument against the use of fuzzy logic for linguistic semantics in 1975. However, the argument assumes that contradictions of the form "A and not A" have semantic value zero. The argument has been recently criticized because sentences of this form are actually not perceived as contradictory by naive speakers. I present new experimental evidence arguing that fuzzy logic still isn't useful for linguistic semantics even if we take such naive speaker judgements at face value. (...) Specifically I show that naive speakers judge "A and not A" in the relevant cases as more true than "B and not A" even when A and B are judged to be equally true. A truth functional semantics such as fuzzy logic cannot account for these intuitions directly. (shrink)

In this article I define a strong conditional for classical sentential logic, and then extend it to three non-classical sentential logics. It is stronger than the material conditional and is not subject to the standard paradoxes of material implication, nor is it subject to some of the standard paradoxes of C. I. Lewis’s strict implication. My conditional has some counterintuitive consequences of its own, but I think its pros outweigh its cons. In any case, one can always augment one’s language (...) with more than one conditional, and it may be that no single conditional will satisfy all of our intuitions about how a conditional should behave. Finally, I suspect the strong conditional will be of more use for logic rather than the philosophy of language, and I will make no claim that the strong conditional is a good model for any particular use of the indicative conditional in English or other natural languages. Still, it would certainly be a nice bonus if some modified version of the strong conditional could serve as one. -/- I begin by exploring some of the disadvantages of the material conditional, the strict conditional, and some relevant conditionals. I proceed to define a strong conditional for classical sentential logic. I go on to adapt this account to Graham Priest’s Logic of Paradox, to S. C. Kleene’s logic K3, and then to J. Łukasiewicz’s logic Ł, a standard version of fuzzy logic. (shrink)

In today's academic circles, many are of the opinion that fuzzy logic has brought the age-old principle of contradiction to an end. In this light, objective reality can no longer be reduced to A and non-A, or to zero and one. But is this presumption correct? Does fuzzy logic really violate the principle of contradiction? Is it true that fuzzy logic - in contrast to the Transcendent Philosophy - is based on the assumption that two contradictories can be true and (...) false at the same time? In this article, the writer intends to examine this question by focusing on the problem of the simultaneous truth or falsehood of two contradictory propositions. (shrink)

While deliberation has traditionally played a central role in philosophical and behavioral accounts of ethical decision-making, several recent studies challenge the value of deliberation. These studies find that deliberative thinking, such as considering divergent views or different perspectives, leads to less ethical decisions. We observe, however, that these studies do not address normative deliberation, in which decision-makers consider or apply a normative standard. We predict that normative deliberation improves ethical decision-making. Across six experiments, we examine the effects of non-normative deliberation (...) and normative deliberation on ethical decision-making. We find that normative deliberation improves ethical decision-making and, in contrast to recent studies, no form of deliberation harms ethical decision-making. (shrink)

In this paper we explore the following question: how weak can a logic be for Rosser's essential undecidability result to be provable for a weak arithmetical theory? It is well known that Robinson's Q is essentially undecidable in intuitionistic logic, and P. Hajek proved it in the fuzzy logic BL for Grzegorczyk's variant of Q which interprets the arithmetic operations as non-total non-functional relations. We present a proof of essential undecidability in a much weaker substructural logic and for a much (...) weaker arithmetic theory, a version of Robinson's R (with arithmetic operations also interpreted as mere relations). Our result is based on a structural version of the undecidability argument introduced by Kleene and we show that it goes well beyond the scope of the Boolean, intuitionistic, or fuzzy logic. (shrink)

In this paper we explore the following question: how weak can a logic be for Rosser’s essential undecidability result to be provable for a weak arithmetical theory? It is well known that Robinson’s Q is essentially undecidable in intuitionistic logic, and P. Hájek proved it in the fuzzy logic BL for Grzegorczyk’s variant of Q which interprets the arithmetic operations as nontotal nonfunctional relations. We present a proof of essential undecidability in a much weaker substructural logic and for a much (...) weaker arithmetic theory, a version of Robinson’s R (with arithmetic operations also interpreted as mere relations). Our result is based on a structural version of the undecidability argument introduced by Kleene and we show that it goes well beyond the scope of the Boolean, intuitionistic, or fuzzy logic. (shrink)

This paper is a contribution to graded model theory, in the context of mathematical fuzzy logic. We study characterizations of classes of graded structures in terms of the syntactic form of their first-order axiomatization. We focus on classes given by universal and universal-existential sentences. In particular, we prove two amalgamation results using the technique of diagrams in the setting of structures valued on a finite MTL-algebra, from which analogues of the Łoś–Tarski and the Chang–Łoś–Suszko preservation theorems follow.

We consider a modal language over crisp frames and formulas evaluated on a finite MTL-chain (a linearly ordered commutative integral residuated lattice). We first show that the basic modal abstract logic with constants for the values of the MTL-chain is the maximal abstract logic satisfying Compactness, the Tarski Union Property and strong invariance for bisimulations. Finally, we improve this result by replacing the Tarski Union Property by a relativization property.

The aim of the paper is to analyze the expressive power of the square operator of Łukasiewicz logic: ∗x=x⊙x⁠, where ⊙ is the strong Łukasiewicz conjunction. In particular, we aim at understanding and characterizing those cases in which the square operator is enough to construct a finite MV-chain from a finite totally ordered set endowed with an involutive negation. The first of our main results shows that, indeed, the whole structure of MV-chain can be reconstructed from the involution and the (...) Łukasiewicz square operator if and only if the obtained structure has only trivial subalgebras and, equivalently, if and only if the cardinality of the starting chain is of the form n+1 where n belongs to a class of prime numbers that we fully characterize. Secondly, we axiomatize the algebraizable matrix logic whose semantics is given by the variety generated by a finite totally ordered set endowed with an involutive negation and Łukasiewicz square operator. Finally, we propose an alternative way to account for Łukasiewicz square operator on involutive Gödel chains. In this setting, we show that such an operator can be captured by a rather intuitive set of equations. (shrink)

In this paper we present two new approaches for dealing with semantic paradoxes and soritical predicates based on fuzzy logic. We show that both of them have conceptual advantages over the more traditional Łukasiewicz approach, and that the second one even avoids standard proofs of ω-nconsistency.

Many individuals have miserable work lives, in which they must toil away at mind-numbing yet exhausting tasks for hours on end, being ordered about by their superiors, perhaps with few guarantees that this source of income will persist for very long. However, this is only half of the story: what is centrally important is that many of those who endure these conditions are denied a fair wage in return for the burdens that they bear. In this article, I reflect on (...) the significance of this fact in order to argue for the evaporation thesis. This thesis holds that individuals’ claims to particular employment-related protections from their government disappear as their earnings increase. In the course of defending this position, I explore the moral difference an employee's wage offer makes to the work conditions that we can expect her to accept, including why there are limits to the role that cash can play here. (shrink)

Many individuals have miserable work lives, in which they must toil away at mind-numbing yet exhausting tasks for hours on end, being ordered about by their superiors, perhaps with few guarantees that this source of income will persist for very long. However, this is only half of the story: what is centrally important is that many of those who endure these conditions are denied a fair wage in return for the burdens that they bear. In this article, I reflect on (...) the significance of this fact in order to argue for the evaporation thesis. This thesis holds that individuals’ claims to particular employment-related protections from their government disappear as their earnings increase. In the course of defending this position, I explore the moral difference an employee's wage offer makes to the work conditions that we can expect her to accept, including why there are limits to the role that cash can play here. (shrink)

Medical knowledge as well as clinical practice are characterized by inescapable uncertainty. There are many reasons this is the case, but foremost among them is that almost everything in medicine is inevitably vague, be it something linguistic such as the term “illness”, or something extra-linguistic such as the condition referred to as illness. If we ask ourselves, then, what the term “illness” means exactly, on the one hand; and how we may precisely delimit the condition illness, on the other; we (...) shall realize that to answer these and similar questions requires specific methods that enable us to adequately cope with vagueness. As we shall see below, fuzzy logic provides us with just such methods. (shrink)

Shared conceptualization, in the sense we take it here, is as recent a notion as the Semantic Web, but its relevance for a large variety of fields requires efficient methods of extraction and representation for both quantitative and qualitative data. This notion is particularly relevant for the investigation into, and construction of, semantic structures such as knowledge bases and taxonomies, but given the required large, often inaccurate, corpora available for search we can get only approximations. We see fuzzy description logic (...) as an adequate medium for the representation of human semantic knowledge and propose a means to couple it with fuzzy semantic networks via the propositional Łukasiewicz fuzzy logic such that these suffice for decidability for queries over a semantic-knowledge base such as “to what degree of sharedness does it entail the instantiation C(a) for some concept C” or “what are the roles R that connect the individuals a and b to degree of sharedness ε.” . (shrink)

Strategies for improving the explainability of artificial agents are a key approach to support the understandability of artificial agents’ decision-making processes and their trustworthiness. However, since explanations are not inclined to standardization, finding solutions that fit the algorithmic-based decision-making processes of artificial agents poses a compelling challenge. This paper addresses the concept of trust in relation to complementary aspects that play a role in interpersonal and human–agent relationships, such as users’ confidence and their perception of artificial agents’ reliability. Particularly, this (...) paper focuses on non-expert users’ perspectives, since users with little technical knowledge are likely to benefit the most from “post-hoc”, everyday explanations. Drawing upon the explainable AI and social sciences literature, this paper investigates how artificial agent’s explainability and trust are interrelated at different stages of an interaction. Specifically, the possibility of implementing explainability as a trust building, trust maintenance and restoration strategy is investigated. To this extent, the paper identifies and discusses the intrinsic limits and fundamental features of explanations, such as structural qualities and communication strategies. Accordingly, this paper contributes to the debate by providing recommendations on how to maximize the effectiveness of explanations for supporting non-expert users’ understanding and trust. (shrink)

In the literature on vagueness one finds two very different kinds of degree theory. The dominant kind of account of gradable adjectives in formal semantics and linguistics is built on an underlying framework involving bivalence and classical logic: its degrees are not degrees of truth. On the other hand, fuzzy logic based theories of vagueness—largely absent from the formal semantics literature but playing a significant role in both the philosophical literature on vagueness and in the contemporary logic literature—are logically nonclassical (...) and give a central role to the idea of degrees of truth. Each kind of degree theory has a strength: the classical kind allows for rich and subtle analyses of the comparative form of gradable adjectives and of various types of gradable precise adjectives, while the fuzzy kind yields a compelling solution to the sorites paradox. This paper argues that the fuzzy kind of theory can match the benefits of the classical kind and hence that the burden is on the latter to match the advantages of the former. In particular, we develop a new version of the fuzzy logic approach that—unlike existing fuzzy theories—yields a compelling analysis of the comparative as well as an adequate account of gradable precise predicates, while still retaining the advantage of genuinely solving the sorites paradox. (shrink)

In 2001, W. Carnielli and Marcos considered a 3-valued logic in order to prove that the schema ϕ ∨ (ϕ → ψ) is not a theorem of da Costa’s logic Cω. In 2006, this logic was studied (and baptized) as G'3 by Osorio et al. as a tool to define semantics of logic programming. It is known that the truth-tables of G'3 have the same expressive power than the one of Łukasiewicz 3-valued logic as well as the one of Gödel (...) 3-valued logic G3. From this, the three logics coincide up-to language, taking into acccount that 1 is the only designated truth-value in these logics. -/- From the algebraic point of view, Canals-Frau and Figallo have studied the 3-valued modal implicative semilattices, where the modal operator is the well-known Moisil-Monteiro-Baaz Δ operator, and the supremum is definable from this. We prove that the subvariety obtained from this by adding a bottom element 0 is term-equivalent to the variety generated by the 3-valued algebra of G'3. The algebras of that variety are called G'3-algebras. From this result, we obtain the equations which axiomatize the variety of G'3-algebras. Moreover, we prove that this variety is semisimple, and the 3-element and the 2-element chains are the unique simple algebras of the variety. Finally an extension of G'3 to first-order languages is presented, with an algebraic semantics based on complete G'3-algebras. The corresponding soundness and completeness theorems are obtained. (shrink)

Introduction. The article is devoted to the epistemology of communicative knowledge. It is argued that the central problem in the analysis of such knowledge is the question of the status of testimony. The author discusses reductionism and non-reductionism as two traditional approaches to the problem of trust to testimony. The aim of the article is to describe the arguments of both approaches and to carry out their critique. Methodology and sources. The author uses the method of conceptual analysis to address (...) the task at hand. The primary sources of the paper include the works of the classics of the theory of knowledge – D. Hume and T. Reid. The secondary sources include works of modern authors, belonging to the Anglo-American philosophical tradition. Results and discussion. Reductionism argues that although testimonial beliefs can be accepted on the basis of the reliability of the informant, the testimony itself does not provide justification. Ultimately, reductionism reduces testimony to another source of justification, such as perception or memory. The article explains that reductionism's weakness is to account for normal social interactions when the reliability of the speaker is unknown. Non-reductionism argues that testimony does not provide justification by reduction to other sources. Testimony itself is a valid form of social proof. The informant does not need additional positive reasons to accept the speaker's claims as valid. Testimony is justified by default unless it is proven false or unreliable. However, the weakness of non-reductionism is the relativistic implication in cases of cognitive asymmetry between the informant and the informant. Conclusion. The article concludes that reductionism and non-reductionism are equally unsatisfactory theories. The author believes that the formation of communicative knowledge does not depend on trust in the informant's testimony. It is proposed to consider the issue of trust in the informant himself as an epistemic agent. It is suggested that such an analysis should start from an virtue epistemology. (shrink)

Hastings Center Report, Volume 52, Issue 2, Page 58-59, March‐April 2022.

In science, there have been no attempts to study institutional trust as an intermediary between the emigration attitude and meta-values, which actualizes this problem. The purpose of the study: to determine the role of institutional trust in the connection of metavalues with the emigration attitude. Research hypothesis: institutional trust mediates the connection of meta-values Conservation, Openness to change, Self-enhancement Self-transcendence with the emigration attitude. The study was carried out on a sample aged 17 to 35 years, including 78% women, using: (...) PVQ-21 – ESS7 version of the questionnaire measuring individual values of Sh. Schwartz, Methods “Scale of migration attitudes” by S. A. Kuznetsova, I. Y. Kuznetsov, A. V. Feshchenko, modifi ed into “Scale of emigration attitudes”; questionnaire “Level of institutional trust” and mediation analysis, through the use of the macro PROCESS to the IBM SPSS 26.0 program. It is established that institutional trust mediates the connection of the emigration attitude with the meta-values of Conservation, Openness to change and Self-enhancement, at the same time it is not a mediator in connection with the emigration attitude with the metavalue of Self-transcendence. The results of the study demonstrate the role of institutional trust in the emergence of an emigration attitude among young people, which allows them to be used to predict the emigration activity of young people, in psychological work with potential emigrants, as well as in the development of state youth policy programs. (shrink)

Business success depends on the ability to build trust. Trusted brands succeed and sustain. Trusted leaders inspire followers, grow companies, revenues, and futures. But sadly, deceit has infected business and become widespread. Far too many leaders now use their own 'alternative facts', to mislead and mis-inform their customers, colleagues, and communities. The skilfulness and ease with which some leaders now lie has become a Lie-Ability. And when customers stop trusting the products, services, or the stories a leader tells, then the (...) business suffers. If business leaders don't lead a truth renaissance, we are all lost. People no longer trust politicians or the media. And many of the institutions and professions we used to turn to have also lost trust. The only people that can really save us now are business leaders. We need to become truth advocates and activists. We must re-establish a new norm where we tell the truth to ourselves, to our employees, to our shareholders, to our customers and to society at large. This book explores the 7 Deadly Lies that business tells itself, the 7 Dark Arts of Deception that are still used with monotonous regularity to manipulate the narrative. We offer C-suite leaders and senior managers a clear path out of deceit. We offer a solution to the Lie-Ability of some leaders by developing a deeper understanding of truth, how to reclaim it and how to build back trust. (shrink)

In this paper we study intermediate logics between the logic G≤∼, the degree preserving companion of Gödel fuzzy logic with involution G∼ and classical propositional logic CPL, as well as the intermediate logics of their finite-valued counterparts G≤n∼. Although G≤∼ and G≤ are explosive w.r.t. Gödel negation ¬, they are paraconsistent w.r.t. the involutive negation ∼. We introduce the notion of saturated paraconsistency, a weaker notion than ideal paraconsistency, and we fully characterize the ideal and the saturated paraconsistent logics between (...) G≤n∼ and CPL. We also identify a large family of saturated paraconsistent logics in the family of intermediate logics for degree-preserving finite-valued Łukasiewicz logics. (shrink)

An AC servomotor which is mostly a two-phase induction motor with two stator field coils placed 90 electrical degrees apart used for controlling position, speed and acceleration in manufacturing industries. In this paper, a two-phase induction motor has been designed with a fuzzy logic and observer based controllers to improve the performance of the system. Comparison of the AC servomotor with the proposed controllers for tracking a step and a square desired position signal input has been done using Matlab/Simulink toolbox (...) and a promising result obtained. (shrink)

Some find it plausible that a sufficiently long duration of torture is worse than any duration of mild headaches. Similarly, it has been claimed that a million humans living great lives is better than any number of worm-like creatures feeling a few seconds of pleasure each. Some have related bad things to good things along the same lines. For example, one may hold that a future in which a sufficient number of beings experience a lifetime of torture is bad, regardless (...) of what else that future contains, while minor bad things, such as slight unpleasantness, can always be counterbalanced by enough good things. Among the most common objections to such ideas are sequence arguments. But sequence arguments are usually formulated in classical logic. One might therefore wonder if they work if we instead adopt many-valued logic. I show that, in a common many-valued logical framework, the answer depends on which versions of transitivity are used as premises. We get valid sequence arguments if we grant any of several strong forms of transitivity of 'is at least as bad as' and a notion of completeness. Other, weaker forms of transitivity lead to invalid sequence arguments. The plausibility of the premises is largely set aside here, but I tentatively note that almost all of the forms of transitivity that lead to valid sequence arguments seem intuitively problematic. Still, a few moderately strong forms of transitivity that might be acceptable lead to valid sequence arguments, although weaker statements of the initial value claims avoid these arguments at least to some extent. (shrink)

Communication presumes trust, but trust presumes risk. The main characteristic of trust is that it offers social stability, gives strength for mutual expectations and makes possible the construction of a common world. These traits make possible to present the temporal, spatial and identical aspects of trust. The confrontation of ‘traditional’ and online trust shows that there is not an essential difference between them but a relational one, the essence of trust appears on his relational mode. The relational approach makes evident (...) that only the risky choice gives content for trust, in the sense that it is capable to open new, creative possibilities for communication. (shrink)

In this article, we first give a normative account of the doctor–patient relationship as: oriented to the good of the patient’s health; motivated by a vocational commitment; and characterized by solidarity and trust. We then look at the difference that Christianity can, and we believe, should, make to that relationship, so understood. In doing so, we consolidate and expand upon some claims we have made in a forthcoming book, Ethics and the Healing Profession.1.

BackgroundThe rise of Big Data-driven health research challenges the assumed contribution of medical research to the public good, raising questions about whether the status of such research as a common good should be taken for granted, and how public trust can be preserved. Scandals arising out of sharing data during medical research have pointed out that going beyond the requirements of law may be necessary for sustaining trust in data-intensive health research. We propose building upon the use of a social (...) licence for achieving such ethical governance.Main textWe performed a narrative review of the social licence as presented in the biomedical literature. We used a systematic search and selection process, followed by a critical conceptual analysis. The systematic search resulted in nine publications. Our conceptual analysis aims to clarify how societal permission can be granted to health research projects which rely upon the reuse and/or linkage of health data. These activities may be morally demanding. For these types of activities, a moral legitimation, beyond the limits of law, may need to be sought in order to preserve trust. Our analysis indicates that a social licence encourages us to recognise a broad range of stakeholder interests and perspectives in data-intensive health research. This is especially true for patients contributing data. Incorporating such a practice paves the way towards an ethical governance, based upon trust. Public engagement that involves patients from the start is called for to strengthen this social licence.ConclusionsThere are several merits to using the concept of social licence as a guideline for ethical governance. Firstly, it fits the novel scale of data-related risks; secondly, it focuses attention on trustworthiness; and finally, it offers co-creation as a way forward. Greater trust can be achieved in the governance of data-intensive health research by highlighting strategic dialogue with both patients contributing the data, and the public in general. This should ultimately contribute to a more ethical practice of governance. (shrink)

2nd edition. Many-valued logics are those logics that have more than the two classical truth values, to wit, true and false; in fact, they can have from three to infinitely many truth values. This property, together with truth-functionality, provides a powerful formalism to reason in settings where classical logic—as well as other non-classical logics—is of no avail. Indeed, originally motivated by philosophical concerns, these logics soon proved relevant for a plethora of applications ranging from switching theory to cognitive modeling, and (...) they are today in more demand than ever, due to the realization that inconsistency and vagueness in knowledge bases and information processes are not only inevitable and acceptable, but also perhaps welcome. The main modern applications of (any) logic are to be found in the digital computer, and we thus require the practical knowledge how to computerize—which also means automate—decisions (i.e. reasoning) in many-valued logics. This, in turn, necessitates a mathematical foundation for these logics. This book provides both these mathematical foundation and practical knowledge in a rigorous, yet accessible, text, while at the same time situating these logics in the context of the satisfiability problem (SAT) and automated deduction. The main text is complemented with a large selection of exercises, a plus for the reader wishing to not only learn about, but also do something with, many-valued logics. (shrink)

A wide family of many-valued logics—for instance, those based on the weak Kleene algebra—includes a non-classical truth-value that is ‘contaminating’ in the sense that whenever the value is assigned to a formula φ⁠, any complex formula in which φ appears is assigned that value as well. In such systems, the contaminating value enjoys a wide range of interpretations, suggesting scenarios in which more than one of these interpretations are called for. This calls for an evaluation of systems with multiple contaminating (...) values. In this paper, we consider the countably infinite family of multiple-conclusion consequence relations in which classical logic is enriched with one or more contaminating values whose behavior is determined by a linear ordering between them. We consider some motivations and applications for such systems and provide general characterizations for all consequence relations in this family. Finally, we provide sequent calculi for a pair of four-valued logics including two linearly ordered contaminating values before defining two-sided sequent calculi corresponding to each of the infinite family of many-valued logics studied in this paper. (shrink)

A common objection to theories of vagueness based on fuzzy logics centres on the idea that assigning a single numerical degree of truth -- a real number between 0 and 1 -- to each vague statement is excessively precise. A common objection to Bayesian epistemology centres on the idea that assigning a single numerical degree of belief -- a real number between 0 and 1 -- to each proposition is excessively precise. In this paper I explore possible parallels between these (...) objections. In particular I argue that the only good objection along these lines to fuzzy theories of vagueness does not translate into a good objection to Bayesian epistemology. An important part of my argument consists in drawing a distinction between two different notions of degree of belief, which I call dispositional degree of belief and epistemic degree of belief. (shrink)

This article argues that resolutions to the sorites paradox offered by epistemic and supervaluation theories fail to adequately account for vagueness. After explaining the paradox, I examine the epistemic theory defended by Timothy Williamson and discuss objections to his semantic argument for vague terms having precise boundaries. I then consider Rosanna Keefe's supervaluationist approach and explain why it fails to accommodate the problem of higher-order vagueness. I conclude by discussing how fuzzy logic may hold the key to resolving the sorites (...) paradox without positing indefensible borders to the correct application of vague terms. (shrink)

In this paper I propose a reconstruction of the onto-cosmological perspective of Plato’s Timaeus and suggest an interpretation of it in the light of some contemporary approaches to ontology and logic, i.e. “ontological sequentialism” and “fuzzy logic”, attempting to use the categories and language of present-day ontology and logic to examine from a different point of view some aspects of the Timaeus onto-cosmology and of its logical scaffolding.

The thesis that the two-valued system of classical logic is insufficient to explanation the various intermediate situations in the entity, has led to the development of many-valued and fuzzy logic systems. These systems suggest that this limitation is incorrect. They oppose the law of excluded middle (tertium non datur) which is one of the basic principles of classical logic, and even principle of non-contradiction and argue that is not an obstacle for things both to exist and to not exist at (...) the same time. However, contrary to these claims, there is no inadequacy in the two-valued system of classical logic in explanation the intermediate situations in existence. The law of exclusion and the intermediate situations in the external world are separate things. The law of excluded middle has been inevitably accepted by other logic systems which are considered to reject this principle. The many-valued and the fuzzy logic systems do not transcend the classical logic. Misconceptions from incomplete information and incomplete research are effective in these criticisms. In addition, it is also effective to move the discussion about the intellectual conception (tasawwur) into the field of judgmental assent (tasdiq) and confusion of the mawhum (imaginable) with the ma‘kûl (intellegible). (shrink)

The Boolean many-valued approach to vagueness is similar to the infinite-valued approach embraced by fuzzy logic in the respect in which both approaches seek to solve the problems of vagueness by assigning to the relevant sentences many values between falsity and truth, but while the fuzzy-logic approach postulates linearly-ordered values between 0 and 1, the Boolean approach assigns to sentences values in a many-element complete Boolean algebra. On the modal-precisificational approach represented by Kit Fine, if a sentence is indeterminate in (...) truth value in some world, it is taken to be true in one precisified world accessible from that world and false in another. This paper points to a way to unify these two approaches to vagueness by showing that Fine’s version of the modal-precisificational approach can be combined with the Boolean many-valued approach instead of supervaluationism, one of the most popular approaches to vagueness. (shrink)

In this position paper we present a logical framework for modelling reasoning with graded predicates. We distinguish several types of graded predicates and discuss their ubiquity in rational interaction and the logical challenges they pose. We present mathematical fuzzy logic as a set of logical tools that can be used to model reasoning with graded predicates, and discuss a philosophical account of vagueness that makes use of these tools. This approach is then generalized to other kinds of graded predicates. Finally, (...) we propose a general research program towards a logic-based account of reasoning with graded predicates. (shrink)

We sketch the development of fuzzy sets and fuzzy logic in Austria during the last 50 years which started, after some early traces, in 1976 in Linz with my own work and in Vienna with Klaus-Peter Adlassnig’s work. Therefore we first discuss the history of our research group at the Johannes Kepler University Linz and at the JKU-Softwarepark Hagenberg. Next we have a closer look at the developments at the Vienna University Medical School, at the logic group at the Vienna (...) University of Technology, and at the work of Reinhard Viertl in statis- tics. Finally we present some achievements made at the University of Innsbruck. (shrink)

In this paper, we will briefly look at the history of mathematical fuzzy logic in Czechoslovakia starting from the 1970s and extending until 2009. The role of P. Ha ́jek in the development of fuzzy logic is especially emphasized.

From Fine and Kamp in the 70’s—through Osherson and Smith in the 80’s, Williamson, Kamp and Partee in the 90’s and Keefe in the 00’s—up to Sauerland in the present decade, the objection continues to be run that fuzzy logic based theories of vagueness are incompatible with ordinary usage of compound propositions in the presence of borderline cases. These arguments against fuzzy theories have been rebutted several times but evidently not put to rest. I attempt to do so in this (...) paper. (shrink)

Historically, there have been some problems that initially were philosophically posed, either in mystical or in metaphysical terms but that, latter on and step-by-step, were translated into scientific terms and through a process of successive clarifications allowing to arrive, finally, at a scientific theory in which its more essential treats are clearly defined and facilitates its measuring.

Justification logics provide a framework for reasoning about justifications and evidence. In this article, we study a fuzzy variant of justification logics in which an agent’s justification for a belief has certainty degree between 0 and 1. We replace the classical base of justification logics with Hájek’s rational Pavelka logic. We introduce fuzzy possible world semantics with crisp accessibility relation and also single world models for our logics. We establish soundness and graded-style completeness for both kinds of semantics. We also (...) introduce extensions with product conjunction. Finally, we offer a solution to a variant of the sorites paradox in our fuzzy justification logics. (shrink)

The aim of the paper is to provide an overview of the existing studies concerning the phenomenon of public trust in government. Low trust in government has been frequently defined as a key problem influencing the policy process in many countries. The economic crises reinforced the importance of trust and triggered public debates on the necessary reforms of the public sector. The paper examines the key theories and research conducted by social scientists with a particular emphasis on the role of (...) trust in risk societies. The review of the existing literature concentrates on the drivers of trust, showing the importance of two interlinked logics: the logic of consequences and the logic of appropriateness. The first one explains trust as a result of outputs and outcomes of government policies and services. The logic of appropriateness claims that trust is built on values and identity and depends on the adoption by governments the rules of integrity, openness, responsiveness and transparency. Trust in government is also deeply rooted in a broader system of rules, norms and values known as the trust culture. The last part of the paper is an attempt to trace an impact of an economic crisis on public trust. Studies of public opinion do not fully confirm the opinions on low trust and a decline in trust in government and trust in public administration in times of crisis. Some studies reveal considerable fluctuations of public trust in selected countries. In other countries, the public evaluation of government and public administration is high and there are only slight modifications in citizens' perception of the government. (shrink)

The combination of Fuzzy Logics and Description Logics has been investigated for at least two decades because such fuzzy DLs can be used to formalize imprecise concepts. In particular, tableau algorithms for crisp Description Logics have been extended to reason also with their fuzzy counterparts. It has turned out, however, that in the presence of general concept inclusion axioms this extension is less straightforward than thought. In fact, a number of tableau algorithms claimed to deal correctly with fuzzy DLs with (...) GCIs have recently been shown to be incorrect. In this paper, we concentrate on fuzzy \, the fuzzy extension of the well-known DL \. We present a terminating, sound, and complete tableau algorithm for fuzzy \ with arbitrary continuous t-norms. Unfortunately, in the presence of GCIs, this algorithm does not yield a decision procedure for consistency of fuzzy \ ontologies since it uses as a sub-procedure a solvability test for a finitely represented, but possibly infinite, system of inequations over the real interval [0,1], which are built using the t-norm. In general, it is not clear whether this solvability problem is decidable for such infinite systems of inequations. This may depend on the specific t-norm used. In fact, we also show in this paper that consistency of fuzzy \ ontologies with GCIs is undecidable for the product t-norm. This implies, of course, that for the infinite systems of inequations produced by the tableau algorithm for fuzzy \ with product t-norm, solvability is in general undecidable. We also give a brief overview of recently obtained decidability results for fuzzy \ w.r.t. other t-norms. (shrink)