scholarly journals Algorithmic correspondence and canonicity for possibility semantics

2021 ◽  
Author(s):  
Zhiguang Zhao
Keyword(s):  
Modal Logic ◽  
Alternative Proof ◽  
Modal Language ◽  
Notable Feature ◽  
Working Paper ◽  
The One ◽  
Regular Open ◽  
Methodology Of Science ◽  
Present Setting ◽  
Nominal Variables

Abstract The present paper develops a unified correspondence treatment of the Sahlqvist theory for possibility semantics, extending the results in the work by Yamamoto (2016, Journal of Logic and Computation, 27, 2411–2430) from Sahlqvist formulas to the strictly larger class of inductive formulas and from the full possibility frames to filter-descriptive possibility frames. Specifically, we define the possibility semantics version of the algorithm Ackermann lemma based algorithm (ALBA) and an adapted interpretation of the expanded modal language used in the algorithm. One notable feature of the adaptation of ALBA to possibility frames setting is that the so-called nominal variables, which are interpreted as complete join-irreducibles in the standard setting, are interpreted as regular open closures of ‘singletons’ in the present setting, which is a novelty of the present paper. We prove the soundness of the algorithm with respect to both (the dual algebras of) full possibility frames and (the dual algebras of) filter-descriptive possibility frames, use the algorithm to give an alternative proof to the one in the work by Holliday (2016, Possibility frames and forcing for modal logic. UC Berkeley Working Paper in Logic and the Methodology of Science. URL. http://escholarship.org/uc/item/9v11r0dq) that the inductive formulas are constructively canonical and show that the algorithm succeeds on inductive formulas. We make some comparisons among different semantic settings in the design of the algorithms and fit possibility semantics into this broader picture.

scholarly journals Reduction of term in scientific theory

2020 ◽  
pp. 1-14 ◽  
Author(s):  
Dmitriy Pavlovich Surovyagin
Keyword(s):  
Scientific Theory ◽  
Functional Equivalence ◽  
Theoretical Terms ◽  
Multiple Approach ◽  
The Subject ◽  
The One ◽  
Definition Of ◽  
Reduction Relation ◽  
Methodology Of Science ◽  
Inverse Operation

The subject of this research is the concept of reduction in logics and methodology of science. On the one hand, reduction is understood as a relation between the term and its defining expression within the scientific theory; while on the other – it represents the relation between two theories. Since the extension of theory is possible through introduction to its vocabulary of new terms by means of nominal definitions, the reduction represents an inverse operation – removing the terms from the vocabulary of the theory. At the same time, the theory itself is defined in accordance with the theoretical-multiple approach as a class of sentences closed in relation to derivability. The scientific novelty consists in examination of semantic and epistemological aspects of the formal definition of reduction. Particularly, the explication of reduction relation between two theories leans in the concept of functional equivalence of the theories. It is established that the list of basic terms of the theory can be set only conventionally. All terms introduces by the means of nominal definitions turn out to be reducible. Therefore, a distinctive feature of theoretical terms is the possibility of its reduction.

scholarly journals CONVENTIONAL AND CONSENSUAL CONCEPTIONS OF SCIENTIFIC KNOWLEDGE NATURE

2020 ◽  
pp. 7-26
Author(s):  
Сергей Александрович Лебедев ◽  
Сергей Николаевич Коськов
Keyword(s):  
Scientific Knowledge ◽  
Scientific Community ◽  
A Priori ◽  
Scientific Work ◽  
Point Of View ◽  
Main Subject ◽  
Pure Experience ◽  
Classical Philosophy ◽  
The One ◽  
Methodology Of Science

В статье излагается содержание двух базовых концепций неклассической философии и методологии науки: конвенционалистской и консенсуалистской теории природы научного знания и научной истины. Каждая из них является альтернативой двум основным парадигмам классической философии и методологии науки: эмпиризму (позитивизму) и рационализму. С точки зрения конвенционализма научное знание не есть ни описание чистого опыта, ни его обобщение. Но оно не является также и результатом некой априорной интуиции и чистого разума. Согласно конвенционализму научное знание - это система доказательной информации, исходные принципы которой имеют характер условных, конвенциональных истин. Отсюда следует, что любая истина в науке не категорична, а условна и имеет форму «если, то». Консенсуалистская концепция природы научного знания возникла в философии науки второй половины XX в. Она была, с одной стороны, обобщением конвенционализма, а с другой - его отрицанием. Если в конвенционализме основным субъектом научного познания является отдельный ученый, то в консенсуалистской эпистемологии таким субъектом является социальный субъект - научное сообщество. Научное познание имеет принципиально коллективный характер как в плане его получения в силу разделения научного труда, так и в плане его легитимации и оценки. Последние операции всегда являются результатом консенсуса научного сообщества. The article examines the content of two basic conceptions of non-classical philosophy and methodology of science: the conventionalist and consensual theory of the nature of scientific knowledge. Each of them is an alternative to the two main paradigms of classical philosophy and the methodology of science: empiricism (positivism) and rationalism. From the point of view of conventionalism, scientific knowledge is neither a description of pure experience nor a generalization of it. But it is also not the result of some a priori intuition and pure reason. According to conventionalism, scientific knowledge is a system of evidence-based information, the initial principles of which have the character of conditional, conventional truths. It follows that any truth in science is not categorical, but conditional and has the form «if, then». The consensual concept of the nature of scientific knowledge emerged in the philosophy of science of the second half of the twentieth century. It was, on the one hand, a generalization of conventionalism; on the other, a negation of it. If in conventionalism the main subject of scientific knowledge is an individual scientist, then in consensual epistemology such a subject is a social subject - the scientific community. Scientific knowledge has a fundamentally collective character, both in terms of its acquisition by virtue of the division of scientific work, and in terms of its legitimization and evaluation. The latest operations are always the result of a consensus of the scientific community.

Finite Kripke models and predicate logics of provability

1990 ◽  
Vol 55 (3) ◽  
pp. 1090-1098 ◽  
Author(s):  
Sergei Artemov ◽  
Giorgie Dzhaparidze
Keyword(s):  
Modal Logic ◽  
Kripke Model ◽  
Finite Model ◽  
Kripke Models ◽  
Model Property ◽  
Logical Formula ◽  
Finite Model Property ◽  
Modal Predicate Logics ◽  
The One ◽  
Arithmetical Interpretation

AbstractThe paper proves a predicate version of Solovay's well-known theorem on provability interpretations of modal logic:If a closed modal predicate-logical formula R is not valid in some finite Kripke model, then there exists an arithmetical interpretation f such that PA ⊬ fR.This result implies the arithmetical completeness of arithmetically correct modal predicate logics with the finite model property (including the one-variable fragments of QGL and QS). The proof was obtained by adding “the predicate part” as a specific addition to the standard Solovay construction.

scholarly journals Niche employment or occupational segmentation? Immigrant women working in the settlement sector in Germany and Canada

2021 ◽  
Author(s):  
Sita Jayaraman ◽  
Harald Bauder
Keyword(s):  
Labour Market ◽  
Professional Growth ◽  
Immigrant Women ◽  
Market Outcomes ◽  
Working Paper ◽  
Integration Of Immigrants ◽  
Settlement Services ◽  
Research Findings ◽  
The One ◽  
The Impact

Much of the research on the settlement sector focuses on the impact of settlement programs on the integration of immigrants. The settlement sector as a field of employment for immigrant women is still an emerging field for research. This working paper examines the experiences of immigrant women working in the settlement sector and compares Germany with Canada in this respect. The central thesis is that immigrant women working in this sector experience occupational segmentation based on their gender, race, and immigration status. Our research findings support this thesis, suggesting that the settlement sector is a deeply segmented labour market where, on the one hand, language and cultural competencies facilitate the employment of racialized immigrant women, while on the other hand, the positions these women occupy are characterized by precarious working conditions with limited opportunities for professional growth. These similar labour market outcomes occur in Germany and Canada, despite the rather different structures of the settlement sector in the two countries. Keywords: immigrant women, labour market experiences, settlement services, occupational segmentation

Reconstructing Chrysippus’ Cosmological Hypothesis. On Plut. Stoic. rep. 1054c–d

Elenchos ◽  
2019 ◽  
Vol 40 (1) ◽  
pp. 67-98
Author(s):  
Michele Alessandrelli
Keyword(s):  
Modal Logic ◽  
Cohesive Force ◽  
The World ◽  
Causal Force ◽  
The One

AbstractTwo literal quotations from Chrysippus’ On Possibles, preserved in Plutarch’s On the Contradictions of the Stoics, seem to contradict the Stoic thesis of the isotropy of the void. According to this thesis the void is an infinite undifferentiated expanse (a wide continuous area) whose center is marked by, and coincides with, the position of the world. Since there is nothing else outside the world, the cohesive force that pervades it is sufficient on its own to guarantee the quasi–indestructibility of the trans–cyclical διακόσμησις (i.e the fact that in the new cosmic cycle the διακόσμησις returns in a form identical to the one it had in the previous cosmic cycle) and the eternity of the οὐσία. Conversely, in these two quotations Chrysippus maintains that there is a central διαφορά equipped with causal force. This seems to imply the anisotropy of the void. Chrysippus’s view here is also at odds with another official Stoic thesis, i.e. that the incorporeal is causally inert. In this paper it will be argued that there is in fact no contradiction, because, in those two quotations, Chrysippus consciously develops a cosmological hypothesis in order to resolve a difficulty concerning the role of fire during the universal conflagration. Chrysippus’ solution to this difficulty belongs to modal logic and consists in distinguishing between the actual universe and the possible ones.

Robert Baron’s Metaphysica generalis on the Nature of Free Judgment

2020 ◽  
pp. 127-139
Author(s):  
Alexander Broadie
Keyword(s):  
Seventeenth Century ◽  
Philosophy Of Mind ◽  
The Other ◽  
Close Attention ◽  
Notable Feature ◽  
Other Hand ◽  
The One ◽  
The Right

This chapter expounds the concept of ‘judgment’, a concept deployed by seventeenth-century Scottish philosophers in their philosophy of mind. Close attention is paid to the discussion on judgment in the Metaphysica generalis of Robert Baron, where he addresses the idea of judgment as a free act. A notable feature of Baron’s treatment of judgment is his contrast between, on the one hand, the logician’s concern with judgment as a bearer of truth in inferences in which canons of inference are deployed that ensure that if the judgments serving as premises are true then so also must be the judgment drawn as a conclusion from those premises; and, on the other hand, a judgment that is passed by an arbiter, a person agreed upon by two parties in dispute who undertake to accept the judgment he makes as to which party is in the right.

Genius, Method, and Morality: Images of Newton in Britain, 1760–1860

1988 ◽  
Vol 2 (2) ◽  
pp. 257-284 ◽  
Author(s):  
Richard Yeo
Keyword(s):  
Nineteenth Century ◽  
Eighteenth Century ◽  
Moral Virtue ◽  
The Other ◽  
Social Conventions ◽  
The One ◽  
The Relationship ◽  
Methodology Of Science

The ArgumentFocusing on the celebrations of Newton and his work, this article investigates the use of the concept of genius and its connection with debates on the methodology of science and the morality of great discoverers. During the period studied, two areas of tension developed. Firstly, eighteenth-century ideas about the relationship between genius and method were challenged by the notion of scientific genius as transcending specifiable rules of method. Secondly, assumptions about the nexus between intellectual and moral virtue were threatened by the emerging conception of genius as marked by an extraordinary personality – on the one hand capable of breaking with established methods to achieve great discoveries, on the other, likely to transgress moral and social conventions. The assesments of Newton by nineteenth-century scientists such as Brewster, Whewell, and De Morgan were informed by these tensions.

scholarly journals Zeta functions on tori using contour integration

2015 ◽  
Vol 12 (02) ◽  
pp. 1550019
Author(s):  
Emilio Elizalde ◽  
Klaus Kirsten ◽  
Nicolas Robles ◽  
Floyd Williams
Keyword(s):  
Functional Equation ◽  
Eisenstein Series ◽  
Zeta Functions ◽  
Contour Integration ◽  
Alternative Proof ◽  
Functional Determinant ◽  
Dedekind Eta Function ◽  
Limit Formula ◽  
Complex Tori ◽  
The One

A new, seemingly useful presentation of zeta functions on complex tori is derived by using contour integration. It is shown to agree with the one obtained by using the Chowla–Selberg series formula, for which an alternative proof is thereby given. In addition, a new proof of the functional determinant on the torus results, which does not use the Kronecker first limit formula nor the functional equation of the non-holomorphic Eisenstein series. As a bonus, several identities involving the Dedekind eta function are obtained as well.

scholarly journals ASYMPTOTIC EXPANSIONS FOR THE GAUSSIAN UNITARY ENSEMBLE

2012 ◽  
Vol 15 (01) ◽  
pp. 1250003 ◽  
Author(s):  
UFFE HAAGERUP ◽  
STEEN THORBJØRNSEN
Keyword(s):  
Asymptotic Expansion ◽  
Asymptotic Expansions ◽  
Mean Value ◽  
Alternative Proof ◽  
Special Focus ◽  
Stieltjes Transform ◽  
Gaussian Unitary Ensemble ◽  
The Mean ◽  
The One ◽  
Unitary Ensemble

Let g : ℝ → ℂ be a C∞-function with all derivatives bounded and let tr n denote the normalized trace on the n × n matrices. In Ref. 3 Ercolani and McLaughlin established asymptotic expansions of the mean value 𝔼{ tr n(g(Xn))} for a rather general class of random matrices Xn, including the Gaussian Unitary Ensemble (GUE). Using an analytical approach, we provide in the present paper an alternative proof of this asymptotic expansion in the GUE case. Specifically we derive for a [Formula: see text] random matrix Xn that [Formula: see text] where k is an arbitrary positive integer. Considered as mappings of g, we determine the coefficients αj(g), j ∈ ℕ, as distributions (in the sense of L. Schwarts). We derive a similar asymptotic expansion for the covariance Cov { Tr n[f(Xn)], Tr n[g(Xn)]}, where f is a function of the same kind as g, and Tr n = n tr n. Special focus is drawn to the case where [Formula: see text] and [Formula: see text] for λ, μ in ℂ\ℝ. In this case the mean and covariance considered above correspond to, respectively, the one- and two-dimensional Cauchy (or Stieltjes) transform of the [Formula: see text].

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