In this paper, a theorem on the existence of complete embedding of partially ordered monoids into complete residuated lattices is shown. From this, many interesting results on residuated lattices and substructural logics follow, including various types of completeness theorems of substructural logics.

In this paper, a theorem on the existence of complete embedding of partially ordered monoids into complete residuated lattices is shown. From this, many interesting results on residuated lattices and substructural logics follow, including various types of completeness theorems of substructural logics.

Substructural logics have received a lot of attention in recent years from the communities of both logic and algebra. We discuss the algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices, and establish a weak form of the deduction theorem that is known as parametrized local deduction theorem. Finally, we study certain interpolation properties and explain how they imply the amalgamation property for certain varieties of residuated lattices.

Both Ambrose St. John (1815–1875) and John Henry Newman (1801–1890), who were received into the Roman Catholic Church in 1845, became members of the Birmingham Oratory. Newman’s closest companion for over three decades, St. John’s death was extremely painful for Newman, not only because it was unexpected, but because of his devotion to Newman as well as his dedication to his spiritual duties. Along with presenting Newman’s narrative of the last few weeks of St. John’s life, this essay raises the (...) question: why did Newman write this “account.”. (shrink)

John Henry Newman has rightly been hailed as a giant in the Catholic intellectual tradition. His contributions to theology, literature, and education have been studied at length; however, his contribution to philosophy has not received appropriate attention. This essay 1) explores Newman’s unique philosophical insights in terms of the phenomenological tradition of Edmund Husserl; 2) analyzes the transcendental approach of certain British scientists—notably Ronald Knox and Charles Darwin; and 3) discusses how Newman might be considered a phenomenologist.

We develop a general algebraic and proof-theoretic study of substructural logics that may lack associativity, along with other structural rules. Our study extends existing work on substructural logics over the full Lambek Calculus [34], Galatos and Ono [18], Galatos et al. [17]). We present a Gentzen-style sequent system that lacks the structural rules of contraction, weakening, exchange and associativity, and can be considered a non-associative formulation of . Moreover, we introduce an equivalent Hilbert-style system and show that the logic associated (...) with and is algebraizable, with the variety of residuated lattice-ordered groupoids with unit serving as its equivalent algebraic semantics. Overcoming technical complications arising from the lack of associativity, we introduce a generalized version of a logical matrix and apply the method of quasicompletions to obtain an algebra and a quasiembedding from the matrix to the algebra. By applying the general result to specific cases, we obtain important logical and algebraic properties, including the cut elimination of and various extensions, the strong separation of , and the finite generation of the variety of residuated lattice-ordered groupoids with unit. (shrink)

Along the same line as that in Ono (Ann Pure Appl Logic 161:246–250, 2009), a proof-theoretic approach to Glivenko theorems is developed here for substructural predicate logics relative not only to classical predicate logic but also to arbitrary involutive substructural predicate logics over intuitionistic linear predicate logic without exponentials QFLe. It is shown that there exists the weakest logic over QFLe among substructural predicate logics for which the Glivenko theorem holds. Negative translations of substructural predicate logics are studied by using (...) the same approach. First, a negative translation, called extended Kuroda translation is introduced. Then a translation result of an arbitrary involutive substructural predicate logics over QFLe is shown, and the existence of the weakest logic is proved among such logics for which the extended Kuroda translation works. They are obtained by a slight modification of the proof of the Glivenko theorem. Relations of our extended Kuroda translation with other standard negative translations will be discussed. Lastly, algebraic aspects of these results will be mentioned briefly. In this way, a clear and comprehensive understanding of Glivenko theorems and negative translations will be obtained from a substructural viewpoint. (shrink)

Jonathan Y. Tsou examines and defends positions on central issues in philosophy of psychiatry. The positions defended assume a naturalistic and realist perspective and are framed against skeptical perspectives on biological psychiatry. Issues addressed include the reality of mental disorders; mechanistic and disease explanations of abnormal behavior; definitions of mental disorder; natural and artificial kinds in psychiatry; biological essentialism and the projectability of psychiatric categories; looping effects and the stability of mental disorders; psychiatric classification; and the validity of the DSM's (...) diagnostic categories. The main argument defended by Tsou is that genuine mental disorders are biological kinds with harmful effects. This argument opposes the dogma that mental disorders are necessarily diseases that result from biological dysfunction. Tsou contends that the broader ideal of biological kinds offers a more promising and empirically ascertainable naturalistic standard for assessing the reality of mental disorders and the validity of psychiatric categories. (shrink)

This study aimed to identify the learning and business incubation processes and their impact on developing the performance of business incubators in Gaza Strip, and the study relied on the descriptive analytical approach, and the study population consisted of all employees working in business incubators in Gaza Strip in addition to experts and consultants in incubators where their total number reached (62) individuals, and the researchers used the questionnaire as a main tool to collect data through the comprehensive survey method, (...) where (55) questionnaires were retrieved with a recovery rate of (88.7%). The results of the study showed that there is a high approval of the variables of the study, where the dimension of incubation operations came with a relative weight (84.89%), followed by the learning dimension which got a relative weight (82.50%), while the performance level of the incubators got a relative weight (80.12%) and as the study results showed There is a positive relationship statistically between the two dimensions of learning and business incubation processes and performance development in business incubators, and the linear regression analysis model showed that the main effect in improving the performance of business incubators is "after business incubation operations" while it showed weak effect after learning. The study came out with several recommendations, the most important of which is that business incubators seek to reinforce the learning process and incubation processes for business, and the need to periodically evaluate their performance, and that a more effective mechanism be designed to follow up with companies after the end of the incubation period and monitor the progress of these companies. (shrink)

We will give here a purely algebraic proof of the cut elimination theorem for various sequent systems. Our basic idea is to introduce mathematical structures, called Gentzen structures, for a given sequent system without cut, and then to show the completeness of the sequent system without cut with respect to the class of algebras for the sequent system with cut, by using the quasi-completion of these Gentzen structures. It is shown that the quasi-completion is a generalization of the MacNeille completion. (...) Moreover, the finite model property is obtained for many cases, by modifying our completeness proof. This is an algebraic presentation of the proof of the finite model property discussed by Lafont [12] and Okada-Terui [17]. (shrink)

In psychiatry, pharmacological research has played a crucial role in the formulation, revision, and refinement of neurobiological theories of psychopathology. Besides being utilized as potential treatments for various mental disorders, pharmacological drugs play an important epistemic role as experimental instruments that help scientists uncover the neurobiological underpinnings of mental disorders (Tsou, 2012). Interventions with psychiatric patients using pharmacological drugs provide researchers with information about the neurobiological causes of mental disorders that cannot be obtained in other ways. This important source of (...) evidence for the biological causes of mental disorder is often overlooked in philosophical analyses of psychiatry, especially in skeptical analyses that debase the biological aspects of psychopathology (e.g., Szasz, 1960; Scheff, 1963; Laing, 1967). In discussing pharmacological interventions as a form of evidence for the physical basis of mental disorders, this paper aims to clarify the nature, reliability, and limitations of this evidence. In addition, it illustrates the central role that pharmacological findings in applied clinical contexts play in the acquisition of neurobiological knowledge in research contexts. (shrink)

Purpose. The dynamics and pace of social and economic transformations that are characteristic of modern society, lead to an increase in tension and the destruction of habitual stereotypes – ideals, values, norms, patterns of behaviour that unite people. These moments encourage us to rethink the understanding of "security" essence, in particular, psychological, which emphasizes the urgency of its study in the philosophical and sociocultural coordinates. Theoretical basis of the research is based on the philosophical methodology of K. Jaspers, E. Fromm (...) and the A. Maslow’s psychological approach to understanding of a person. Originality. Psychological security is considered at different levels: first and foremost, society is a characteristic of social security, that is an analysis of how today’s social technologies, social changes affect the quality of life of the country’s population; secondly, the social environment – the family, the immediate environment, reference groups, training teams; thirdly, a person is an experience of his own security-insecurity, when it is possible to talk about the manifestations of psychological violence, when certain behavioral acts contribute to the violation of the security of the other or to self-destruction. It is found out that the knowledge of psychological security is closely connected with the socio-historical conditions of being, with the level of development of material and spiritual culture, with the interests and values prevailing in society, which determines its ontological, epistemological and axiological features. The presented issue is considered in the correlation of psychological security with types of scientific rationality – classical, nonclassical and post-nonclassical approaches, within the framework of which various perspectives, aspects, forms and types of psychological security are studied. Conclusions. The concept of security requires a systematic description of its manifestations, types, levels, concepts: security as the absence of dangers ; security as a certain activity to ensure or to prevent any threats or dangers ; security as a conscious necessity, the value of the individual. The study systematizes various ideas about psychological security in accordance with the logic of scientific knowledge: in the mainstream of classical, non-classical and post-nonclassical approaches. (shrink)

We prove that certain natural sequent systems for bi-intuitionistic logic have the analytic cut property. In the process we show that the (global) subformula property implies the (local) analytic cut property, thereby demonstrating their equivalence. Applying a version of Maehara technique modified in several ways, we prove that bi-intuitionistic logic enjoys the classical Craig interpolation property and Maximova variable separation property; its Halldén completeness follows.

In this paper, we will develop an algebraic study of substructural propositional logics over FLew, i.e. the logic which is obtained from intuitionistic logics by eliminating the contraction rule. Our main technical tool is to use residuated lattices as the algebraic semantics for them. This enables us to study different kinds of nonclassical logics, including intermediate logics, BCK-logics, Lukasiewicz’s many-valued logics and fuzzy logics, within a uniform framework.

Glivenko-type theorems for substructural logics are comprehensively studied in the paper [N. Galatos, H. Ono, Glivenko theorems for substructural logics over FL, Journal of Symbolic Logic 71 1353–1384]. Arguments used there are fully algebraic, and based on the fact that all substructural logics are algebraizable 279–308] and also [N. Galatos, P. Jipsen, T. Kowalski, H. Ono, Residuated Lattices: An Algebraic Glimpse at Substructural Logics, in: Studies in Logic and the Foundations of Mathematics, vol. 151, Elsevier, 2007] for the details). As (...) a complementary work to the algebraic approach developed in [N. Galatos, H. Ono, Glivenko theorems for substructural logics over FL, Journal of Symbolic Logic 71 1353–1384], we present here a concise, proof-theoretic approach to Glivenko theorems for substructural logics. This will show different features of these two approaches. (shrink)

Using the corpus of JSTOR articles, we investigate the role of gender in collaboration patterns across the scholarly landscape by analyzing gender-based homophily--the tendency for researchers to co-author with individuals of the same gender. For a nuanced analysis of gender homophily, we develop methodology necessitated by the fact that the data comprises heterogeneous sub-disciplines and that not all authorships are exchangeable. In particular, we distinguish three components of gender homophily in collaborations: a structural component that is due to demographics and (...) non-gendered authorship norms of a scholarly community, a compositional component which is driven by varying gender representation across sub-disciplines, and a behavioral component which we define as the remainder of observed homophily after its structural and compositional components have been taken into account. Using minimal modeling assumptions, we measure and test for behavioral homophily. We find that significant behavioral homophily can be detected across the JSTOR corpus and show that this finding is robust to missing gender indicators in our data. In a secondary analysis, we show that the proportion of female representation in a field is positively associated with significant behavioral homophily. (shrink)

This paper shows a role of the contraction rule in decision problems for the logics weaker than the intuitionistic logic that are obtained by deleting some or all of structural rules. It is well-known that for such a predicate logic L, if L does not have the contraction rule then it is decidable. In this paper, it will be shown first that the predicate logic FLec with the contraction and exchange rules, but without the weakening rule, is undecidable while the (...) propositional fragment of FLec is decidable. On the other hand, it will be remarked that logics without the contraction rule are still decidable, if our language contains function symbols. (shrink)

An intermediate predicate logicS + n (n>0) is introduced and investigated. First, a sequent calculusGS n is introduced, which is shown to be equivalent toS + n and for which the cut elimination theorem holds. In § 2, it will be shown thatS + n is characterized by the class of all linear Kripke frames of the heightn.

LetL be any modal or tense logic with the finite model property. For eachm, definer L (m) to be the smallest numberr such that for any formulaA withm modal operators,A is provable inL if and only ifA is valid in everyL-model with at mostr worlds. Thus, the functionr L determines the size of refutation Kripke models forL. In this paper, we will give an estimation ofr L (m) for some linear modal and tense logicsL.

Planteamiento de la naturaleza, de la filosof a y de su raz n hist rica, al contemplar panor micamente la totalidad de su pasado e intentar reconstruir el dram tico suceso de su origen.

This is also where we begin investigating lattices of logics and varieties, rather than particular examples.

It is well known that classical propositional logic can be interpreted in intuitionistic propositional logic. In particular Glivenko's theorem states that a formula is provable in the former iff its double negation is provable in the latter. We extend Glivenko's theorem and show that for every involutive substructural logic there exists a minimum substructural logic that contains the first via a double negation interpretation. Our presentation is algebraic and is formulated in the context of residuated lattices. In the last part (...) of the paper, we also discuss some extended forms of the Kolmogorov translation and we compare it to the Glivenko translation. (shrink)

The present paper deals with the predicate version MTL of the logic MTL by Esteva and Godo. We introduce a Kripke semantics for it, along the lines of Ono''s Kripke semantics for the predicate version of FLew (cf. [O85]), and we prove a completeness theorem. Then we prove that every predicate logic between MTL and classical predicate logic is undecidable. Finally, we prove that MTL is complete with respect to the standard semantics, i.e., with respect to Kripke frames on the (...) real interval [0,1], or equivalently, with respect to MTL-algebras whose lattice reduct is [0,1] with the usual order. (shrink)