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.

Some of the basic substructural logics are shown by Ono to have the disjunction property (DP) by using cut elimination of sequent calculi for these logics. On the other hand, this syntactic method works only for a limited number of substructural logics. Here we show that Maksimova's criterion on the DP of superintuitionistic logics can be naturally extended to one on the DP of substructural logics over FL. By using this, we show the DP for some of the substructural logics (...) for which syntactic methods don't work well. (shrink)

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)

Classification of certain group-like FL $_e$ -chains is given: We define absorbent-continuity of FL $_e$ -algebras, along with the notion of subreal chains, and classify absorbent-continuous, group-like FL $_e$ -algebras over subreal chains: The algebra is determined by its negative cone, and the negative cone can only be chosen from a certain subclass of BL-chains, namely, one with components which are either cancellative (that is, those components are negative cones of totally ordered Abelian groups) or two-element MV-algebras, and with (...) no two consecutive cancellative components. It is shown that the classification theorem does not hold if we drop the absorbent-continuity condition. Our result is the first classification theorem in the literature on FL $_e$ -algebras that does not assume the condition of being naturally ordered (which, under certain conditions, corresponds to continuity of the monoid operation). In our classification theorem, continuity is replaced by the much weaker absorbent-continuity. (shrink)

Consider a general class of structural inference rules such as exchange, weakening, contraction and their generalizations. Among them, some are harmless but others do harm to cut elimination. Hence it is natural to ask under which condition cut elimination is preserved when a set of structural rules is added to a structure-free logic. The aim of this work is to give such a condition by using algebraic semantics. We consider full Lambek calculus (FL), i.e., intuitionistic logic without any structural rules, (...) as our basic framework. Residuated lattices are the algebraic structures corresponding to FL. In this setting, we introduce a criterion, called the propagation property, that can be stated both in syntactic and algebraic terminologies. We then show that, for any set R of structural rules, the cut elimination theorem holds for FL enriched with R if and only if R satisfies the propagation property. As an application, we show that any set R of structural rules can be "completed" into another set R*, so that the cut elimination theorem holds for FL enriched with R*, while the provability remains the same. (shrink)

This paper investigates how people conceive and evaluate nature through language, in a climate change context. With material consisting of 1,200 answers to open-ended questions in nationally representative surveys in Norway, we explore what semantic roles and values the respondents attribute to nature as well as to how they interact with the public debate about climate change. We observe that different conceptions and valuations of nature are tied to different perspectives on the climate change issue: some address the responsibilities of (...) causing climate change, others its consequences, and others yet its potential solutions. The study provides knowledge about the variety of conceptions of nature that can be mobilised by individuals and suggests that policy measures and public communication could benefit by taking this diversity into account. (shrink)

Guttorm Fløistad. therefore fundamentally misunderstand both freedom and force (power). They presuppose that words have a force or power that they do not have , that is, coercive power. In addition, of course, such laws express a lack of ...

This paper is a discussion of which kinds of knowledge Spinoza himself employs in developing the system of the Ethics. The problem is raised by Professor D. Savan and further discussed by G. H. R. Parkinson. The thesis is (1) that no occurrence of the first kind of knowledge is to be found in the Ethics (against Parkinson), (2) that the main part of the analysis in the Ethics is conducted on the level of the second kind of knowledge (in (...) agreement with Parkinson), and (3) that the third kind of knowledge occurs frequently and plays a most important role in the Ethics (in part against Parkinson). The relation between knowledge and language, the distinction between two types of imagination, or two ways of imagining things, the translation of knowledge of modes of extension into knowledge of the mind, and the relation between the second and third kind of knowledge are main parts of the argument. The third kind of knowledge derives its significance in the Ethics from the definitions and axioms, particularly in Part 1. These definitions and axioms form the basis of the whole system of the Ethics, and at least some of them, it is suggested, belong to the third kind of knowledge. (shrink)

This volume examines a variety of philosophical approaches that seek to formulate practical guidelines or norms for human actions and behavior in different areas of society, including politics, cultural traditions, the environment, business management, architecture, and medicine. Written by a team of international authors, this volume features thirteen surveys. It begins with an exploration of ethics in politics and cultural traditions. From genocide to the unequal distribution of wealth, it examines many of the harms that currently affect societies throughout the (...) world and considers a way that those in politics can follow to provide better care for all their populations. Next, the book looks at the relation between ethics and cultural traditions. It features a paper that examines the tension that often exists between the past and the present, with a special focus on the history of India. This volume also considers the idea of a universal system of ethics, presents a practical approach to value-based management in private and public organizations, and examines ethics in medicine. In addition, this volume includes coverage of a new type of ethics called Eco-ethica, proposed by the Japanese philosopher Tomonobu Imamichi, which seeks to answer the question of how men and women can live better or live together with each other in a systematized, technological age. (shrink)

Volume 1 in the new series, Philosophical Problems Today, contains articles on standard problems in European and American philosophy. Quine writes on truth and discusses various difficulties connected with the clear definition of the correspondence theory of truth. Strawson, in his articles on individuals, disputes the empiricist test for the status of entity of object. Sufficient identity-conditions are satisfied by a much wider range of objects. The concept of meaning is further extended and differentiated in the article by Habermas on (...) speech acts and actions. The notion of communicative action is central to his argument. The study of formalism, by Agazzi, is in an important sense also a study of meaning. Although for the most part developed within mathematics, formal ways of thinking have been a basic tenet within philosophy and science ever since Aristotle. In his article, Ricoeur observes that the present philosophy of history no longer engages in the speculative system building as presented in the philosophy of Hegel, Marx and Toynbee. Our philosophy of history is rather a critical reflection of various issues connected with the transmission of historical meaning. (shrink)

This paper is a presentation and discussion of Spinoza's view on the knower, or the mind, as an agent. The knower is on his view to be regarded as an active or generative complex cognitive experience. Imagination, reason and intuition are the cognitive principles. On account of their intrinsic relation to “the first law of nature”, that of selfpreservation, together with the thesis of the mind as constituted by ideas or knowledge, these principles function at the same time as moral (...) principles. Consequently, it makes sense to speak of an individual's moral attitude toward everything be knows. A discussion of imagination, reason and intuition mainly as cognitive principles is followed by some concluding remarks on the cognitive and moral relation between human beings: To know another human being is to know his knowledge. The moral attitude of individuals to each other is a function of their mutual knowledge of knowledge. (shrink)

This paper begins by critically examining the inadequacies of production culture in organizations based primarily on impersonal, professional relationships and argues that many of the ills of modern industry like absenteeism and interpersonal conflicts stem from this culture. The author suggests that the culture of community characterized by social competence, personal relationships, cooperation, care and recognition can best serve the real purpose of organizations than mere professionalism. Culture of community implies values-based management or ethical management whereby an indi vidual or (...) an organization is bound to accept certain norms for the well-being of the community. Thus, ethics ought to become a project for commitment to values which have gradually been eroded in our mass media society where religions no longer inspire men to live ethically. The author delves into Norwegian history and recalls the case of Hans Nielsen Hauge, whose inspirational leadership was summed up in his simple gospel: 'Fear of God, temperance and hard work'. Hauge's leadership style of management by building community cultures has, according to the author, great significance for modern enterprises. (shrink)

In his milestone textbook Lattice Theory, Garrett Birkhoff challenged his readers to develop a "common abstraction" that includes Boolean algebras and lattice-ordered groups as special cases. In this paper, after reviewing the past attempts to solve the problem, we provide our own answer by selecting as common generalization of ������������ and ������������ their join ������������∨������������ in the lattice of subvarieties of ������ℒ (the variety of FL-algebras); we argue that such a solution is optimal under several respects and we give an (...) explicit equational basis for ������������∨������������ relative to ������ℒ. Finally, we prove a Holland-type representation theorem for a variety of FL-algebras containing ������������∨������������. (shrink)