This article investigates the proof theory of the Quantified Argument Calculus as developed and systematically studied by Hanoch Ben-Yami [3, 4]. Ben-Yami makes use of natural deduction, we, however, have chosen a sequent calculus presentation, which allows for the proofs of a multitude of significant meta-theoretic results with minor modifications to the Gentzen’s original framework, i.e., LK. As will be made clear in course of the article LK-Quarc will enjoy cut elimination and its corollaries.

Free logics is a family of first-order logics which came about as a result of examining the existence assumptions of classical logic. What those assumptions are varies, but the central ones are that the domain of interpretation is not empty, every name denotes exactly one object in the domain and the quantifiers have existential import. Free logics usually reject the claim that names need to denote in, and of the systems considered in this paper, the positive free logic concedes that (...) some atomic formulas containing non-denoting names are true, while negative free logic rejects even the latter claim. Inclusive logics, which reject, are likewise considered. These logics have complex and varied axiomatizations and semantics, and the goal of this paper is to present an orderly examination of the various systems and their mutual relations. This is done by first offering a formalization, using sequent calculi which possess all the desired structural properties of a good proof system, including admissibility of contraction and cut, while streamlining free logics in a way no other approach has. We then present a simple and unified system of abstract semantics, which allows for a straightforward demonstration of the meta-theoretical properties, and offers insights into the relationship between different logics. The final part of this paper is dedicated to extending the system with modalities by using a labeled sequent calculus, and here we are again able to map out the different approaches and their mutual relations using the same framework. (shrink)

This is a study of all the recent literature on william james written from a phenomenological perspective with the purpose of showing that william james made fundamental contributions to the phenomenological theory of the intentionality of consciousness, To the phenomenological theory of self-Identity, And to the phenomenological conception of noetic freedom as the basic concept of ethical theory.

The Quantified argument calculus (Quarc) has received a lot of attention recently as an interesting system of quantified logic which eschews the use of variables and unrestricted quantification, but nonetheless achieves results similar to the Predicate calculus (PC) by employing quantifiers applied directly to predicates instead. Despite this noted similarity, the issue of the relationship between Quarc and PC has so far not been definitively resolved. We address this question in the present paper, and then expand upon that result. Utilizing (...) recent developments in structural proof theory, we develop a G3-style sequent calculus for Quarc and briefly demonstrate its structural properties. We put these properties to use immediately to construct direct proofs of the meta-theoretical properties of the system. We then incorporate an abstract (and, as we shall see, logical) predicate into the system in a way that preserves all the structural properties. This allows us to identify a system of Quarc which is deductively equivalent to PC, and also yields a constructive method of demonstrating the Craig interpolation theorem (which speaks in favor of the aforementioned predicate being logical). We further generalize this extension to develop a bivalent system of Quarc with defining clauses that still maintains all the desirable properties of a good proof system. (shrink)

This note is a generalization and improved interpretation of the main result of Karni and Schmeidler. A decision-maker is supposed to possess a preference relation on acts and another preference relation on state-prize lotteries, both of which are assumed to satisfy the von Neumann–Morgenstern axioms. In addition, the two preference relations restricted to a state of nature are assumed to agree. We show that these axioms are necessary and sufficient for the existence of subjective expected utility over acts with state-dependent (...) utility functions and a subjective probability measure. This subjective probability measure is unique when conditioned on the set of states of nature in which not all the prizes are equally desirable. (shrink)

Provides an overview of the complex history of the secular tradition of science and its interactions with religions and spiritual traditions.

The relative rate of success of parliamentary vs. governmental legislative initiative is quite different. The examination of one, resp. two full legislative term, for amendments, resp. bills introduced, shows thatparliamentary legislative initiative by far exceeds «regular» governmental initiative : in a ratio of 3 to 1 for bills, and of 4 to 1 for amendments. But the results are almost inverse : governmental initiative accounts for 76 % of the bills, and for 67 % of the amendments eventually voted. The (...) government succeeds in «pushing through» more than 90 % of its own initiatives, whereas parliamentary initiative hardly obtains an overall 10 % realization score. In an interrogative manner, the conclusion pointsto a few elements that may account for this situation. (shrink)

Free logics are a family of first-order logics which came about as a result of examining the existence assumptions of classical logic (Hintikka _The Journal of Philosophy_, _56_, 125–137 1959 ; Lambert _Notre Dame Journal of Formal Logic_, _8_, 133–144 1967, 1997, 2001 ). What those assumptions are varies, but the central ones are that (i) the domain of interpretation is not empty, (ii) every name denotes exactly one object in the domain and (iii) the quantifiers have existential import. Free (...) logics reject the claim that names need to denote in (ii). _Positive_ free logic concedes that some atomic formulas containing non-denoting names (including self-identity) are true, _negative_ free logic treats them as uniformly false, and _neutral_ free logic as taking a third value. There has been a renewed interest in analyzing proof theory of free logic in recent years, based on intuitionistic logic in Maffezioli and Orlandelli (_Bulletin of the Section of Logic_, _48_(2), 137–158 2019 ) as well as classical logic in Pavlović and Gratzl (_Journal of Philosophical Logic_, _50_, 117–148 2021 ), there for the positive and negative variants. While the latter streamlines the presentation of free logics and offers a more unified approach to the variants under consideration, it does not cover neutral free logic, since there is some lack of both clear formal intuitions on the semantic status of formulas with empty names, as well as a satisfying account of the conditional in this context. We discuss extending the results to this third major variant of free logics. We present a series of G3 sequent calculi adapted from Fjellstad (_Studia Logica_, _105_(1), 93–119 2017, _Journal of Applied Non-Classical Logics_, _30_(3), 272–289 2020 ), which possess all the desired structural properties of a good proof system, including admissibility of contraction and all versions of the cut rule. At the same time, we maintain the unified approach to free logics and moreover argue that greater clarity of intuitions is achieved once neutral free logic is conceptualized as consisting of two sub-varieties. (shrink)

In the presence of incomplete risk attitudes, choices between noncomparable risky prospects are random. A random choice model advanced by Karni, 2021) includes the hypothesis that choices among noncomparable risky prospects are prompted by signals drawn from personal distributions. This paper introduces a scheme designed to elicit subjects’ assessments of their personal likelihoods of choices among noncomparable risky prospects and describes experiments designed to test the aforementioned hypothesis.

This chapter contains sections titled: Scientific Reasons Motivated by Morality? The Science of Religion Notes.

This paper extends the investigations into logical properties of the quantified argument calculus (Quarc) by suggesting a series of proper subsystems which, although retaining the entire vocabulary of Quarc, restrict quantification in such a way as to make the result decidable. The proof of decidability is via a procedure that prunes the infinite branches of a derivation tree in what is a syntactic counterpart of semantic filtration. We demonstrate an application of one of these systems by showing that Aristotle’s assertoric (...) syllogistic is embeddable within, thus also providing another method of showing its decidability. (shrink)

Background: Microbiome biomarker discovery for patient diagnosis, prognosis, and risk evaluation is attracting broad interest. Selected groups of microbial features provide signatures that characterize host disease states such as cancer or cardio-metabolic diseases. Yet, the current predictive models stemming from machine learning still behave as black boxes and seldom generalize well. Their interpretation is challenging for physicians and biologists, which makes them difficult to trust and use routinely in the physician-patient decision-making process. Novel methods that provide interpretability and biological insight (...) are needed. Here, we introduce "predomics", an original machine learning approach inspired by microbial ecosystem interactions that is tailored for metagenomics data. It discovers accurate predictive signatures and provides unprecedented interpretability. The decision provided by the predictive model is based on a simple, yet powerful score computed by adding, subtracting, or dividing cumulative abundance of microbiome measurements. -/- Results: Tested on >100 datasets, we demonstrate that predomics models are simple and highly interpretable. Even with such simplicity, they are at least as accurate as state-of-the-art methods. The family of best models, discovered during the learning process, offers the ability to distil biological information and to decipher the predictability signatures of the studied condition. In a proof-of-concept experiment, we successfully predicted body corpulence and metabolic improvement after bariatric surgery using pre-surgery microbiome data. -/- Conclusions: Predomics is a new algorithm that helps in providing reliable and trustworthy diagnostic decisions in the microbiome field. Predomics is in accord with societal and legal requirements that plead for an explainable artificial intelligence approach in the medical field. (shrink)

This paper introduces a logic game which can be used to demonstrate the working of Boolean connectives. The simplicity of the system turns out to lead to some interesting meta-theoretical properties, which themselves carry a philosophical import. After introducing the system, we demonstrate an interesting feature of it—that it, while being an accurate model of propositional logic Booleans, does not contain any tautologies nor contradictions. This result allows us to make explicit a limitation of application of propositional logic to those (...) sentences with relatively stable truth values. (shrink)

Background: Food biofortification practices in agricultural sectors involve the process of employing biotechnology to enhance the nutritional content of crops during their growth process. Biofortification makes foods even more nutritious and highly functional for addressing malnutrition among children. These practices in farming industries need guidance and legal support from various national policies to support high-quality supplies of school meals fully. Aim: This study aims to analyze the association between various national policies and the implementation of food biofortification practices in agricultural (...) sectors among countries implementing school meal programs. Methods: The Bayesian Mindsponge Framework, combining the reasoning strengths of Mindsponge Theory and inference advantages of Bayesian analysis, was employed on a dataset of 126 government representatives who manage large-scale school meal programs in 126 different countries. Results: Findings showed that food safety policy was positively associated with food biofortification practices in agricultural sectors among countries implementing school meal programs. In contrast, nutrition policy had a significant negative association with these practices. Additionally, policies of school feeding, health, agriculture, and the private sector had unclear associations with food biofortification. Conclusions: Findings underscore the strong position of food safety policy in guiding food biofortification practices in agricultural sectors among countries implementing school meal programs. There is a need to re-assess the implemented nutrition policy due to its significant negative association with these practices. Enhancing and strengthening the policies of school feeding, health, agriculture, and the private sector may increase their potencies in giving positive impacts on food biofortification practices in agricultural sectors to ensure high-quality school meal supplies. (shrink)

While concern about public irrationality and antiscientific movements is not new, the increasing power of right-wing populist movements that promote distrust of expertise and of scientific institutions gives such concerns a new context. Experience with classic pseudosciences such as creationism, and the long-running efforts by defenders of science to oppose such pseudosciences, may also help us understand today’s post-truth populism. The politics of creationism and science education in the United States and in Turkey does not, however, suggest easy answers. Moreover, (...) there are important features of politics in liberal democracies that drive a populist backlash, which makes it counterproductive for defenders of science to call for deference to all forms of expertise claimed by professionals. There is a danger that the rhetoric of reason that is used to defend science will become part of a more general apologetics for an unsustainable status quo. (shrink)

Atheists, conservative theists, and religious liberals often read the history of science in ways that support their own position. Atheists expect continual mutual support between science and nonbelief, conservatives emphasize theistic metaphysical foundations for science; and liberals find a historical development toward separate spheres for science and religion. The rise of science was more complicated than anticipated by any of these stories. Atheism and science have usually developed almost independently, with weak connections. Today, the naturalism of modern scientific descriptions of (...) the world is consonant with an atheistic position. But even now, significant tensions between science and atheism remain. (shrink)