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)

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.

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)

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)

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)

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.

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.

I examine mystical experience through the history of European religious thought, its modern state, and different spiritual practices of the Patristic epoch. The survey gives some definitions: mystical experience is situated in the field of spirituality along with practices of its acquisition -- ascetics; and the fruits of it -- theology and doctrine. The second part of the article is devoted to a wide field of Christian texts as a representative example of the same experience of the crystallization of mystical (...) experience in ancient tradition, providing a few general types. Reading of religious texts is related very closely with the spiritual condition of the reader and supposes that he/she changes radically in the process of reading, being involved in some existential-hermeneutic circle. (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.

According to Michael Tomasello’s evolutionary anthropological approach, joint attention is one of the essential keys to understanding the difference between human and animal. The present paper discusses a recent phenomenological account of the anthropological difference inspired by Tomasello’s conception. A criticism of this account is put forward, while an alternative view is also introduced that stresses the impact of differential rearing experiences on the socio-cognitive development of human and non-human animals.

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.

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.

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)

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)

Social networks can influence people’s behaviour and therefore it is assumed that central individuals in social networks, also called “opinion leaders”, play a key role in driving change in agricultural and food systems. I analyse the outcomes of an intervention (that encouraged Sulawesi smallholder farmers to take a specific action toward improving the health of their cocoa trees) to assess the impact of engaging opinion leaders in agricultural programs that aim to change farmers’ practices. The intervention has been implemented through (...) (a) 18 opinion leaders identified by interviews and a social network survey of 1885 cocoa farmers; and (b) 18 randomly selected farmers who were not central in local social networks. The obtained social networks and statistical data were quantitatively analysed and the results were interpreted with input from the field staff. Contrary to expectations, the highly socially central opinion leaders were not more effective in promoting the initiative in their communities. On average, randomly selected low-centrality farmers convinced almost twice as many of their peers to take the recommended action as compared to the identified opinion leaders (17.1 versus 8.6) but the variation within the random group was also significantly higher. Importantly, while the identified opinion leaders were mostly senior men, women performed better in influencing others into taking action even when their centrality in local social networks of agricultural advice was lower. I discuss the implications of the conventional selection of perceived opinion leaders as model farmers for achieving sustainable and equitable change at scale in agriculture and propose practical alternatives. (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)

Axiomatic set theory with full comprehension is known to be consistent in Łukasiewicz fuzzy predicate logic. But we cannot assume the existence of natural numbers satisfying a simple schema of induction; this extension is shown to be inconsistent.

We ask how to use machine learning to expand observability, which presently depends on human learning that informs conceivability. The issue is engaged by considering the question of correspondence between conceived observability counterfactuals and observable, yet so far unobserved or unconceived, states of affairs. A possible answer lies in importing out of reference frame content which could provide means for conceiving further observability counterfactuals. They allow us to define high-fidelity observability, increasing the level of correspondence in question. To achieve high-fidelity (...) observability, we propose to use generative machine learning models as the providers of the out of reference frame content. From an applied point of view, such a role of generative machine learning models shows an emerging dimension of human-machine cooperation. (shrink)

The environmental costs and energy constraints have become emerging issues for the future development of Machine Learning (ML) and Artificial Intelligence (AI). So far, the discussion on environmental impacts of ML/AI lacks a perspective reaching beyond quantitative measurements of the energy-related research costs. Building on the foundations laid down by Schwartz et al., 2019 in the GreenAI initiative, our argument considers two interlinked phenomena, the gratuitous generalisation capability and the future where ML/AI performs the majority of quantifiable inductive inferences. The (...) gratuitous generalisation capability refers to a discrepancy between the cognitive demands of a task to be accomplished and the performance (accuracy) of a used ML/AI model. If the latter exceeds the former because the model was optimised to achieve the best possible accuracy, it becomes inefficient and its operation harmful to the environment. The future dominated by the non-anthropic induction describes a use of ML/AI so all-pervasive that most of the inductive inferences become furnished by ML/AI generalisations. The paper argues that the present debate deserves an expansion connecting the environmental costs of research and ineffective ML/AI uses (the issue of gratuitous generalisation capability) with the (near) future marked by the all-pervasive Human-Artificial Intelligence Nexus. (shrink)

Language is an instrument of formulating and communicating ideas. Since not every idea can be (precisely) formulated in language and not all linguistic formulations represent some idea, the user of language is in danger of using linguistic nonsense. An explication of the concept of linguistic nonsense is given by the means of transparent intensional logic of Pavel Tichý.

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)

Studies man in view of what he may become. Describes how a man must work simultaneously on his knowledge and his being to find inner unity.

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)

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.

Two variants of monadic fuzzy predicate logic are analyzed and compared with the full fuzzy predicate logic with respect to finite model property (properties) and arithmetical complexity of sets of tautologies, satisfiable formulas and of analogous notion restricted to finite models.

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.

As our epistemic ambitions grow, the common and scientific endeavours are becoming increasingly dependent on Machine Learning (ML). The field rests on a single experimental paradigm, which consists of splitting the available data into a training and testing set and using the latter to measure how well the trained ML model generalises to unseen samples. If the model reaches acceptable accuracy, an a posteriori contract comes into effect between humans and the model, supposedly allowing its deployment to target environments. Yet (...) the latter part of the contract depends on human inductive predictions or generalisations, which infer a uniformity between the trained ML model and the targets. The paper asks how we justify the contract between human and machine learning. It is argued that the justification becomes a pressing issue when we use ML to reach ‘elsewheres’ in space and time or deploy ML models in non-benign environments. The paper argues that the only viable version of the contract can be based on optimality (instead of on reliability which cannot be justified without circularity) and aligns this position with Schurz’s optimality justification. It is shown that when dealing with inaccessible/unstable ground-truths (‘elsewheres’ and non-benign targets), the optimality justification undergoes a slight change, which should reflect critically on our epistemic ambitions. Therefore, the study of ML robustness should involve not only heuristics that lead to acceptable accuracies on testing sets. The justification of human inductive predictions or generalisations about the uniformity between ML models and targets should be included as well. Without it, the assumptions about inductive risk minimisation in ML are not addressed in full. (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)