At present, large teams are at work in virtually all branches of Soviet historical scholarship writing major works of synthesis that present the results of long years of research into the history of literature, economic and political thought, ethics, esthetics, philosophy, and sociology. These works deal with currents that have played any significant role whatever in the history of Russian thought. The greatest attention is given to the Decembrists, the Revolutionary Democrats, the Narodniks, and the Russian Marxists. These trends in (...) the intellectual and socio-political movements have been studied in greater or lesser detail, with the exception perhaps of the Narodnik movement, to which, however, the attention of many historians is now being directed. (shrink)

Consider a set of shuffled observations drawn from a fixed probability distribution over some instance domain. What enables learning of inductive generalizations which proceed from such a set of observations? The scenario is worthwhile because it epistemically characterizes most of machine learning. This kind of learning from observations is also inverse and ill-posed. What reduces the non-uniqueness of its result and, thus, its problematic epistemic justification, which stems from a one-to-many relation between the observations and many learnable generalizations? The paper (...) argues that this role belongs to any complexity regularization which satisfies Norton’s Material Theory of Induction (MTI) by localizing the inductive risk to facts in the given domain. A prime example of the localization is the Lottery Ticket Hypothesis (LTH) about overparameterized neural networks. The explanation of MTI’s role in complexity regularization of neural networks is provided by analyzing the stability of Empirical Risk Minimization (ERM), an inductive rule that controls the learning process and leads to an inductive generalization on the given set of observations. In cases where ERM might become asymptotically unstable, making the justification of the generalization by uniform convergence unavailable, LTH and MTI can be used to define a local stability. A priori, overparameterized neural networks are such cases and the combination of LTH and MTI can block ERM’s trivialization caused by equalizing the strengths of its inductive support for risk minimization. We bring closer the investigation of generalization in artificial neural networks and the study of inductive inference and show the division of labor between MTI and the optimality justifications (developed by Gerhard Schurz) in machine learning. (shrink)

Could the employment of large language models (LLMs) in place of human advisors improve the problem-solving ability of democratic assemblies? LLMs represent the most significant recent incarnation of artificial intelligence and could change the future of democratic governance. This paper assesses their potential to serve as expert advisors to democratic representatives. While LLMs promise enhanced expertise availability and accessibility, they also present specific challenges. These include hallucinations, misalignment and value imposition. After weighing LLMs’ benefits and drawbacks against human advisors, I (...) argue that time-tested democratic procedures, such as deliberation and aggregation by voting, provide safeguards that are effective against human and machine advisor shortcomings alike. Additional protective measures may include custom training for advisor LLMs or boosting representatives’ competencies in query formulation. Implementation of adversarial proceedings in which LLM advisors would debate each other and provide dissenting opinions is likely to yield further epistemic benefits. Overall, promising interventions that would mitigate the LLM risks appear feasible. Machine advisors could thus empower human decision-makers to make more autonomous, higher-quality decisions. On this basis, I defend the hypothesis that LLMs’ careful integration into policymaking could augment democracy’s ability to address today’s complex social problems. (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)

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)

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)

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.

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.

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)

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.

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)

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 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...

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.

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)

The pace of technological change continues to outstrip the evolution of democratic institutions, creating an urgent need for innovative approaches to democratic reform. However, the experimentation bottleneck - characterized by slow speed, high costs, limited scalability, and ethical risks - has long hindered progress in democracy research. This paper proposes a novel solution: employing generative artificial intelligence (GenAI) to create synthetic data through the simulation of digital homunculi, GenAI-powered entities designed to mimic human behavior in social contexts. By enabling rapid, (...) low-risk experimentation with alternative institutional designs, this approach could significantly accelerate democratic innovation. I examine the potential of GenAI-assisted research to mitigate current limitations in democratic experimentation, including the ability to simulate large-scale societal interactions and test complex institutional mechanisms. While acknowledging potential risks such as algorithmic bias, reproducibility challenges, and AI alignment issues, I argue that the benefits of synthetic data are likely to outweigh their drawbacks if implemented with proper caution. To address existing challenges, I propose a range of technical, methodological, and institutional adaptations. The paper concludes with a call for interdisciplinary collaboration in the development and implementation of GenAI-assisted methods in democracy research, highlighting their potential to bridge the gap between democratic theory and practice in an era of rapid technological change. (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)

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

What makes safety claims about general purpose AI systems such as large language models trustworthy? We show that rather than the capabilities of security tools such as alignment and red teaming procedures, it is security practices based on these tools that contributed to reconfiguring the image of AI safety and made the claims acceptable. After showing what causes the gap between the capabilities of security tools and the desired safety guarantees, we critically investigate how AI security practices attempt to fill (...) the gap and identify several shortcomings in diversity and participation. We found that these security practices are part of securitization processes aiming to support (commercial) development of general purpose AI systems whose trustworthiness can only be imperfectly tested instead of guaranteed. We conclude by offering several improvements to the current AI security practices. (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)

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.

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.

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)

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)

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.

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)