scholarly journals De Finettian Logics of Indicative Conditionals Part II: Proof Theory and Algebraic Semantics

Author(s):  
Paul Égré ◽  
Lorenzo Rossi ◽  
Jan Sprenger

AbstractIn Part I of this paper, we identified and compared various schemes for trivalent truth conditions for indicative conditionals, most notably the proposals by de Finetti (1936) and Reichenbach (1935, 1944) on the one hand, and by Cooper (Inquiry, 11, 295–320, 1968) and Cantwell (Notre Dame Journal of Formal Logic, 49, 245–260, 2008) on the other. Here we provide the proof theory for the resulting logics and , using tableau calculi and sequent calculi, and proving soundness and completeness results. Then we turn to the algebraic semantics, where both logics have substantive limitations: allows for algebraic completeness, but not for the construction of a canonical model, while fails the construction of a Lindenbaum-Tarski algebra. With these results in mind, we draw up the balance and sketch future research projects.

2010 ◽  
Vol 3 (3) ◽  
pp. 351-373 ◽  
Author(s):  
MEHRNOOSH SADRZADEH ◽  
ROY DYCKHOFF

We consider a simple modal logic whose nonmodal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of axioms corresponding to the characteristic axioms of (e.g.) T, S4, and S5, such logics are useful, as shown in previous work by Baltag, Coecke, and the first author, for encoding and reasoning about information and misinformation in multiagent systems. For the propositional-only fragment of such a dynamic epistemic logic, we present an algebraic semantics, using lattices with agent-indexed families of adjoint pairs of operators, and a cut-free sequent calculus. The calculus exploits operators on sequents, in the style of “nested” or “tree-sequent” calculi; cut-admissibility is shown by constructive syntactic methods. The applicability of the logic is illustrated by reasoning about the muddy children puzzle, for which the calculus is augmented with extra rules to express the facts of the muddy children scenario.


Author(s):  
Jianhua Dai

The collection of the rough set pairs <lower approximation, upper approximation> of an approximation (U, R) can be made into a Stone algebra by defining two binary operators and one unary operator on the pairs. By introducing a more unary operator, one can get a regular double Stone algebra to describe the rough set pairs of an approximation space. Sequent calculi corresponding to the rough algebras, including rough Stone algebras, Stone algebras, rough double Stone algebras, and regular double Stone algebras are proposed in this paper. The sequent calculi are called rough Stone logic (RSL), Stone logic (SL), rough double Stone logic (RDSL), and double Stone Logic (DSL). The languages, axioms and rules are presented. The soundness and completeness of the logics are proved.


2018 ◽  
Vol 28 (5) ◽  
pp. 712-746 ◽  
Author(s):  
Bruno Da Ré ◽  
Federico Pailos ◽  
Damian Szmuc

AbstractInfectious logics are systems that have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated (i) as a way to treat different pathological sentences (like the Liar and the Truth-Teller) differently, namely, by allowing some of them to be truth-value gluts and some others to be truth-value gaps and (ii) as a way to treat the semantic pathology suffered by at least some of these sentences as infectious. This leads us to consider four distinct four-valued logics: one where truth-value gaps are infectious, but gluts are not; one where truth-value gluts are infectious, but gaps are not; and two logics where both gluts and gaps are infectious, in some sense. Additionally, we focus on the proof theory of these systems, by offering a discussion of two related topics. On the one hand, we prove some limitations regarding the possibility of providing standard Gentzen sequent calculi for these systems, by dualizing and extending some recent results for infectious logics. On the other hand, we provide sound and complete four-sided sequent calculi, arguing that the most important technical and philosophical features taken into account to usually prefer standard calculi are, indeed, enjoyed by the four-sided systems.


Author(s):  
Jianhua Dai

The collection of the rough set pairs <lower approximation, upper approximation> of an approximation (U, R) can be made into a Stone algebra by defining two binary operators and one unary operator on the pairs. By introducing a more unary operator, one can get a regular double Stone algebra to describe the rough set pairs of an approximation space. Sequent calculi corresponding to the rough algebras, including rough Stone algebras, Stone algebras, rough double Stone algebras, and regular double Stone algebras are proposed in this paper. The sequent calculi are called rough Stone logic (RSL), Stone logic (SL), rough double Stone logic (RDSL), and double Stone Logic (DSL). The languages, axioms and rules are presented. The soundness and completeness of the logics are proved.


2020 ◽  
Vol 26 (26) ◽  
pp. 3096-3104 ◽  
Author(s):  
Shuai Deng ◽  
Yige Sun ◽  
Tianyi Zhao ◽  
Yang Hu ◽  
Tianyi Zang

Drug side effects have become an important indicator for evaluating the safety of drugs. There are two main factors in the frequent occurrence of drug safety problems; on the one hand, the clinical understanding of drug side effects is insufficient, leading to frequent adverse drug reactions, while on the other hand, due to the long-term period and complexity of clinical trials, side effects of approved drugs on the market cannot be reported in a timely manner. Therefore, many researchers have focused on developing methods to identify drug side effects. In this review, we summarize the methods of identifying drug side effects and common databases in this field. We classified methods of identifying side effects into four categories: biological experimental, machine learning, text mining and network methods. We point out the key points of each kind of method. In addition, we also explain the advantages and disadvantages of each method. Finally, we propose future research directions.


Author(s):  
J. R. B. Cockett ◽  
R. A. G. Seely

This chapter describes the categorical proof theory of the cut rule, a very basic component of any sequent-style presentation of a logic, assuming a minimum of structural rules and connectives, in fact, starting with none. It is shown how logical features can be added to this basic logic in a modular fashion, at each stage showing the appropriate corresponding categorical semantics of the proof theory, starting with multicategories, and moving to linearly distributive categories and *-autonomous categories. A key tool is the use of graphical representations of proofs (“proof circuits”) to represent formal derivations in these logics. This is a powerful symbolism, which on the one hand is a formal mathematical language, but crucially, at the same time, has an intuitive graphical representation.


2021 ◽  
Vol 7 (2) ◽  
pp. 111
Author(s):  
María Jesús Carrasco-Santos ◽  
Antonio Manuel Ciruela-Lorenzo ◽  
Juan Gabriel Méndez Pavón ◽  
Carmen Cristófol Rodríguez

This research analyzed the online reputation of Marbella as a tourist destination and the profiles of the reviewers according to sociodemographic characteristics. A correlational, quantitative research technique was used in this study based on the manual extraction of more than 4000 reviews generated on TripAdvisor. The data used in this study were collected from the TripAdvisor website, taking, as a sample, tourists who had visited the city in the last three years. Ratings that did not provide full data on the variables were excluded. The findings show that Marbella is considered a luxury shopping destination. The preliminary conclusions allow us to generalize about the sociodemographic profile of its tourists. The findings of the study will provide valuable information for Marbella’s Destination Management Organization (DMO). On the one hand, this study highlights the importance of ranking the attractions of the city to create better communication strategies and enhance the appeal of those attractions that receive the best ratings, establishing the true vocation of Marbella as a tourist destination. On the other hand, it provides information on what tourists perceive to be negative elements, allowing the administration to create an improvement plan. The novelty of this research paper is that it delves into Marbella’s online reputation through an analysis of specific attractions’ ratings. Areas that require further attention in future research have been highlighted, along with specific advice on each attraction that contributes to the tourist offerings of the city.


2021 ◽  
Vol 13 (11) ◽  
pp. 5870
Author(s):  
Philipp Kruse

Social Entrepreneurship (SE) describes a new entrepreneurial form combining the generation of financial and social value. In recent years, research interest in SE increased in various disciplines with a particular focus on the characteristics of social enterprises. Whereas a clear-cut definition of SE is yet to be found, there is evidence that culture and economy affect and shape features of SE activity. In addition, sector-dependent differences are supposed. Building on Institutional Theory and employing a mixed qualitative and quantitative approach, this study sheds light on the existence of international and inter-sector differences by examining 161 UK and Indian social enterprises. A content analysis and analyses of variance were employed and yielded similarities as well as several significant differences on an international and inter-sector level, e.g., regarding innovativeness and the generation of revenue. The current study contributes to a more nuanced picture of the SE landscape by comparing social enterprise characteristics in a developed and a developing country on the one hand and different sectors on the other hand. Furthermore, I highlight the benefits of jointly applying qualitative and quantitative methodologies. Future research should pay more attention to the innate heterogeneity among social enterprises and further consolidate and extend these findings.


2021 ◽  
Vol 13 (2) ◽  
pp. 534
Author(s):  
Isabel Saz-Gil ◽  
Ignacio Bretos ◽  
Millán Díaz-Foncea

How cooperatives generate and absorb social capital has attracted a great deal of attention due to the fact that they are collective organizations owned and democratically managed by their members, and, accordingly, are argued to be closely linked to the nature and dynamics of social capital. However, the extant literature and knowledge on the relationship between cooperatives and social capital remain unstructured and fragmented. This paper aims to provide a narrative literature review that integrates both sides of the relationship between cooperatives and social capital. On the one hand, one side involves how cooperatives create internal social capital and spread it in their immediate environment, and, on the other hand, it involves how the presence of social capital promotes the creation and development of cooperatives. In addition, our theoretical framework integrates the dark side of social capital, that is, how the lack of trust, reciprocal relationships, transparency, and other social capital components can lead to failure of the cooperative. On the basis of this review, we define a research agenda that synthesizes key trends and promising research avenues for further advancement of theoretical and empirical insights about the relationship between cooperatives and social capital, placing particular emphasis on rural and agricultural cooperatives.


Author(s):  
Judson B. Murray

Confucian mysticism is a subfield in academic areas of study including Chinese thought, Chinese religions, Confucian studies, and comparative mysticism. Important topics examined in this subfield include, first, a view of the human self that is fundamentally relational, both in an interpersonal sense and because Confucians presuppose various correlations and an integration between, on the one hand, the matter–energy, capacities, processes, and activities comprising the self and, on the other, the elements, forces, patterns, and processes of the world it inhabits. One paradigmatic way Confucians conceptualize the interrelation between the self and the cosmos is their idea and ideal of the “unity of Heaven and humanity.” The Confucian mystical self, provided failings such as unbalanced emotions, selfish desires, and self-centeredness are effectively curtailed, contributes vitally to, because of its profound reverence for life, the generative and life-sustaining process of change that pervades and animates the cosmos. Second, practitioners use various techniques of religious praxis in combination to form multifaceted training regimens aimed at self-cultivation and self-transformation. Examples include a form of meditation called “quiet-sitting,” rituals, textual study, “investigating things,” self-examination and self-monitoring, filial piety, and “reverent attentiveness.” Third, training in these practices can achieve the different mystical aims, experiences, and transformations they seek, all of which relate to the overarching ideal of the unity of Heaven and humanity. These objectives, broadly speaking, include self-understanding, accurately grasping the “principles” of things and affairs, effortless moral virtuosity, “forming one body with all things” (and other types of Confucian mystical union), and exemplifying “sincerity.” Accomplishing them collapses the conventional divide separating several specious dichotomies, such as thought and action, self and other, humankind and nature, internal and external, the subjective and the objective, and moral ought and is. Fourth, the influence that precedent and tradition exert in Confucianism has prompted scholars to devote attention both to notable continuities and to intriguing innovations in comparing ancient mystical ideas, practices, experiences, and aims to later expressions and elaborations of them. At present, much of the scholarship on Confucian mysticism contributes to efforts attempting to provide rich and nuanced analyses of the tradition’s core doctrines, practices, experiences, and ethical and religious aims, by viewing these subjects through the lens of Confucianism’s mystical and spiritual dimensions. Less scholarly attention has been devoted to identifying and explicating the possible contributions that studying Confucian mysticism can make to the scholarship on theories of mysticism and comparative mysticism. Scholars of mysticism have not yet availed themselves of the wealth of data, the possible additional perspectives on contested issues, and the new trajectories for future research that Confucianism offers to these fields. Also, few studies employ the definitions, categories, and theories that have been developed in the contemporary study of mysticism as a methodology for studying Confucian mysticism.


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